| 单词 | algebraic |
| 例句 | I loved the fact that Damaris was Black like me, smart, and also reveled in spending her summer learning about cell reproduction and the best way to solve algebraic inequalities. Proud 2018-07-24T00:00:00Z Or “Look! There’s Renee Albert in a bikini. But please try to keep your mind on algebraic functions.” Drums, Girls, and Dangerous Pie 2004-01-01T00:00:00Z I stayed indoors, memorizing algebraic equations, trying to live as I had before—to imagine my life at the university as disconnected from my life on Buck’s Peak. Educated 2018-02-20T00:00:00Z I decided one day in the middle of an algebraic equation to change my luckless life by changing my hands. Jacob Have I Loved 1980-01-01T00:00:00Z It was covered with algebraic equations, but at the moment algebra was frankly the last thing on my mind. The Secret History 1992-10-16T00:00:00Z “Perspective drawing . . . algebraic equations . . . music theory . . .” Now giggling at the impossibility of keeping up, the children fetched books at random and stacked the volumes at their governess’s feet. The Incorrigible Children of Ashton Place: Book I: The Mysterious Howling 2011-01-25T00:00:00Z Abstruse calculations, geometric forms and algebraic terms, unusual correlations—all have been used to adorn the silliest drivel. Innumeracy: Mathematical Illiteracy and Its Consequences 1988-01-01T00:00:00Z “Would you rather it be more difficult? I can cook up some algebraic equations if you’d like.” Amari and the Night Brothers 2021-01-19T00:00:00Z “We think of flavor as an infinite-dimensional Hilbert space,” he says, referring to the mathematical concept of a complex algebraic system with an infinite number of variables. Food for thought: will an era of hyper-personalized meals leave a sour taste? 2018-05-23T04:00:00Z Their stories play out in various permutations across 19 scenes in a scheme that seems almost algebraic. Review: ‘Collective Rage’ Is ‘The Vagina Monologues’ Times 5 2018-09-13T04:00:00Z Mr. Wilson operates according to his own algebraic laws, and if you don’t stop thinking and just give yourself over to them, you’re sunk. Theater Review: ‘The Old Woman’ Stars Dafoe and Baryshnikov 2013-07-08T21:03:21Z Like "Surface Envy," the best songs on "No Cities" are beautiful algebraic equations that solve problems that researchers never even knew existed, moving logically yet filled with left-turn riff maneuvers. Sleater-Kinney continues the conversation in 'No Cities to Love' 2015-01-14T05:00:00Z The human body is "the heavy sac of yourself" and Einstein's algebraic figures resemble, and become, "mandibles". Poem of the week: Things I Say to Myself While Hanging Laundry by Ruth Stone 2011-08-01T09:17:06Z The algebraic “Tetras” might appear a world away. Getting to know JACK 2017-01-16T05:00:00Z A group whose rhythms and time signatures on first listen read like a precisely written algebraic equation overtaking a mathematician's chalkboard, Deerhoof has etched a singular line through its two decades as a band. Essential tracks: Deerhoof, an Elliott Smith tribute and Moon Duo 2015-03-07T05:00:00Z They’re those gatherings in which people waste time by talking about how to be more productive, with algebraic visual aids and a corporate jargon of uplift that turns sensitive souls suicidal. Review: ‘Miles for Mary,’ a Sendup of the Interminable Meeting From Hell 2016-10-09T04:00:00Z I know that sounds algebraic, but it's hard to sum up. "Drunk History" may be the most necessary show on TV now 2019-01-29T05:00:00Z The Math section of the Redesigned SAT will increase its focus on algebraic and general problem solving, as well as data interpretation. 5 Things Students Must Know About the New SAT 2015-05-21T04:00:00Z We in The Times theater department, not particularly of an algebraic bent, are merely providing the numbers. The Price of Stardom 2010-05-14T03:21:00Z "At an oversimplified level, he is transforming algebraic geometry to derived algebraic geometry," notes the MacArthur Foundation, "making it applicable to other areas in new ways." Meet MacArthur's new 'genius grant' winners 2014-09-17T04:00:00Z While there may not be one "ideal" ice cream formula, one can assemble one much like an algebraic equation based on the desired end result. The science behind the scoop: Four key factors to consider when making ice cream 2021-11-26T05:00:00Z And whether expressed in algebraic logic or ancient Greek hymn, its chorus is the same throughout the universe: Be fruitful and multiply. The "missing law" of nature was here all along 2023-10-22T04:00:00Z With all respect, they need human beings to just sit with them and work through fractions and algebraic equations and all the other operations that make math so beautiful and tricky. Warning for Seattle: The schools’ pandemic hangover is not easing 2023-10-11T04:00:00Z But in algebraic geometry, I would say intersection theory is especially interesting when we work with moduli spaces. How Mathematical Objects Are like People and Other Mysteries of Intersection Theory 2023-09-26T04:00:00Z Ancient Egyptian mathematicians, who are perhaps best known for their geometric advances, were skilled in solving simple algebraic problems. The Mysterious Origins of ‘X’ in Algebra 2023-08-10T04:00:00Z But ∛2 belongs to the algebraic numbers, which can be written as solution of a polynomial equation. These Are the Most Bizarre Numbers in the Universe 2023-05-23T04:00:00Z Early in his career, he primarily dealt with the properties of polynomials, algebraic expressions with multiple terms, until he completed his doctorate at the University of Buenos Aires. Top Math Prize Awarded for Describing the Dynamics of the Flow of Rivers and the Melting of Ice 2023-03-23T04:00:00Z In other words, she came up with a proof that the ratio of the long sides to the short sides are “algebraic numbers,” a major topic in number theory. The Quest to Find Rectangles in a Square 2023-02-07T05:00:00Z Intersection theory, one of Larson’s specialties, is a branch of a field called algebraic geometry. How Mathematical Objects Are like People and Other Mysteries of Intersection Theory 2023-09-26T04:00:00Z The ancient Babylonians of Mesopotamia used many different words for unknowns in their algebraic system – typically words meaning length, width, area or volume, even if the problem itself was not geometric in nature. The Mysterious Origins of ‘X’ in Algebra 2023-08-10T04:00:00Z Melanie Matchett Wood, 41, Cambridge, Massachusetts, mathematician whose statistical analyses have helped answer questions related to number theory and algebraic geometry. Who are the 2022 MacArthur ‘genius grant’ fellows? 2022-10-12T04:00:00Z It is not accidental that the same equations are obtained by graphical analysis as by algebraic techniques. College Physics for AP Courses 2015-08-12T00:00:00Z The Hardy-Weinberg model of population dynamics is an algebraic representation of the relationships among genotype frequencies, F, and the probability of the dominant allele A, p, and the recessive allele a, q. Biology for AP Courses 2022-06-09T00:00:00Z Basic functions have unique shapes, characteristics, and algebraic equations. College Algebra with Corequisite Support 2020-09-23T00:00:00Z In a transitional syncopated phase, authors used some symbolic notation, but algebraic ideas were still presented mainly rhetorically. The Mysterious Origins of ‘X’ in Algebra 2023-08-10T04:00:00Z Algebraic problems require students to apply algebraic manipulations demonstrated in the section. College Algebra 2021-12-21T00:00:00Z But if the cells oppose one another, such as when one is put into an appliance backward, the total emf is less, since it is the algebraic sum of the individual emfs. College Physics for AP Courses 2015-08-12T00:00:00Z This form is used to help you distinguish the statistical context from the algebraic context. High School Statistics 2020-03-27T00:00:00Z When given an equation of the form where and are algebraic expressions, we can use the one-to-one property of logarithms to solve the equation for the unknown. College Algebra with Corequisite Support 2020-09-23T00:00:00Z Indian mathematicians made additional algebraic discoveries and developed what are essentially the modern symbols for each of the decimal digits. The Mysterious Origins of ‘X’ in Algebra 2023-08-10T04:00:00Z Technology problems encourage exploration through use of a graphing utility, either to visualize or verify algebraic results or to solve problems via an alternative to the methods demonstrated in the section. College Algebra 2021-12-21T00:00:00Z To get an expression for rotational kinetic energy, we must again perform some algebraic manipulations. College Physics for AP Courses 2015-08-12T00:00:00Z The equation we solved in the previous example had only one algebraic solution, but it was an extraneous solution. Intermediate Algebra 2020-05-06T00:00:00Z This form is used to help readers distinguish the statistical context from the algebraic context. Introductory Statistics 2013-09-19T00:00:00Z One especially influential Indian mathematician was Brahmagupta, whose algebraic techniques could handle any quadratic equation. The Mysterious Origins of ‘X’ in Algebra 2023-08-10T04:00:00Z This property will also help you work with algebraic fractions—which are also quotients. Elementary Algebra 2020-04-22T00:00:00Z The learning objectives covered under Big Idea 7 of the AP Physics Curriculum Framework are supported in this chapter through descriptive, algebraic, and graphical representations. College Physics for AP Courses 2015-08-12T00:00:00Z In the next example we get two algebraic solutions. Intermediate Algebra 2020-05-06T00:00:00Z The advantage of the algebraic approach is it yields solutions that may be difficult to read from the graph. Precalculus 2021-12-01T00:00:00Z Like vector addition and subtraction, the dot product has several algebraic properties. Calculus, Volume 3 2016-03-30T00:00:00Z We did not get 2 or − 2 as algebraic solutions. Elementary Algebra 2020-04-22T00:00:00Z By elementary function, we mean a function that can be written using a finite number of algebraic combinations or compositions of exponential, logarithmic, trigonometric, or power functions. Calculus, Vol 2 2016-03-30T00:00:00Z In some cases, all the algebraic solutions are extraneous. Intermediate Algebra 2020-05-06T00:00:00Z If we wanted to then rewrite the equation in slope-intercept form, we apply algebraic techniques. Precalculus 2021-12-01T00:00:00Z We have already seen how some of the algebraic properties of vectors, such as vector addition and scalar multiplication, can be extended to three dimensions. Calculus, Volume 3 2016-03-30T00:00:00Z The equation we solved in Example 8.64 had only one algebraic solution, but it was an extraneous solution. Elementary Algebra 2020-04-22T00:00:00Z However, with a little algebraic manipulation, we can relate f to a geometric series. Calculus, Vol 2 2016-03-30T00:00:00Z The only algebraic solution was x = 3, but we said that x = 3 would make a denominator equal to zero. Intermediate Algebra 2020-05-06T00:00:00Z We provide examples of equations with terms involving these functions and illustrate the algebraic techniques necessary to solve them. Calculus, Volume 1 2016-03-30T00:00:00Z This is a good example of obtaining useful information for an integration by making individual measurements over a grid, instead of trying to find an algebraic expression for a function. Calculus, Volume 3 2016-03-30T00:00:00Z If any values found in Step 1 are algebraic solutions, discard them. Elementary Algebra 2020-04-22T00:00:00Z For example, if an integral contains a logarithmic function and an algebraic function, we should choose u to be the logarithmic function, because L comes before A in LIATE. Calculus, Vol 2 2016-03-30T00:00:00Z In this chapter, you will review the language of algebra and take your first steps toward working with algebraic concepts. Intermediate Algebra 2020-05-06T00:00:00Z Most of this material will be a review for you, but it serves as a handy reference to remind you of some of the algebraic techniques useful for working with functions. Calculus, Volume 1 2016-03-30T00:00:00Z For the following exercises, use the information to find a linear algebraic equation model to use to answer the question being asked. Algebra and Trigonometry 2015-02-13T00:00:00Z Translate “6 less than twice x” into an algebraic expression. Elementary Algebra 2020-04-22T00:00:00Z Because A comes before T in LIATE, we chose u to be the algebraic function. Calculus, Vol 2 2016-03-30T00:00:00Z When we have to simplify algebraic expressions, we can often make the work easier by applying the Commutative Property or Associative Property first. Intermediate Algebra 2020-05-06T00:00:00Z By combining root functions with polynomials, we can define general algebraic functions and distinguish them from the transcendental functions we examine later in this chapter. Calculus, Volume 1 2016-03-30T00:00:00Z We can also give an algebraic expression as the input to a function. Algebra and Trigonometry 2015-02-13T00:00:00Z We have also translated English sentences into algebraic equations and solved some word problems. Elementary Algebra 2020-04-22T00:00:00Z Taylor series for functions can often be derived by algebraic operations with a known Taylor series or by differentiating or integrating a known Taylor series. Calculus, Vol 2 2016-03-30T00:00:00Z Translate “six less than twice x” into an algebraic expression. Intermediate Algebra 2020-05-06T00:00:00Z An algebraic function is one that involves addition, subtraction, multiplication, division, rational powers, and roots. Calculus, Volume 1 2016-03-30T00:00:00Z What is the fundamental difference in the algebraic representation of a polynomial function and a rational function? Algebra and Trigonometry 2015-02-13T00:00:00Z That way, when we solve a rational equation we will know if there are any algebraic solutions we must discard. Elementary Algebra 2020-04-22T00:00:00Z I once asked André Weil, a legendary climber of mathematical peaks, if it bothered him that few people knew of his accomplishments in number theory and algebraic geometry, and fewer still understood them. Should Machines Replace Mathematicians? 2022-07-07T04:00:00Z A monomial is an algebraic expression with one term. Intermediate Algebra 2020-05-06T00:00:00Z Two types of algebraic functions are rational functions and root functions. Calculus, Volume 1 2016-03-30T00:00:00Z This also applies when the exponents are algebraic expressions. Algebra and Trigonometry 2015-02-13T00:00:00Z We did not get 0 as an algebraic solution. Elementary Algebra 2020-04-22T00:00:00Z In his analysis, Dr. Thaddeus, who specializes in algebraic geometry, found that key supporting data submitted by Columbia was “inaccurate, dubious or highly misleading.” Columbia Won’t Participate in the Next U.S. News Rankings 2022-06-30T04:00:00Z Since monomials are algebraic expressions, we can use the properties of exponents to multiply monomials. Intermediate Algebra 2020-05-06T00:00:00Z By allowing for compositions of root functions and rational functions, we can create other algebraic functions. Calculus, Volume 1 2016-03-30T00:00:00Z We can also use the inverse trigonometric functions to find compositions involving algebraic expressions. Algebra and Trigonometry 2015-02-13T00:00:00Z We did not get 4 or 3 as algebraic solutions. Elementary Algebra 2020-04-22T00:00:00Z Beyond posting absurd public displays of frustration, many Americans are now grasping for ways to save money by changing work hours or by weighing the algebraic trade-offs of driving farther to find a cheaper pump. The Quest to Beat High Gas Prices 2022-06-25T04:00:00Z Then, translate the English sentence into an algebraic equation. Intermediate Algebra 2020-05-06T00:00:00Z Some functions, however, cannot be described by basic algebraic operations. Calculus, Volume 1 2016-03-30T00:00:00Z They are the basic tools of trigonometry used in solving trigonometric equations, just as factoring, finding common denominators, and using special formulas are the basic tools of solving algebraic equations. Algebra and Trigonometry 2015-02-13T00:00:00Z The only algebraic solution was 4, but we said that 4 would make a denominator equal to zero. Elementary Algebra 2020-04-22T00:00:00Z Purely topologically, without any physics—those operations are basic algebraic operations. Math in 3-D: Q&A with Abel Prize Winner Dennis Sullivan 2022-04-05T04:00:00Z Solving radical equations containing an even index by raising both sides to the power of the index may introduce an algebraic solution that would not be a solution to the original radical equation. Intermediate Algebra 2020-05-06T00:00:00Z This function cannot be written as a formula that involves only basic algebraic operations, so it is transcendental. Calculus, Volume 1 2016-03-30T00:00:00Z This seems like a lot of trouble for a simple sum, but it illustrates a powerful result that will be useful once we introduce algebraic terms. Algebra and Trigonometry 2015-02-13T00:00:00Z Translate the English phrase into an algebraic expression: the quotient of the difference of m and n, and p. Elementary Algebra 2020-04-22T00:00:00Z The reciprocity conjecture connects to the work of Alexander Grothendieck, famous for his research in algebraic geometry, including his prediction of “motives.” The Evolving Quest for a Grand Unified Theory of Mathematics 2022-03-21T04:00:00Z We will now look at how to find an inverse using an algebraic equation. Intermediate Algebra 2020-05-06T00:00:00Z As in part b., this function cannot be written using a formula involving basic algebraic operations only; therefore, this function is transcendental. Calculus, Volume 1 2016-03-30T00:00:00Z An algebraic expression is a collection of constants and variables joined together by the algebraic operations of addition, subtraction, multiplication, and division. Algebra and Trigonometry 2015-02-13T00:00:00Z Now as an algebra student, you can just translate English sentences into algebraic equations and then solve the equations. Elementary Algebra 2020-04-22T00:00:00Z “In the last year the stage has been set with various kinds of investigations,” he says, including his own work involving the use of algebraic geometry and number theory in the context of quantum matter. The Evolving Quest for a Grand Unified Theory of Mathematics 2022-03-21T04:00:00Z The substitution method is an algebraic method that will work well in many situations. Intermediate Algebra 2020-05-06T00:00:00Z Just as with algebraic functions, we can apply transformations to trigonometric functions. Calculus, Volume 1 2016-03-30T00:00:00Z Any variable in an algebraic expression may take on or be assigned different values. Algebra and Trigonometry 2015-02-13T00:00:00Z That way, when we solve a rational equation for example, we will know whether the algebraic solutions we find are allowed or not. Elementary Algebra 2020-04-22T00:00:00Z Michael Thaddeus, who specializes in algebraic geometry at Columbia, has challenged the university’s No. 2 ranking this year with a statistical analysis that found that key supporting data was “inaccurate, dubious or highly misleading.” U.S. News Ranked Columbia No. 2, but a Math Professor Has His Doubts 2022-03-17T04:00:00Z Some of our absolute value equations could be of the form |u| = |v| where u and v are algebraic expressions. Intermediate Algebra 2020-05-06T00:00:00Z Functions that involve the basic operations of addition, subtraction, multiplication, division, and powers are algebraic functions. Calculus, Volume 1 2016-03-30T00:00:00Z When that happens, the value of the algebraic expression changes. Algebra and Trigonometry 2015-02-13T00:00:00Z We will also begin our use of algebraic notation and vocabulary. Elementary Algebra 2020-04-22T00:00:00Z A Times classic: The algebraic equation that says “I love you.” Follow the Science? 2022-02-11T05:00:00Z If two algebraic expressions are equal in absolute value, then they are either equal to each other or negatives of each other. Intermediate Algebra 2020-05-06T00:00:00Z These new methods are more algebraic in nature and we explore them in the next section; however, at this point we introduce two special limits that are foundational to the techniques to come. Calculus, Volume 1 2016-03-30T00:00:00Z To evaluate an algebraic expression means to determine the value of the expression for a given value of each variable in the expression. Algebra and Trigonometry 2015-02-13T00:00:00Z The first step will be to translate an English phrase to an algebraic expression. Elementary Algebra 2020-04-22T00:00:00Z When measuring intelligence, cognitive scientists emphasize an organism's ability to effective adapt to its surroundings, not human-centric activities like reading a book or solving an algebraic equation. Stupid turkeys? Scientists say that the unfairly maligned bird may actually be stuffed with smarts 2021-11-26T05:00:00Z Now, we will use them to translate English phrases into algebraic expressions. Intermediate Algebra 2020-05-06T00:00:00Z These basic results, together with the other limit laws, allow us to evaluate limits of many algebraic functions. Calculus, Volume 1 2016-03-30T00:00:00Z If the algebraic expression contains more than one variable, replace each variable with its assigned value and simplify the expression as before. Algebra and Trigonometry 2015-02-13T00:00:00Z Translate to an algebraic expression and simplify if possible: the product of −2 and 14. Elementary Algebra 2020-04-22T00:00:00Z The tools used to attack it, however, include key advances in algebraic number theory in the late 19th century, as well as in modular forms in the early 20th century. Gnarly, Centuries-Old Mathematical Quandaries Get New Solutions 2021-10-14T04:00:00Z In algebra, it is easiest if we just translate English sentences into algebraic equations and then solve the equations. Intermediate Algebra 2020-05-06T00:00:00Z One method is purely algebraic and the other is geometric. Calculus, Volume 1 2016-03-30T00:00:00Z TRY IT #8 List the constants and variables for each algebraic expression. Algebra and Trigonometry 2015-02-13T00:00:00Z TRY IT : : 1.122 Translate to an algebraic expression and simplify if possible: the quotient of −72 and −9. Elementary Algebra 2020-04-22T00:00:00Z With sufficient experience, mathematicians can know what to expect when they encounter a new type of algebraic structure. Infinity Category Theory Offers a Bird’s-Eye View of Mathematics 2021-09-14T04:00:00Z Sometimes the solution of a radical equation results in two algebraic solutions, but one of them may be an extraneous solution! Intermediate Algebra 2020-05-06T00:00:00Z We begin by tackling the problem from an algebraic point of view. Calculus, Volume 1 2016-03-30T00:00:00Z We can use the same properties in formulas because they contain algebraic expressions. Algebra and Trigonometry 2015-02-13T00:00:00Z Translate the English sentence into an algebraic equation. Elementary Algebra 2020-04-22T00:00:00Z Is it invertible?—one arrives at the standard algebraic structures: the groups, rings and fields. Infinity Category Theory Offers a Bird’s-Eye View of Mathematics 2021-09-14T04:00:00Z Juliette Bruce is an NSF postdoctoral fellow in mathematics at the University of California, Berkley, who works in the field of algebraic geometry. Modern Mathematics Confronts Its White, Patriarchal Past 2021-08-12T04:00:00Z However, we may also approach limit proofs from a purely algebraic point of view. Calculus, Volume 1 2016-03-30T00:00:00Z This also applies when the arguments are algebraic expressions. Algebra and Trigonometry 2015-02-13T00:00:00Z Even if you know the solution right away, using good algebraic techniques here will better prepare you to solve problems that do not have obvious answers. Elementary Algebra 2020-04-22T00:00:00Z In the process, students learn to solve problems by converting concrete numerical values — distances walked, liquids measured — to abstract algebraic symbols. Bob Moses, 1960s civil rights leader who saw math as road to equality, dies at 86 2021-07-25T04:00:00Z He added that the concepts courses wouldn't eliminate algebraic ideas but rather interweave multiple strands of mathematics throughout the courses. Virginia moving to eliminate all accelerated math courses before 11th grade as part of equity-focused plan 2021-04-22T04:00:00Z In many cases, an algebraic approach may not only provide us with additional insight into the definition, it may prove to be simpler as well. Calculus, Volume 1 2016-03-30T00:00:00Z When given an equation of the form where is an algebraic expression, we can use the definition of a logarithm to rewrite the equation as the equivalent exponential equation and solve for the unknown. Algebra and Trigonometry 2015-02-13T00:00:00Z Translate the English sentence into an algebraic equation. Elementary Algebra 2020-04-22T00:00:00Z Narratives, not analytical constructs or algebraic solutions, are what engage the human mind. Review | Why false narratives so often trump reality 2021-02-24T05:00:00Z While we certainly care about a system that produces good leaders, our interest in the partisan selection process isn’t an algebraic one in which we try to solve for a desired outcome. Power Rankings: Iowa swings for the fences 2020-06-29T04:00:00Z Furthermore, an algebraic approach is the primary tool used in proofs of statements about limits. Calculus, Volume 1 2016-03-30T00:00:00Z When given an equation of the form where and are algebraic expressions, we can use the one- to-one property of logarithms to solve the equation for the unknown. Algebra and Trigonometry 2015-02-13T00:00:00Z Sometimes an application requires the solution to be a whole number, but the algebraic solution to the inequality is not a whole number. Elementary Algebra 2020-04-22T00:00:00Z To oversimplify a bit, algebraic geometry is like your high school algebra classes—understanding relationships between symbolic equations and geometric figures in a plane or higher-dimensional space—turned up a notch. The Very Special Triangles 2020-03-14T04:00:00Z But for many algebra students, the jumble of algebraic symbols is still confusing. This professor’s ‘amazing’ trick makes quadratic equations easier 2020-02-10T05:00:00Z You will find that, in general, the more complex a function, the more likely it is that the algebraic approach is the easiest to apply. Calculus, Volume 1 2016-03-30T00:00:00Z Linear equations in one variable may take the form and are solved using basic algebraic operations. Algebra and Trigonometry 2015-02-13T00:00:00Z In that case, we must round the algebraic solution to a whole number. Elementary Algebra 2020-04-22T00:00:00Z But there is a final artistic flourish after the curtain call, as a bonus scene shows Christopher using the full scope of the theater’s technology to giddily solve a complex algebraic formula. At Round House Theatre, video projections express the inner life of a boy on the spectrum 2019-11-26T05:00:00Z They drill down on multiplying fractions and algebraic equations. These Baltimore teens’ summer job: Boosting their SAT scores 2019-08-07T04:00:00Z The algebraic approach is also more useful in proving statements about limits. Calculus, Volume 1 2016-03-30T00:00:00Z Solving linear equations in one variable involves the fundamental properties of equality and basic algebraic operations. Algebra and Trigonometry 2015-02-13T00:00:00Z Because of this, it is an important skill to be able to translate an everyday situation into algebraic language. Elementary Algebra 2020-04-22T00:00:00Z I suspect most physicists can remember the moment when, after a few algebraic tricks with currents and voltages, the speed of light appeared, as if by magic. A struggle for the soul of theoretical physics 2019-04-15T04:00:00Z If you can grapple with simple graphs and algebraic equations, you can grasp the details of the origins, genesis and meaning of calculus and the role of infinity. From counting with stones to artificial intelligence: the story of calculus 2019-04-01T04:00:00Z The derivatives of inverse trigonometric functions are quite surprising in that their derivatives are actually algebraic functions. Calculus, Volume 1 2016-03-30T00:00:00Z However, we may proceed to solve the equation in its original form by performing algebraic operations. Algebra and Trigonometry 2015-02-13T00:00:00Z Translate the English phrase into an algebraic expression: ⓐ Seventeen more than y ⓑ Nine less than 9x2. Elementary Algebra 2020-04-22T00:00:00Z For example, an algebraic number is the solution to a polynomial equation. The Unknowability of the Number Line 2019-01-12T05:00:00Z The p-adics are an alternative number system, sometimes more useful than the real numbers for tackling problems in algebraic geometry and number theory. The Numbers Behind a Fields Medalist's Math 2018-09-03T04:00:00Z Previously, derivatives of algebraic functions have proven to be algebraic functions and derivatives of trigonometric functions have been shown to be trigonometric functions. Calculus, Volume 1 2016-03-30T00:00:00Z Our goal is to perform algebraic operations so that the variables appear in the numerator. Algebra and Trigonometry 2015-02-13T00:00:00Z TRY IT : : 1.119 Translate to an algebraic expression and simplify if possible: the product of −5 and 12. Elementary Algebra 2020-04-22T00:00:00Z This opens up a lot of new numbers, like √2 and -1/31/12, but the set of algebraic numbers is once again countable. The Unknowability of the Number Line 2019-01-12T05:00:00Z Dr. Birkar won the award for his work on categorizing different kinds of polynomial equations, revealing that seemingly unrelated algebraic equations share something in common and can be classified into a smaller number of groups. Fields Medal Is Stolen Minutes After It’s Given in Brazil 2018-08-02T04:00:00Z The algebraic limit laws and squeeze theorem we introduced in Introduction to Limits also apply to limits at infinity. Calculus, Volume 1 2016-03-30T00:00:00Z Solving any equation, however, employs the same basic algebraic rules. Algebra and Trigonometry 2015-02-13T00:00:00Z TRY IT : : 1.120 Translate to an algebraic expression and simplify if possible: the product of 8 and −13. Elementary Algebra 2020-04-22T00:00:00Z Dr. Birkar’s field is algebraic geometry, which investigates connections between numbers and shapes. Fields Medals Awarded to 4 Mathematicians 2018-08-01T04:00:00Z In one classroom, students are at the edge of their seats learning about sound engineering; in another, they’re tackling algebraic equations. In jail, a school of second chances 2018-03-17T04:00:00Z Comparing functions by their graphs as well as by their algebraic expressions can often give new insight into the process of integration. Calculus, Volume 1 2016-03-30T00:00:00Z Where A, and sometimes B, represents an algebraic expression dependent on a variable x. Algebra and Trigonometry 2015-02-13T00:00:00Z Translate to an algebraic expression and simplify if possible: the quotient of −56 and −7. Elementary Algebra 2020-04-22T00:00:00Z A theme emerging for proposed new categories is for fields that mix traditional disciplines — such as ‘algebraic statistics’ and ‘numerical algebraic geometry’. Maths classification is getting a revision 2018-02-06T05:00:00Z Voevodsky joins a line of great mathematicians, including Bernhard Riemann and Alexander Grothendieck, who built algebraic geometry into a deep and powerful science over the past two centuries. Vladimir Voevodsky (1966–2017) As the name sort of suggests, they use algebraic tools to study geometry, often looking at problems relating to where the zero sets of certain polynomials are. Household Chores for Mathematicians 2017-10-21T04:00:00Z There are two basic approaches to solving absolute value inequalities: graphical and algebraic. Algebra and Trigonometry 2015-02-13T00:00:00Z TRY IT : : 1.121 Translate to an algebraic expression and simplify if possible: the quotient of −63 and −9. Elementary Algebra 2020-04-22T00:00:00Z Among the fields in which he made contributions are the homotopy theory of schemes, algebraic K-theory, and interrelations between algebraic geometry and algebraic topology. Vladimir Voevodsky, acclaimed mathematician who won Fields Medal, dies at 51 2017-10-07T04:00:00Z His homepage on MIT’s website includes this line: “Right now, I spend most of my time thinking about discrete Schrödinger operators, high dimensional data compression, algebraic multigrid, and Voronoi diagrams.” Perspective | John Urschel made a smart decision to quit football, but the players he’s leaving behind aren’t stupid 2017-07-27T04:00:00Z You will often find algebraic geometers discussing fields and sheaves because they secretly wish they were farmers. Household Chores for Mathematicians 2017-10-21T04:00:00Z The advantage of the algebraic approach is that solutions are exact, as precise solutions are sometimes difficult to read from a graph. Algebra and Trigonometry 2015-02-13T00:00:00Z When we have to simplify algebraic expressions, we can often make the work easier by applying the commutative or associative property first, instead of automatically following the order of operations. Elementary Algebra 2020-04-22T00:00:00Z “To solve it I remember I had to set up a system of algebraic equations and basically just solve them simultaneously,” said the 17-year-old from Fairfax. This math whiz is getting a master’s in the subject — before graduating high school 2017-05-19T04:00:00Z And the Fortran language remains popular in some circles, especially among scientists, because it is uniquely suited to work with algebraic algorithms of the sort that apply to physical motion, Dr. Downey said. Geniuses Wanted: NASA Challenges Coders to Speed Up Its Supercomputer 2017-05-08T04:00:00Z His textbooks on algebraic geometry, translated into English, are regarded as classics in the field. Igor Shafarevich, Russian Mathematician With a Mixed Political Legacy, Dies at 93 2017-03-13T04:00:00Z At least we can check the algebraic solutions by graphing, as we cannot depend on a visual for a precise solution. Algebra and Trigonometry 2015-02-13T00:00:00Z Before we get to it, we need to introduce some algebraic notation. Elementary Algebra 2020-04-22T00:00:00Z “This is probably more math-y black and Hispanic kids than I’ve seen in my whole career,” said Dr. Bernstein, who received a Ph.D. in algebraic geometry from Harvard in the 1990s. Equations and Inequalities: Math, Race and Fellowship 2017-02-17T05:00:00Z There was Dorothy Vaughan, working with the white “East Computers” to write a textbook on algebraic methods for the mechanical calculating machines that were their constant companions. The hidden history of Nasa’s black female scientists 2017-02-05T05:00:00Z On the song, Liebezeit delivered a sequence built on a rolling snare, an antsy-footed kick drum and cymbals that crash at algebraic intervals. Percussionist Jaki Liebezeit of Can, whose 'krautrock' rhythms influenced generations of art-rockers and beat producers, has died 2017-01-23T05:00:00Z Another way is to carry out the usual algebraic operations on functions, such as addition, subtraction, multiplication and division. Algebra and Trigonometry 2015-02-13T00:00:00Z “The complexity explodes as you average them all up. I wrote a computer program just to do all the algebraic steps. I can’t keep track of it all.” Milk or Sugar in Your Low-Viscosity-Liquid Dynamic? Scientists Seek the Perfect Cup of Coffee 2016-12-19T05:00:00Z No simple algebraic formula can take into account such a dynamic global economy. A Computer Can’t Do the Fed’s Job 2016-12-18T05:00:00Z Conceptual problems involve verbal reasoning, graphs, algebraic manipulation and familiar non-mathematical contexts. New study by Everett instructor shows value of real-world context in teaching algebra 2016-12-07T05:00:00Z I laughed at how simply the three-act structure of the novel was laid out, as though art could be made by plugging random variables into an algebraic formula. How to write a Man Booker novel: six shortlisted authors share their secrets 2016-10-22T04:00:00Z An algebraic form of a function can be written from an equation. Algebra and Trigonometry 2015-02-13T00:00:00Z Successful investing doesn't require a Wall Street financial advisor, just the ability to read analytically and calculate algebraic functions. Pension Holders Need a New Retirement Plan, Not Stock Tips 2016-06-21T04:00:00Z When a textbook that he found on the topic began with algebraic formulas, he prodded his older brother to explain them. Miracle Microbes? 2016-06-13T04:00:00Z They might be learning a pattern – early childhood patterning is something that's very fundamental step toward algebraic thinking, and dance and patterning is a perfect fit because a pattern is a fundamental part of dance. Engineering 101, With Acting Lessons and a Touch of Drama 2016-05-10T04:00:00Z To someone just dropping in, it might seem that Gabriel is teaching chemistry or math because he refers to enzymes, specific gravity and algebraic formulas. Davenport man offers craft brewing classes 2016-01-31T05:00:00Z Sometimes we have to factor expressions, expand expressions, find common denominators, or use other algebraic strategies to obtain the desired result. Algebra and Trigonometry 2015-02-13T00:00:00Z Dr. Kadanoff was also credited with helping discover the algebraic terms needed to describe the complex processes he was studying. Leo Kadanoff, influential physicist, dies at 78 2015-11-04T05:00:00Z He wrote scientific papers on how to represent logical relations as symbols AND algebraic equations. Smooth operator 2015-11-02T05:00:00Z Boole first contemplated the ideas which were to grow into his major contribution to mathematics—the expression of logical relations in symbolic or algebraic form. The Bicentennial of George Boole, the Man Who Laid the Foundations of the Digital Age 2015-11-02T05:00:00Z He left an indelible mark on the field of algebraic geometry but withdrew from society completely. A Close Encounter with Grothendieck and His Fence 2015-10-15T04:00:00Z For the following exercises, evaluate the algebraic expressions. Algebra and Trigonometry 2015-02-13T00:00:00Z Pruitt said students will use the beads and bottle caps to calculate algebraic equations and to learn the history of the person or place depicted. Bead Town Gary project designed to transform city’s schools 2015-09-14T04:00:00Z She wrote: “We may say most aptly that the Analytical Engine weaves algebraic patterns just as the Jacquard-loom weaves flowers and leaves.” Computer science: Enchantress of abstraction : Nature : Nature Publishing Group 2015-09-01T04:00:00Z In this light, the title “N” is not just an abbreviation of “ninja,” but an acknowledgment of the algebraic “N,” upon which all operations are performed. N++ review: One of the most peculiar series in video games has its best entry yet 2015-08-04T04:00:00Z Having taken Advanced Placement Calculus in high school and a semester of Calculus in college, I had long heard and used the algebraic formula; however, I had never seen it proven in two-dimensional reality. STEM Study Starts With Liberal Arts 2015-08-05T04:00:00Z Solving by factoring depends on the zero-product property, which states that if then or where a and b are real numbers or algebraic expressions. Algebra and Trigonometry 2015-02-13T00:00:00Z Among mathematicians, Nash is best known for his work in real algebraic geometry and nonlinear partial differential equations. John Forbes Nash (1928-2015) : Nature : Nature Publishing Group 2015-06-23T04:00:00Z Many of Nash’s fellow mathematicians were more impressed by his work in algebraic geometry. The Triumph (and Failure) of John Nash’s Game Theory 2015-05-27T04:00:00Z He described his first breakthrough in pure mathematics, in his early 20s, as “a nice discovery relating to manifolds and real algebraic varieties”. John Nash's unique approach produced quantum leaps in economics and maths 2015-05-24T04:00:00Z Their goal is to help improve everything from school bus routes and classroom cleanliness to reading comprehension and knowledge of algebraic equations. School Districts Embrace Business Model of Data Collection 2015-05-11T04:00:00Z The same algebraic rules apply, except for one: multiplying or dividing by a negative number reverses the inequality. Algebra and Trigonometry 2015-02-13T00:00:00Z He had been studying the different ways of representing the structure of a mysterious entity called the monster group, a gargantuan algebraic object that, mathematicians believed, captured a new kind of symmetry. Mathematicians Chase Moonshine’s Shadow 2015-04-07T04:00:00Z And yet there’s a way in which they’re truer to elliptic paraboloids and conic points than the models, for geometric surfaces and algebraic functions are not plaster concoctions. See How Man Ray Made Elliptic Paraboloids Sexy At This Phillips Collection Photography Exhibit 2015-02-13T05:00:00Z Zhang’s professor insisted, though, that he change his major to algebraic geometry, his own field. Solving an Unsolvable Math Problem 2015-01-26T05:00:00Z He was awarded the Fields medal in 1966 for his work in algebraic geometry. Alexander Grothendieck (1928-2014) : Nature : Nature Publishing Group 2015-01-13T05:00:00Z If it is possible to express the function output with a formula involving the input quantity, then we can define a function in algebraic form. Algebra and Trigonometry 2015-02-13T00:00:00Z During the 19th century, mathematicians realized that they could distill this type of arithmetic into an algebraic entity called a group. Mathematicians Chase Moonshine’s Shadow 2015-04-07T04:00:00Z In mathematics, he revolutionized the field known as algebraic geometry. The Lives of Alexander Grothendieck, a Mathematical Visionary 2014-11-25T05:00:00Z The Jacobian conjecture, a problem in algebraic geometry that was introduced in 1939 and is still unsolved, stipulates certain simple conditions that, if satisfied, enable someone to solve a series of complicated equations. Solving an Unsolvable Math Problem 2015-01-26T05:00:00Z Harvard mathematician Jacob Lurie’s work in the field of algebraic geometry has provided a powerful framework for other researchers. New England editorial roundup 2014-09-20T04:00:00Z Q&A Are there relationships expressed by an equation that do represent a function but which still cannot be represented by an algebraic formula? Algebra and Trigonometry 2015-02-13T00:00:00Z Jacob Lurie, a mathematician at Harvard University in Cambridge, Massachusetts, studies derived algebraic geometry. Prime Numbers Scholar Wins 2014 MacArthur "Genius Grant" 2014-09-17T04:00:00Z This is an example of an algebraic equation, one that involves only products of powers of coordinates, such as x2 or x3y5. The Lives of Alexander Grothendieck, a Mathematical Visionary 2014-11-25T05:00:00Z It is acknowledged as being beyond the capacities of a graduate student and approachable by only the most accomplished algebraic geometrists. Solving an Unsolvable Math Problem 2015-01-26T05:00:00Z Harvard University mathematician who created a new conceptual foundation for derived algebraic geometry. List of 2014 MacArthur ‘genius grant’ recipients 2014-09-17T04:00:00Z What two algebraic methods can be used to find the horizontal intercepts of a quadratic function? Algebra and Trigonometry 2015-02-13T00:00:00Z The game avatar needs to solve a series of algebraic problems to be able to open doorways and move forward. This Video Game Blurs The Line Between Education And Entertainment 2014-09-10T04:00:00Z “What Maryam discovered is that in another regime, the dynamical orbits are tightly constrained to follow algebraic laws,” said Curtis T. McMullen, a professor at Harvard who was Dr. Mirzakhani’s doctoral adviser. Top Math Prize Has Its First Female Winner 2014-08-12T04:00:00Z Mirzakhani found that in dynamical systems evolving in ways that twist and stretch their shape, the systems' trajectories “are tightly constrained to follow algebraic laws”, says McMullen. Iranian is first woman to nab highest prize in maths 2014-08-11T04:00:00Z Jacob Lurie, for instance, explores the intersection of topology and algebraic geometry. With Prizes Like This, Who Needs a Nobel? 2014-06-23T04:00:00Z None of the algebraic tools discussed so far is sufficient to solve We know that and so it is clear that must be some value between 2 and 3, since is increasing. Algebra and Trigonometry 2015-02-13T00:00:00Z Dr. Lurie was cited for cutting-edge advances in esoteric fields like “higher category theory” and “derived algebraic geometry.” The Multimillion-Dollar Minds of 5 Mathematical Masters 2014-06-23T04:00:00Z If the intent is to foster an atmosphere conducive to learning, why would spaghetti straps interfere with an understanding of algebraic equations? Whose Dress Code Is It, and Why? 2014-06-16T04:00:00Z But they are certainly ready for algebraic thinking. If Euclid Played Video Games This Is The App He'd Build To Teach Geometry 2014-05-24T04:00:00Z In it, she discusses the algebraic curve, now known as the witch of Agnesi. Maria Gaetana Agnesi is celebrated by Google's doodle, but who was she? 2014-05-16T04:00:00Z To find an algebraic solution, we must introduce a new function. Algebra and Trigonometry 2015-02-13T00:00:00Z In person, he’s so reserved that it often appears as if he’s working out a difficult algebraic formula in his head. John Henry and the Making of a Red Sox Baseball Dynasty 2014-04-24T10:00:07Z A speed-reader of pertinent information, he often handicapped in what seemed algebraic fashion. The Jockey 2013-08-14T13:07:46Z Were my kids simply learning mechanical processes, algebraic procedure? It Only Takes About 42 Minutes To Learn Algebra With Video Games 2013-07-01T11:01:00Z Algebraic geometry explores the geometric objects that are sets of solutions to algebraic equations — for example, a circle of radius r can be described by x2+y2=2. Belgian Mathematician Wins Abel Prize for Shaping Algebraic Geometry 2013-03-20T20:15:00.363Z Solving trigonometric equations requires the same techniques as solving algebraic equations. Algebra and Trigonometry 2015-02-13T00:00:00Z About an hour and a half later he was solving junior high level algebraic equations. Can Video Games Make Your Kids Smarter? 2012-12-11T14:52:39Z But do we really want to throw in the algebraic towel just because it’s, like, rilly hard? Make Us Do the Math 2012-08-14T15:15:15.030Z So we worked for many hours on the algebraic basics. Math Rules 2012-04-29T12:15:00.240Z In modern mathematical parlance, these shapes are called algebraic varieties. Belgian Mathematician Wins Abel Prize for Shaping Algebraic Geometry 2013-03-20T20:15:00.363Z Problems involving the reciprocals of the primary trigonometric functions need to be viewed from an algebraic perspective. Algebra and Trigonometry 2015-02-13T00:00:00Z Of or pertaining to algebra; containing an operation of algebra, or deduced from such operation; as, algebraic characters; algebraical writings. Webster's Unabridged Dictionary 2012-03-24T02:00:23.513Z He used an array of synonyms to disparage that approach, calling it “formulaic,” “algebraic,” “mathematically geometrically accurate” and “an algorithm.” Supreme Court Examines Roles of Jury and Judge in Setting Fines 2012-03-20T00:37:46Z An array of clever tricks has extended their life to about ten microseconds—enough to perform the simple algebraic operations that are the lifeblood of computing. Quantum computing: An uncertain future 2012-02-23T17:07:45Z Since completing the work that secured his reputation, he has applied tools such as l-adic cohomology to extend algebraic geometry and to relate it to other areas of maths. Belgian Mathematician Wins Abel Prize for Shaping Algebraic Geometry 2013-03-20T20:15:00.363Z We can use substitution to make the equation appear simpler, and then use the same techniques we use solving an algebraic quadratic: factoring, the quadratic formula, etc. Algebra and Trigonometry 2015-02-13T00:00:00Z To perform by algebra; to reduce to algebraic form. Webster's Unabridged Dictionary 2012-03-24T02:00:23.513Z Transcendental curves are curves that cannot be defined by algebraic equations. Transcendentalism in New England A History 2012-02-18T03:00:16.210Z Still he did like his studies very much, for he was just beginning to appreciate the inspiration of Virgil, the wonders of the science work, and the sturdy exactness of algebraic equations. The White Crystals Being an Account of the Adventures of Two Boys 2012-01-13T03:00:11.507Z Optional Cube root of algebraic expressions.Cube root of arithmetical numbers. A Review of Algebra 2012-01-11T03:00:29.300Z Transforming equations between polar and rectangular forms means making the appropriate substitutions based on the available formulas, together with algebraic manipulations. Algebra and Trigonometry 2015-02-13T00:00:00Z Our ideas are simply the algebraic notation of our impressions and movements. Outlines of a Philosophy of Religion based on Psychology and History 2012-01-01T03:00:07.953Z Another application of groups of finite order is to the theory of linear differential equations whose integrals are algebraic functions. Encyclopaedia Britannica, 11th Edition, Volume 12, Slice 6 "Groups, Theory of" to "Gwyniad" 2011-12-16T03:00:12.320Z It is unlikely that it does so following the precise, algebraic rules children learn in grade school. Probing the Unconscious Mind 2011-12-14T13:45:00.203Z On his computer screen, a series of multiple choice questions ask him to select the correct answer to algebraic equations using negative numbers. Online Schools Score Better on Wall Street Than in Classrooms 2011-12-13T04:24:19Z By learning to interpret standard forms of equations, we are bridging the relationship between algebraic and geometric representations of mathematical phenomena. Algebra and Trigonometry 2015-02-13T00:00:00Z The notion is like an algebraic expression which ideally represents a given quantity, but it is not the quantity itself. Outlines of a Philosophy of Religion based on Psychology and History 2012-01-01T03:00:07.953Z The complete determination of the class of linear differential equations of the second order with all their integrals algebraic, whose group has the greatest possible order, viz. Encyclopaedia Britannica, 11th Edition, Volume 12, Slice 6 "Groups, Theory of" to "Gwyniad" 2011-12-16T03:00:12.320Z Their meaning had become so well known that, by the time of �schylus, they were expressed in algebraic terms. Atlantic Classics, Second Series 2011-12-09T03:00:20.203Z The column of brief answers, read by the clerk, are so many algebraic symbols to the majority, and convey no particular meaning; and this explains the conduct of the Andover Guardians, which is otherwise inexplicable. Blackwood's Edinburgh Magazine, Vol. 60, No. 373, November 1846 2011-10-21T02:00:17.417Z The formula provides an algebraic rule for determining the terms of the sequence. Algebra and Trigonometry 2015-02-13T00:00:00Z You have $10, and each day you are able to save $2,” the student must convert the word problem into an algebraic expression. Grading the Digital School: A Classroom Software Boom, but Mixed Results Despite the Hype 2011-10-08T20:34:29Z The chief application of the theory of groups of finite order is to the theory of algebraic equations. Encyclopaedia Britannica, 11th Edition, Volume 12, Slice 6 "Groups, Theory of" to "Gwyniad" 2011-12-16T03:00:12.320Z We’ll spare you the equation Rauser showed on the screen, but essentially it is a set of algebraic equations with three unknowns. Amazon's John Rauser on "What Is a Data Scientist?" 2011-10-07T20:58:02Z So also was the algebraic working out of the different problems, except, indeed, that relating to the numbers of Bernoulli, which I had offered to do to save Lady Lovelace the trouble. Ada Lovelace and the Luddites. 2011-10-07T16:15:05.467Z Just as with arithmetic series, we can do some algebraic manipulation to derive a formula for the sum of the first terms of a geometric series. Algebra and Trigonometry 2015-02-13T00:00:00Z It can be proved that the order of the numbers in algebraic order of magnitude agrees with the order on the line of the associated points. Encyclopaedia Britannica, 11th Edition, Volume 11, Slice 6 "Geodesy" to "Geometry" 2011-09-19T02:00:10.473Z The principle applies, however, to ordinary words, as well as to algebraic signs; they also enable us to use meanings so as to get results without thinking. How We Think 2011-09-16T02:00:18.973Z By the latter he meant integrals of algebraic functions. Encyclopaedia Britannica, 11th Edition, Volume 11, Slice 3 "Frost" to "Fyzabad" 2011-08-15T02:00:28.473Z “This problem in quadratic equations is a terror,” the girl at the desk suddenly remarked, her finger pointing to a row of algebraic symbols on the paper she was still clutching. Marjorie Dean, High School Junior 2011-07-25T02:00:16.780Z We use algebraic techniques throughout this text, as they consist of the fundamental rules of mathematics. Algebra and Trigonometry 2015-02-13T00:00:00Z Analytical Geometry: the representation of geometrical figures and their relations by algebraic equations. Encyclopaedia Britannica, 11th Edition, Volume 11, Slice 6 "Geodesy" to "Geometry" 2011-09-19T02:00:10.473Z There is poetry in an algebraic sign, when it is the emblem of a difficulty solved, and a wonderful result simply arrived at. A Logic Of Facts Or, Every-day Reasoning 2011-07-22T02:00:18.543Z The single valued functions which occur, as explained above, in the inversion of algebraic integrals of the first kind, for p > 1, are meromorphic. Encyclopaedia Britannica, 11th Edition, Volume 11, Slice 3 "Frost" to "Fyzabad" 2011-08-15T02:00:28.473Z Miss Dean herself has admitted that she solved an algebraic problem for you. Marjorie Dean, High School Junior 2011-07-25T02:00:16.780Z In fact, we use algebraic techniques constantly to simplify trigonometric expressions. Algebra and Trigonometry 2015-02-13T00:00:00Z Their true significance is best seen by stating them in an algebraic form. Encyclopaedia Britannica, 11th Edition, Volume 11, Slice 6 "Geodesy" to "Geometry" 2011-09-19T02:00:10.473Z Unable to explain the nature or cause of this wonderful revelation, Roentgen gave to the light an algebraic name for the unknown—the X rays. Inventions in the Century 2011-07-20T02:00:14.643Z In recent years developments have been made which point to a similar unity of conception as possible for surfaces, or indeed for algebraic constructs of any number of dimensions. Encyclopaedia Britannica, 11th Edition, Volume 11, Slice 3 "Frost" to "Fyzabad" 2011-08-15T02:00:28.473Z Her qualifications, which hitherto might have been expressed, according to her own estimate, by the algebraic X, now assumed a value only to be indicated by a cipher. Joan Thursday 2011-06-25T02:00:19.897Z This is one example of recognizing algebraic patterns in trigonometric expressions or equations. Algebra and Trigonometry 2015-02-13T00:00:00Z The genesis of such relations from algebraic identities is very simple. Encyclopaedia Britannica, 11th Edition, Volume 11, Slice 6 "Geodesy" to "Geometry" 2011-09-19T02:00:10.473Z Keeping the refrigerator in balance with Mr. Russell there part time, Ms. Einhorn finds, “is like working an algebraic equation.” In the Family: Baby Makes Four, and Complications 2011-06-19T11:04:29Z When this is so it can be shown that the linear system of curves is contained in an algebraic system whose dimension is greater by pg − pa than the dimension of the linear system. Encyclopaedia Britannica, 11th Edition, Volume 11, Slice 3 "Frost" to "Fyzabad" 2011-08-15T02:00:28.473Z He is then confronted with what reads like a catalogue of fossil insects diversified by stepladder algebraic formulas, the mere parenthesis of which are enough to make a school teacher shudder. The Universe a Vast Electric Organism 2011-06-09T02:00:22.450Z Using algebraic properties and formulas makes many trigonometric equations easier to understand and solve. Algebra and Trigonometry 2015-02-13T00:00:00Z The research team found similar results in high school sophomores who practiced with the software that Wynn Haimer used, working to match algebraic equations with graphs. Brain Calisthenics for Abstract Ideas 2011-06-06T21:50:25Z I was even allowed to look over the garden books, as accurate as algebraic demonstrations, and as neat as copy books. Donald McElroy, Scotch Irishman 2011-06-04T02:00:12.520Z The points of intersection geometrically were equivalent to the common solution of the associated algebraic equations. Our Legal Heritage June 2011 (Sixth) Edition 2011-06-03T02:00:23.737Z God is not a being of logic, whose nature can be explained by way of deduction, and by means of algebraic equations. Lectures on the true, the beautiful and the good 2011-05-25T02:00:17.943Z And at the folded praying claws or hands of the general of the Capuchins--these algebraic exponents or heraldic devices of two forequarters of pork--aimed he alike in vain. Flower, Fruit, and Thorn Pieces; or, the Wedded Life, Death, and Marriage of Firmian Stanislaus Siebenkaes, Parish Advocate in the Burgh of Kuhschnappel. 2011-05-20T02:00:42.297Z There have no doubt been many up and down movements along this belt, of which 148 the present mountain wall is the algebraic sum. North America 2011-05-05T02:00:20.027Z We should also observe, and put into the notes of speech all the bodily after sounds of poetic, algebraic, artistic, numismatic, and anatomic ideas. The Campaner Thal and Other Writings 2011-04-26T02:00:29.827Z But, as in the analogous cases of algebraic equations and definite integrals, it may be quite possible to find, by methods of approximation, an arithmetical solution which is sufficient for the purpose in hand.—Bibliography: The New Gresham Encyclopedia Volume 4, Part 1: Deposition to Eberswalde 2011-04-14T02:00:57.977Z It is not that the algebraical solution, or algebraic formula for the roots, when n is greater than 4, has not been discovered; it does not exist. The New Gresham Encyclopedia Volume 4, Part 2: Ebert to Estremadura 2011-04-14T02:00:56.200Z During my first hour in that room, I saw him call a young man to the blackboard, and give him an algebraic problem to solve. All the Days of My Life: An Autobiography The Red Leaves of a Human Heart 2011-03-31T02:00:16.763Z Mr. Steuer, another Tammany loyalist, was famous for relentlessly challenging hostile witnesses, peppering one with questions in French and algebraic. City Room: Triangle Fire: New Leaders Emerge 2011-03-24T11:36:17Z By using some algebraic gymnastics, we translate the player’s win shares into an estimate of how much the team’s power rating would be impacted if the player had been absent for the entire season. FiveThirtyEight: How We Made Our N.C.A.A. Picks 2011-03-14T16:42:51Z A more general equation, viz. x� − ax + a� = 0, is the algebraic equivalent of the problem to divide a line in medial section; this is solved in Euclid, ii. Encyclopaedia Britannica, 11th Edition, Volume 9, Slice 7 "Equation" to "Ethics" 2011-02-27T03:00:31.973Z Expressed as an algebraic equation the situation becomes much clearer. Readings in Money and Banking Selected and Adapted 2011-02-01T03:00:14.553Z It gives rise to complications, however, as to the meaning of the algebraic terms employed, which we shall have to study with care. The Value of Money 2011-01-04T03:01:12.363Z There was a boy, too, in the room—the Lennarts' son—a brown-faced lad of thirteen whose algebraic séance with his beloved mother we had most brutally interrupted. The Sick-a-Bed Lady And Also Hickory Dock, The Very Tired Girl, The Happy-Day, Something That Happened in October, The Amateur Lover, Heart of The City, The Pink Sash, Woman's Only Business 2011-01-04T03:01:00.723Z No tablet bears the well-known algebraic equation, that the squares of the two smaller sides of a right-angled triangle equal the square of the hypotenuse. An Exhibition That Gets to the (Square) Root of Sumerian Math 2010-11-22T22:35:00Z It is possible that Diophantus was in possession of an algebraic solution of quadratics; he recognized, however, only one root, the interpretation of both being first effected by the Hindu Bhaskara. Encyclopaedia Britannica, 11th Edition, Volume 9, Slice 7 "Equation" to "Ethics" 2011-02-27T03:00:31.973Z The algebraic derivation of this equation is, of course, essentially the same as the arithmetical derivation previously given. Readings in Money and Banking Selected and Adapted 2011-02-01T03:00:14.553Z This proposition may require algebraic formulation, but to the present writer it does not seem to require any formulation at all. The Value of Money 2011-01-04T03:01:12.363Z And truth be told, I was no algebraic genius. Can You Solve for X? 2010-08-10T17:43:00Z Knowing these variations it becomes possible to represent by integration the value of the elements as algebraic expressions containing the time, and the elements with which we started. Encyclopaedia Britannica, 11th Edition, Volume 2, Slice 7 "Arundel, Thomas" to "Athens" Corresponding to these two aspects, there are two typical methods by which equations can be solved, viz. the algebraic and geometric. Encyclopaedia Britannica, 11th Edition, Volume 9, Slice 7 "Equation" to "Ethics" 2011-02-27T03:00:31.973Z The algebraic analysis, even as verified, presents the relations between magnitudes without showing the cause of high prices. Readings in Money and Banking Selected and Adapted 2011-02-01T03:00:14.553Z Analysis, in mathematics, is, in the widest sense, the expression and development of the functions of quantities by calculation; in a narrower sense the resolving of problems by algebraic equations. The New Gresham Encyclopedia. Vol. 1 Part 2 Amiel to Atrauli Boole, Jevons, and others have applied the algebraic method not only to formal logic but to political economy.—Bibliography: The New Gresham Encyclopedia. Vol. 1 Part 1 A to Amide The computations are, as a general rule, simpler, and the algebraic expressions less complex, than when the computations of the longitude itself are calculated. Encyclopaedia Britannica, 11th Edition, Volume 2, Slice 7 "Arundel, Thomas" to "Athens" They were the only means of an age whose mathematics was almost entirely geometrical for accomplishing what a later generation could accomplish by an algebraic theory of functions. Creative Intelligence Essays in the Pragmatic Attitude Here the algebraic formula would be invoked to support his reasoning since M´ and V and V´ may be regarded as factors in the demand for gold. Readings in Money and Banking Selected and Adapted 2011-02-01T03:00:14.553Z By the use of such symbols propositions could be reduced to the form of equations, and the syllogistic conclusion from two premises was obtained by eliminating the middle term according to ordinary algebraic rules. Encyclopaedia Britannica, 11th Edition, Volume 4, Slice 2 "Bohemia" to "Borgia, Francis" The board is also used for algebra, another set of type furnishing the algebraic symbols. Encyclopaedia Britannica, 11th Edition, Volume 4, Slice 1 "Bisharin" to "Bohea" Moreover, he was a typical product of an age which scoffs at superstition and is impatient of all things irreducible to the terms of algebraic formulas. The King of Arcadia It was an algebraic quantity misstated; and, on looking down, I remarked that the mistake was repeated over and over, through a long series of figures. Sir Jasper Carew His Life and Experience We now come to the strict algebraic statement of the equation of exchange.... Readings in Money and Banking Selected and Adapted 2011-02-01T03:00:14.553Z Or did some wise people invent them, assigning certain letters to certain phases of thought, as mathematicians express unknown quantities by freely chosen algebraic exponents? Lectures on The Science of Language And the tenth grade math teacher was almost driven to distraction by a classroom discussion of the algebraic symbology equating matter and time—all of which was entirely over his head. Adolescents Only It seems desirable to add here certain results, largely of algebraic character, which naturally arise in connexion with the theory of contact transformations. Encyclopaedia Britannica, 11th Edition, Volume 8, Slice 4 "Diameter" to "Dinarchus" On this, however, an attempt at a desk had been made, and here, to my astonishment, were now masses of papers covered with figures from top to bottom,—algebraic signs and calculations without end! Sir Jasper Carew His Life and Experience The story of a carpenter-boy studying Euclid and solving algebraic problems, made a stir in the village of Willington, where he then lived. Memoir of Jared Sparks, LL.D. This extensive theorem of algebraic reciprocity includes many known theorems of symmetry in the theory of Symmetric Functions. Encyclopaedia Britannica, 11th Edition, Volume 6, Slice 7 "Columbus" to "Condottiere" Let us take an ordinary algebraic quantity a. Landmarks of Scientific Socialism "Anti-Duehring" Like many young mathematicians he attacked the problem of resolving the higher algebraic equations, notwithstanding Abel’s proof that a solution by radicles was impossible. Encyclopaedia Britannica, 11th Edition, Volume 6, Slice 6 "Cockaigne" to "Columbus, Christopher" Yes: it enables us to subject the formulæ to algebraic manipulation. Logic, Inductive and Deductive In his theory of graphs, or geometrical representations of algebraic functions, there are valuable suggestions which have been worked out by others. Encyclopaedia Britannica, 11th Edition, Volume 6, Slice 5 "Clervaux" to "Cockade" The results obtained were not only valuable in themselves, but also threw considerable light upon the theory of algebraic series. Encyclopaedia Britannica, 11th Edition, Volume 6, Slice 7 "Columbus" to "Condottiere" Here we have, for example, the homologous series of compounds of carbon of which many are known and each has its own algebraic formula. Landmarks of Scientific Socialism "Anti-Duehring" The mathematical tortures to which he put that unhappy amount; the arithmetical abuse which he heaped upon it, and the algebraic contumely with which he overwhelmed it, almost defy description. The Witches of New York An algebraic formula is very fascinating, but at the same time it is very dangerous. The Blue Goose He also published several papers on algebraic forms and projective geometry. Encyclopaedia Britannica, 11th Edition, Volume 6, Slice 5 "Clervaux" to "Cockade" Euler’s pioneering work in the subject rests on the observation that the algebraic multiplication xa � xb � xc � ... xa+b+c+ ... is equivalent to the arithmetical addition of the exponents a, b, c, ... Encyclopaedia Britannica, 11th Edition, Volume 6, Slice 7 "Columbus" to "Condottiere" Numbers, geometric forms, and algebraic transformations are fascinating to him, and there is something beautiful, to his mind, in the relationships that are discovered. Psychology A Study Of Mental Life I love you best For what no compasses can test, For graces not to be expressed In terms however algebraic. Punch, or the London Charivari, Vol. CLVIII, January 7, 1920 It is a relatively simple algebraic one, but need not be repeated here. A History of Science, Volume 5(of 5) Aspects Of Recent Science With the aid of geometric figures and algebraic signs, he knows something of extension and quantity. Émile or, Concerning Education; Extracts And he overcame that lie by knowing the truth––just as you overcome the thought that you cannot solve your algebraic problems by knowing the truth that will and does solve them.” Carmen Ariza To attain it, we should have to reason naked in a desert with algebraic symbols. Shelley, Godwin and Their Circle Like Sibyl's leaves the papers strew his floor Wrought-out examples, 'wrinkles' by the score, Conundrums algebraic, 'tips' on Conics And thorny 'props' remembered by mnemonics. Literary Tours in The Highlands and Islands of Scotland We speak of algebraic or chemical formulas, municipal ordinances, military orders, army regulations, ecclesiastical canons, the rules of a business house. English Synonyms and Antonyms With Notes on the Correct Use of Prepositions Three or four boys went forward to confer with Mr. Beaver about certain vexing algebraic problems. The Boy Scouts Book of Stories He is the author of the Cartesian system of algebraic or analytic geometry, which has been so powerful an engine of research, far easier to wield than the old synthetic geometry. Pioneers of Science It is not simply a symbol in western algebraic balances of trade. China, Japan and the U.S.A. Present-Day Conditions in the Far East and Their Bearing on the Washington Conference Obviously, the algebraic sum of these amounts will give the true weight of the carbon dioxide absorbed. Respiration Calorimeters for Studying the Respiratory Exchange and Energy Transformations of Man Find the algebraic difference between the latitudes and longitudes respectively. Lectures in Navigation They drifted out into the cloister with the rest of the class, having certain problems of their own, not algebraic. The Boy Scouts Book of Stories “Moral sense,” “intuitive truth,” “general utility”—their ultimate appeal—is just as far out of reach of algebraic logic as any of the propositions are which they reject because these cannot be proved thus. The Voyage Alone in the Yawl "Rob Roy" In fact, the whole machinery of our intelligence, our general ideas and laws, fixed and external objects, principles, persons, and gods, are so many symbolic, algebraic expressions. The Sense of Beauty Being the Outlines of Aesthetic Theory The factors which must remain unknown necessarily lead the engineer to the Page 14 provision of a margin of safety, which makes mathematical refinement and algebraic formulæ ridiculous. Principles of Mining Valuation, Organization and Administration Find the algebraic difference between Longitude in and Longitude sought and call this difference of Longitude. Lectures in Navigation The word "Cosike" is an adjective that was used for a long time in Germany as equivalent to algebraic, being derived from the Italian cosa, which stood for the unknown quantity. A Budget of Paradoxes, Volume II It enlightened me not a little upon many algebraic processes, which, to speak truth, presented, otherwise, but slender claims to my consideration. The International Magazine, Volume 2, No. 3, February, 1851 An algebraic term for an equation in which the unknown quantity rises to two or more several powers. The Sailor's Word-Book An Alphabetical Digest of Nautical Terms, including Some More Especially Military and Scientific, but Useful to Seamen; as well as Archaisms of Early Voyagers, etc. His swart disciples knit their brows O’er algebraic signs; They build their byres, they milk their cows On scientific lines. Punch, or the London Charivari, Vol. 147, July 29, 1914 Find the algebraic difference of the Latitude and Declination, and from Table 45 take out the Natural Haversine of this algebraic difference angle. Lectures in Navigation He has studied the best French masters, and he has adopted their methods quite simply, as one selects an algebraic formula to solve his particular problem. A Collection of Stories, Reviews and Essays So, for the moment turning away from algebraic formulæ and abstruse calculations, wrote Ada, Lady Lovelace, in her twenty-eighth year. The Works of Lord Byron. Vol. 2 They found the music stupid, devoid of melody and form, and bristling with "algebraic" harmonies. Lippincott's Magazine, Vol. 22, November, 1878 of Popular Literature and Science So, spurred on by the thought of competition, Nan did her best; went through the declensions with a rush, and quite outstripped her fellow-student in the matter of algebraic problems. The Governess On this matter it may be urged that Boer reports differ from ours, but Boer veracity may be defined by the algebraic quantity x, and cannot be accepted. South Africa and the Transvaal War, Vol. 1 (of 6) From the Foundation of Cape Colony to the Boer Ultimatum of 9th Oct. 1899 He has simply taken a method which has been most successfully applied in the study of French life and applied it in studying American life, as one uses certain algebraic formulae to solve certain problems. A Collection of Stories, Reviews and Essays No woman can be summed up in an algebraic formula, and when a mathematician does a problem to his lady's eyebrow, he forgets entirely that femininity forever equals x. Little Journeys to the Homes of the Great Philosophers, Volume 8 His specialty was the solution of algebraic problems mentally. A Budget of Paradoxes, Volume I Next day, the diminutive African does not appear; but, as it is believed that Spanish officials prefer gold even to mortal flesh, his algebraic equivalent is unquestionably furnished in the shape of shining ounces! Captain Canot or, Twenty Years of an African Slaver Every effort has been made to present in the clearest light each subject discussed, and to give in matter and methods the best training in algebraic analysis at present attainable. The Hindu-Arabic Numerals In Sarah's room the two students were diligently at work, Sarah in the rôle of preceptress, hearing Amanda's French verbs, or helping to discover the perplexing value of X in an algebraic equation. Blue Bonnet's Ranch Party For two questions very different from Mr Morris’s kept on appealing to him, neither of them algebraic or dealing with Euclid. Glyn Severn's Schooldays But Mike’s restlessness increased: he fidgeted and shuffled about in his chair, shook the table, and tried all kinds of positions to help him in solving his algebraic problem, but without avail. Cormorant Crag A Tale of the Smuggling Days Although chemical equations are quantitative, it must be clearly understood that they are not algebraic. An Elementary Study of Chemistry A number or letter put before an algebraic expression, to show that one is to be divided by the other. The Wonder Island Boys: The Mysteries of the Caverns It arouses in the human mind much the same interest as an algebraic problem, which it greatly resembles. Short Story Writing A Practical Treatise on the Art of The Short Story But the most enormous and mysterious algebraic equation, full of letters, brackets, and fractions, may all cancel out at last and be equal to nothing. George Bernard Shaw There it was constantly, and translated itself into Latin, conjugated and declined itself, and then became compound algebraic equations, with both. Cormorant Crag A Tale of the Smuggling Days God is not a logical Being, whose Nature may be explained by deduction, and by means of algebraic equations. Morals and Dogma of the Ancient and Accepted Scottish Rite of Freemasonry Then, touching a knob, he established communication with the Central Concert Hall, whence our greatest maestros send out to subscribers their delightful successions of accords determined by recondite algebraic formulas. In the Year 2889 At the time it had seemed intensely comical to see two enraged combatants—for so I amused myself by fancying them—hurling algebraic formulæ, of frightful complexity, at each other's heads. The Reminiscences of an Astronomer All of them may be represented by numbers and algebraic symbols, and these condensed formulæ enable us to conduct investigations with the certainty and precision of pure Mathematics. The Continental Monthly, Vol. 4, No. 6, December 1863 Devoted to Literature and National Policy Then the position of rest is half the algebraic sum of two readings. A Text-book of Assaying: For the Use of Those Connected with Mines. Such, at least, seems to be the algebraic sum of its holdings in Arizona v. The Constitution of the United States of America: Analysis and Interpretation Annotations of Cases Decided by the Supreme Court of the United States to June 30, 1952 In like manner the sign x suggests an unknown quantity in relation to the algebraic problem; in relation to phonics it is a double sound; in relation to numeration, the number ten. Ontario Normal School Manuals: Science of Education The pleasure of intellectual exercise in demonstrating or analyzing a geometrical problem, or solving an algebraic equation, seemed to be your only object. The Reminiscences of an Astronomer This series of experiments offers a rare example of the verification of algebraic calculation by direct demonstration. Scientific American Supplement, No. 315, January 14, 1882 He felt as he had when puzzling over the unknown quantity in an algebraic equation. Jerome, A Poor Man A Novel And if I may change the metaphor, an algebraic formula is like a magnificent diamond, cutting its way through the thick and opaque glass, which represents the unknown! The Tree of Appomattox The gentleman with the algebraic bump may figure this out to suit himself. The Princess Elopes All love is mathematically just, as much as the two sides of an algebraic equation.—Emerson. Many Thoughts of Many Minds A Treasury of Quotations from the Literature of Every Land and Every Age The one-to-one correspondence between geometric forms and algebraic analysis is subject to many and important exceptions. An Elementary Course in Synthetic Projective Geometry The subject is treated in the algebraic method, without diagrams to assist the conception. Memoir, Correspondence, And Miscellanies, From The Papers Of Thomas Jefferson, Volume 2 Everything has been done according to the best algebraic formulae. The Tree of Appomattox In order to arrive at a definitive conclusion on this subject, it is indispensable to have recourse to the actual solution of the algebraic equation above referred to. Biographies of Distinguished Scientific Men The morning meal was not quite ready, when Barbican, raising his head, showed Ardan a page covered with algebraic signs at the end of which stood the following formula:— "Which means?" asked Ardan. All Around the Moon Thus, by means of the mechanism employed in analytic geometry, algebraic theorems are made to yield geometric ones, and vice versa. An Elementary Course in Synthetic Projective Geometry He uses his characters like algebraic symbols to work out certain problems with; they are rather more and yet rather less than flesh and blood individuals. Initial Studies in American Letters Why every algebraic problem from the very nature of its being is surcharged with it! The Tree of Appomattox The subject of algebraic analysis above mentioned, which Fourier had studied with a perseverance so remarkable, is not an exception to this rule. Biographies of Distinguished Scientific Men And then, for the benefit of her father, she rattled off into a spirited account of her struggles with the algebraic x and the Urdu compound verb. The Wings of the Morning The first few lines resembled a confused array of algebraic formula. Mr. Fortescue An Andean Romance He had often spoken of the gigantic forces of Nature, but the words had been like algebraic formulae; now he saw the reality, and his rebellious mind was humbled. A Dream of the North Sea At least," said Warner, "it's best to apply to the problem a good algebraic formula. The Tree of Appomattox But yes, my friend; for bullion is the algebraic formula that represents comfort. At a Winter's Fire And in ether, just as in water, the motion of every particle is the algebraic sum of all the separate motions imparted to it. Six Lectures on Light Delivered In The United States In 1872-1873 Abstractly considered, the thing seemed preposterous enough for the plot of a dime novel, while in the light of her sweet presence the development of his love seemed as logical as an algebraic problem. Ilka on the Hill-Top and Other Stories Pronouns are among the latest products of language, and, in the sphere of language, are akin to algebraic symbols in the sphere of mathematics or to a machine in the sphere of labor. Evolution Of The Japanese, Social And Psychic It's a simple algebraic problem which I could demonstrate to you by the liberal use of x and y, but in your case it's not necessary. The Tree of Appomattox Each cake had its weight, and value, and result of assay stamped upon it, and I was told that it was assayed again at St. Petersburg to guard against the algebraic process of substitution. Overland through Asia; Pictures of Siberian, Chinese, and Tartar Life Now, no matter how numerous these waves may be, the law holds good that the motion of every particle of the water is the algebraic sum of all the motions imparted to it. Six Lectures on Light Delivered In The United States In 1872-1873 "I have tried mechanical mental work," a lady writes, "such as solving arithmetical or algebraic problems, but it does no good; in fact it seems only to increase the excitement." Studies in the Psychology of Sex, Volume 6 Sex in Relation to Society I have tried mechanical mental work, such as solving arithmetical or algebraic problems, but it does no good; in fact, it seems only to increase the excitement. Studies in the Psychology of Sex, Volume 3 Analysis of the Sexual Impulse; Love and Pain; The Sexual Impulse in Women The points of intersection geometrically was equivalent to the common solution of the associated algebraic equations. Our Legal Heritage, 5th Ed. And so we invent an ingenious theory, and fortify it all around with ponderous algebraic artillery for defense against all attack. Q. E. D., or New Light on the Doctrine of Creation We are too apt to put the Incarnation more or less in algebraic form: x+y=a, where a stands for the historical Jesus Christ, and x and y respectively for God and man. The Jesus of History Can you calculate what the methematicians call vectors, without putting a single algebraic symbol on paper? Back to Methuselah At times, I think they may find salvation while they are finding the value of x in an algebraic equation, and possibly this is true. Reveries of a Schoolmaster Still to-day in England the average leading citizen matches word against word,—using them as algebraic formulas,—rather than picture against picture, when he arranges his thoughts under the eaves of his mind. The Art of the Moving Picture The simplest solution of such a problem is reached through algebraic methods. An Introductory Course of Quantitative Chemical Analysis With Explanatory Notes And the other lady with the fascinating algebraic climax to her name,—she, too, is impossible; it seems that I can’t get the money by marrying her. The House of a Thousand Candles Our mathematicians express its measurements in algebraic equations. Back to Methuselah Diophantus, a Greek mathematician, born in Alexandria; lived presumably about the 4th century; left works in which algebraic methods are employed, and is therefore credited with being the inventor of algebra. The Nuttall Encyclopædia Being a Concise and Comprehensive Dictionary of General Knowledge He returned to his algebraic problem, with a desperate plunge at its solution. Bart Ridgeley A Story of Northern Ohio Others are more complex but they can be reduced to algebraic expressions and solved by their aid. An Introductory Course of Quantitative Chemical Analysis With Explanatory Notes This is a universal algebraic formula, by which we can solve all organic problems. Delsarte System of Oratory This philosopher first applied the algebraic analysis to the solution of geometrical problems; and in this brilliant discovery lay the germ of a sudden growth of interest in the pure mathematics. The Atlantic Monthly, Volume 03, No. 20, June, 1859 League is a vague term, and, like x in an algebraic equation, stands for an unknown quantity. The Atlantic Monthly, Volume 06, No. 33, July, 1860 He shall place Abscissa's digits in yours and bless you both with an algebraic formula. Stories by American Authors, Volume 5 "That I admit," answered Michel; "and I understand it, although your x's and zero's, and algebraic formula, are rattling in my head like nails in a bag." From the Earth to the Moon; and, Round the Moon Boolean ———- Search algorithm built on the algebraic theories of the English mathematician George Booles. The Online World The Dean - Dr. Peacock, of algebraic and Trinity College fame - was good enough to promise 'to keep an eye' on me. Tracks of a Rolling Stone In the first place, the necessity is generally recognised of abandoning the old arbitrary and algebraic type in favour of a classification which shall correspond more accurately with the facts of the case. Criminal Sociology These various propositions are supported by all sorts of evidence,— physical, algebraic, and metaphysical. System of Economical Contradictions; or, the Philosophy of Misery In short, the true value of a thing is invariable in its algebraic expression, although it may vary in its monetary expression. What is Property? Therefore f1 and f2 must have different algebraic signs, or the system must be composed of a collective and a dispersive lens. The Project Gutenberg Encyclopedia Volume 1 of 28 He was constantly pondering her words and motions; they were as interesting as the factors in an algebraic problem. The Europeans Foo/foobar A sort of online algebraic place holder, for example: "If you want to know when another site is run by a for- profit company, look for an address in the form of foo@foobar.com." Big Dummy's Guide to the Internet And the mathematician finds in it a new beauty, from its marvellous correspondence with the motions of a pendulum,—the algebraic expression of the two being identical. The Atlantic Monthly, Volume 05, No. 30, April, 1860 He had lately guessed that a certain algebraic process could be shortened exceedingly if the method which his imagination suggested should prove to be a true one—that is, an algebraic law. A Dish of Orts : Chiefly Papers on the Imagination, and on Shakespeare This is also possible if the lenses have the same algebraic sign. The Project Gutenberg Encyclopedia Volume 1 of 28 If her various graces were, as I have said, the factors in an algebraic problem, the answer to this question was the indispensable unknown quantity. The Europeans For the dear lady was providentially deficient in humor: the least hint of the real thing clouded her lovely eye like the hovering shadow of an algebraic problem. The Greater Inclination And still another is the well-known instance of the change in polarization predicted by Fresnel from the mere interpretation of an algebraic symbol. The Atlantic Monthly, Volume 05, No. 30, April, 1860 Your first glass of hermitage is the algebraic sign for five-and-thirty,—the glorious burst is over; the pace is still good, to be sure, but the great enthusiasm is past. Charles O'Malley, The Irish Dragoon, Volume 2 The effect soon made itself felt upon the ardent reader, fresh from his undigested algebraic studies. The Life of John Clare It is a long row of figures which, like some other long rows of algebraic symbols added up, amount just to zero. Expositions of Holy Scripture: St. John Chaps. XV to XXI There is an algebraic formula expressive of the truth that "1" is an infinitely greater number of times than "0." Bertram Cope's Year The comparison is, indeed, exaggerated; but it often seems to me, in unrolling a compact Latin sentence, as if I were writing out in words the meaning of an algebraic formula. De Amicitia, Scipio's Dream He had so crammed himself with unknown quantities, that his mind—like a gourmand's stomach—had broken down under the effort, and he was now sobbing out algebraic positions under his counterpane. The Three Clerks It may be equal to the algebraic sum of these, or to their difference, according to whether the external conditions on the field were locally and individually favorable or unfavorable. Species and Varieties, Their Origin by Mutation I know of no School Arithmetic which does not groan under a weight of sham practical work, and that does not, with an absurd priggishness, exclude the use of algebraic symbols. Mankind in the Making Writers, and people who are in society and talk much are apt to be satisfied with an algebraic symbol for a man of note, and their work is done not with him but with x. Pages from a Journal with Other Papers Time, therefore, vanishes from the equation: it is a quantity as regularly exterminated as in any algebraic problem. Miscellaneous Essays Adj. numeral, numerical; arithmetical, analytic, algebraic, statistical, numerable, computable, calculable; commensurable, commensurate; incommensurable, incommensurate, innumerable, unfathomable, infinite. Roget's Thesaurus of English Words and Phrases For literal minds the full comprehension of even a slight display of his humor, such as the following dialogue affords, is better exercise than the solution of an algebraic problem. Halleck's New English Literature Arithmetic turns pale when she glances at them, and, striking her multiplication table with her algebraic knuckles, demands to know why the Express does not add a Cube-it to its THATCHER. Punchinello, Volume 1, No. 18, July 30, 1870 The reference is evidently to Kant's essay upon the advantages of introducing into philosophy the algebraic idea of negative quantities. Note Book of an English Opium-Eater But then it is all the more remarkable that, without the aid of algebraic analysis, they were able to solve such difficult problems as occupied the minds of Archimedes and Apollonius. The Old Roman World, : the Grandeur and Failure of Its Civilization. Looking up and seeing Mr. Fulton's eyes on him, a twinkle in their depths, he threw down the latest collection of algebraic formulas and walked over. Boy Scouts of the Air on Lost Island By algebraic equations we may solve the values of each of the separate elements. Shop Management A disagreeable taste and an agreeable odor may be experienced together, but they cannot be treated as an algebraic sum. A Handbook of Ethical Theory There will be wonderful word-spinnings in the reviews, and the dominant pessimism will be justified by algebraic analogies. Without Prejudice The sight also of algebraic characters pursuing each other across quires of paper, like the grotesque forces of some broken, impish army, filled her indolent mind with a wondering admiration that was akin to fear. Stella Fregelius Mr. Barnes, a great big Englishman, said never a word, but pulled a slide-rule out of his pocket and mumbled algebraic formulae. Memoirs (Vieux Souvenirs) of the Prince de Joinville This link is found in the well-known definition of physical force as a product of 'mass' and 'acceleration' - in algebraic symbols F=ma. Man or Matter A more modern notation is the algebraic notation, which has been adopted in most countries. Chess Strategy Then there is complexion—fair or dark—which makes sixty-four, for you know how, by algebraic calculations, every new possibility multiplies into all the others. Without Prejudice Moreover, knowledge only attracts attention by its rarity, as in algebraic equations common factors count for nothing. Emile What, indeed, despite the algebraic character of the tone-language, may not a lively fancy conjure out of, or, rather, into, this etude! Chopin : the Man and His Music It was beyond the power of figures, even in algebraic denominations, to describe her moral weight. The Kellys and the O'Kellys Ktge2 O—O In most books in which the algebraic notation is used, both squares of a move are written out for the benefit of the student. Chess Strategy In the algebraic notation the files are lettered from a to h, starting from the file on White's left. Chess and Checkers : the Way to Mastership And when I look and look upon the labour of a moujik or a labourer, I am thrown into hysterics for shame at my algebraic calculations. Yama: the pit These algebraic expressions would contain, besides the time, the elements of the planetary orbits to be derived from observation. Side-Lights on Astronomy and Kindred Fields of Popular Science It was an island lost in the immensity of the Pacific Ocean between the Equator and the Tropic of Cancer—an island most appropriately named by Robur in this algebraic fashion. Robur the Conqueror He sat in his armchair, and pen in hand he began what looked very much like algebraic formula: I followed with my eyes his trembling hands, I took count of every movement. A Journey to the Interior of the Earth Does Mr. Wilson expect us to use algebraic signs? Theodore Roosevelt; an Autobiography —I replied with my usual forbearance.—Certainly, to give up the algebraic symbol, because A or B is often a cover for ideal nihility, would be unwise. Complete Project Gutenberg Oliver Wendell Holmes, Sr. Works The problem, as it presented itself to their minds, was to find algebraic expressions for the positions of the planets at any time. Side-Lights on Astronomy and Kindred Fields of Popular Science With algebraic formulae and Euclid's propositions her fine memory saved her. The Doctor : a Tale of the Rockies I did so and found Captain Nemo busy with calculations in which there was no shortage of X and other algebraic signs. Twenty Thousand Leagues Under the Sea The languages of the foundations of geometry and of algebraic, differential, or topological geometry are as different as the practical experiences from which they are derived. The Civilization of Illiteracy As I passed slowly in his review, I saw in my mind's eye the algebraic equation of Snow, the equals sign, and the answer in the man before me. Waifs and Strays Part 1 They may therefore be regarded as functions of the time, and the problem was to express these functions by algebraic formulae. Side-Lights on Astronomy and Kindred Fields of Popular Science Of the date of this origin, however, I grieve that I can only speak with that species of indefinite definiteness which mathematicians are, at times, forced to put up with in certain algebraic formulae. The Works of Edgar Allan Poe — Volume 4 With much real stoicism; not without a stiff-jointed algebraic kind of piety, almost pathetic in its sort. History of Friedrich II of Prussia — Volume 19 The dynamic law of attraction and reaction needed only a Newton to fix it in algebraic form. The Education of Henry Adams But it proved impossible to make them really understand the new games, which, on the departure of the Kergarouets, were voted head-splitters, algebraic problems, and intolerably difficult to play. Beatrix In a city where social problems are solved by algebraic equations, adventurers have many chances in their favor. Sarrasine Four sentences, precise as algebraic formulas, sufficed him usually to grasp and solve all difficulties of life and commerce: "I don't know; I cannot; I will not; I will see about it." Eugenie Grandet |
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英语例句辞典收录了117811条英语例句在线翻译词条，基本涵盖了全部常用单词及词组的例句翻译及用法，是英语学习的有利工具。