| 单词 | parabola |
| 例句 | Auk XXX vaulted off the pad similarly, its parabola drifting up to twenty-three thousand feet. October Sky 1999-04-01T00:00:00Z Instead of trying to measure the area inside a parabola as the Greeks did, early algebraists sought to find the solutions to equations that encode relationships between different numbers. Zero: The Biography of a Dangerous Idea 2000-02-07T00:00:00Z The parabola has a special property: it takes the rays of light from the sun, or any distant source, and focuses them to a point, concentrating all the light’s energy on a very small area. Zero: The Biography of a Dangerous Idea 2000-02-07T00:00:00Z This was the beginning of the discipline of projective geometry, where mathematicians look at the shadows and projections of geometric figures to uncover hidden truths even more powerful than the equivalence of parabolas and ellipses. Zero: The Biography of a Dangerous Idea 2000-02-07T00:00:00Z The first step was to inscribe a triangle inside the parabola. Zero: The Biography of a Dangerous Idea 2000-02-07T00:00:00Z A parabola is simply an ellipse with one focus at infinity. Zero: The Biography of a Dangerous Idea 2000-02-07T00:00:00Z Any mirror that could set ships afire must be in the shape of a parabola. Zero: The Biography of a Dangerous Idea 2000-02-07T00:00:00Z For instance, if you have a ball in free fall, it moves in a parabola, while a frictionless spring wobbles back and forth forever, and a spring with friction slowly comes to rest. Zero: The Biography of a Dangerous Idea 2000-02-07T00:00:00Z Thus, Kepler’s point at infinity proved that parabolas and ellipses are actually the same thing. Zero: The Biography of a Dangerous Idea 2000-02-07T00:00:00Z In later works Archimedes figured out the volumes of parabolas and circles, rotated around a line, which any math student knows are early homework problems in a calculus course. Zero: The Biography of a Dangerous Idea 2000-02-07T00:00:00Z All of a sudden the ellipse becomes a parabola, and all of the lines that converged to a point become parallel lines. Zero: The Biography of a Dangerous Idea 2000-02-07T00:00:00Z Capsule goes up, capsule comes down, its path defined by a big parabola, its landing place the Atlantic Ocean. Hidden Figures 2016-09-06T00:00:00Z All of a sudden, the ellipse opens up and becomes a parabola. Zero: The Biography of a Dangerous Idea 2000-02-07T00:00:00Z To figure out the volume of a barrel or the area under a parabola, mathematicians added infinite zeros together; to find out the tangent of a curve, they divided zero by itself. Zero: The Biography of a Dangerous Idea 2000-02-07T00:00:00Z The bridge rose up over the river in a graceful parabola, its steel cables strung with red lights. Middlesex: A Novel 2002-06-05T00:00:00Z After a long, involved set of calculations, Archimedes summed the areas of the infinite triangles and divined the area of the parabola. Zero: The Biography of a Dangerous Idea 2000-02-07T00:00:00Z The black knight and his horse revolved rapidly toward their sinister side, left the ground together in a handsome parabola, and came down again with a dash. The Once and Future King 1958-01-01T00:00:00Z The shells come patiently, each round whizzing over at a predictable interval, scratching a long scarlet parabola over the roof. All the Light We Cannot See 2014-05-06T00:00:00Z Triangles and circles were easy to measure, but slightly more irregular curves like the parabola were beyond the ken of the Greek mathematicians of the day. Zero: The Biography of a Dangerous Idea 2000-02-07T00:00:00Z Take a cone and cut it up; you get circles, ellipses, parabolas, and hyperbolas, depending on how you slice it. Zero: The Biography of a Dangerous Idea 2000-02-07T00:00:00Z He digs a parabola into the sand with his foot and sighs. Paper Towns 2008-10-16T00:00:00Z “We need to head to your mom’s hotel. See if there are any more magical jelly beans lying around. I want to get my parabola on, too.” The Smartest Kid in the Universe 2020-12-01T00:00:00Z To understand the parabola, Archimedes had to learn how to measure it; for instance, nobody knew how to determine the area of a section of a parabola. Zero: The Biography of a Dangerous Idea 2000-02-07T00:00:00Z “No. I used geometry and focused on the parabola of my shots. I also knew exactly when to feed you the ball, based on timing and patterns I was seeing on the floor.” The Smartest Kid in the Universe 2020-12-01T00:00:00Z The subject that grew out of this critical insight, analytic geometry, is essential to understanding calculus; yet our students are coming out of high school unable to graph straight lines or parabolas. Innumeracy: Mathematical Illiteracy and Its Consequences 1988-01-01T00:00:00Z However, Archimedes figured out a way to measure the parabola’s area by resorting to the infinite. Zero: The Biography of a Dangerous Idea 2000-02-07T00:00:00Z The gleaming white parabolas of the facade are composed of 465 flat, interlocking, precast concrete panels of different shapes and sizes. | The Tel Aviv Museum of Art 2011-10-28T15:15:47Z If you graph the height of her head throughout a grand jeté, it resembles more of a plateau than a peaked parabola. ‘100 Essential Things You Didn’t Know About Math and the Arts’ 2015-02-12T05:00:00Z To acclimate fliers, G-Force One starts with gentle parabolas that offer Martian gravity, at one-third body weight on Earth, and lunar gravity, at one-sixth. Space tourism will surely be a blast, but can it also improve life on Earth? 2017-11-28T05:00:00Z Suddenly it was around us: hundreds of thousands of silvery fishes splitting into two great aisles, and reforming, moving as one, weaving parabolas up, down and under, millions of scales glinting sunlight. Bonaire: Where Coral and Cactus Thrive, and the Sea Soothes the Soul 2019-02-18T05:00:00Z Home to stone behemoths like the Metropolitan Opera House and Avery Fisher Hall, Lincoln Center has grown itself a parabola of green that opened last year as part of a campus redevelopment project. New Art for Lincoln Center: Lawn Care 2011-04-27T11:00:00Z But onstage, he was a dynamo — jumping wildly, curling his body into a parabola as he shouted to the sky, and inciting his tens of thousands of fans to mosh. Rolling Loud Brings Melting Rap Songs and Moshing Crowds to New York 2019-10-14T04:00:00Z No other female parts have such a sustained dramatic parabola – the others tend to come and go a bit, as queens do. Are Shakespeare's women second-class citizens? 2012-07-19T11:09:28Z His response describes a parabola: rising, seeming to converge, dropping away. Books of The Times: Paolo Giordano?s ?Solitude of Prime Numbers?: Scarred Souls 2010-03-11T22:53:00Z About 200 photographs show his surviving buildings, ranging from Colonial Revival colonnaded homes to Modernist concrete parabolas. Antiques: ?Auction Hunters? and Other Buy-and-Sell TV 2010-10-21T21:30:00Z Sometimes, she finds herself closing her eyes, trying to channel the elation of that first parabola. Space tourism will surely be a blast, but can it also improve life on Earth? 2017-11-28T05:00:00Z When she booked a Las Vegas residency at 46, yet avoided a downward slope on the fame parabola? What Is the ‘J. Lo Effect’? 2021-08-05T04:00:00Z They can stroll inside the striking wooden parabola of the Velodrome, now called the Lee Valley VeloPark, an indoor cycling track where visitors can rent a bike and learn the basics of track cycling. In London, an Olympic Park Anchors a Resurgence 2015-02-03T05:00:00Z It wasn’t that our next stop, the village of Passikudah, which sprawled along a parabola of Indian Ocean coastline, didn’t have its appeal. With civil war and a tsunami behind it, Sri Lanka’s east coast is opening up to tourism 2016-12-08T05:00:00Z “The parabola is the perfect concentrator of all energy to a single focal point,” said Eversley, now 81, who remembers being the only African American in the school of engineering at Carnegie Mellon. The Artist Who Throws Newton a Curve 2022-09-06T04:00:00Z “I’m kind of like a parabola antenna, so that I can magnify the small voices of people who aren’t often heard.” Her Antenna Is Tuned to the Quietest Voices 2020-11-27T05:00:00Z Comets return, sometimes unexpectedly, on their unknown parabolas around the solar system. British Art Show 7: have I got spews for you 2010-10-25T20:30:00Z The shortage of shells meant Danylo couldn’t fire his gun from a distance as he would an artillery piece, the round arcing in a parabola. 'More comfortable than a Rolls-Royce': Ukrainian tank drivers eagerly await Western rides 2023-04-10T04:00:00Z They interlock, forming a three-dimensional-looking beam comprised of geometric patterns — a rotated hyperbolic parabola . 16 high-intensity lasers, 800 pounds of blood-red yarn: The Hammer goes big in new immersive spaces 2023-03-22T04:00:00Z Among his discoveries was a need to move his takeoff point farther back for higher jumps, so he could change the apex of the parabola shape of his jump to clear the bar. ‘Fosbury Flop’ high jumper Dick Fosbury dies at 76 2023-03-13T04:00:00Z Seen from the ground, their ephemeral parabolas look like calligraphic brushstrokes. Rome’s starlings create a stunning spectacle -- and a huge mess If the mirror had the shape of a parabola, the rays would all cross at a single point, and the mirror would have a well-defined focal point. College Physics for AP Courses 2015-08-12T00:00:00Z The circle, ellipse, parabola, and hyperbola are all formed by the intersection of a plane with a cone. Astronomy 2016-10-13T00:00:00Z For the following exercises, rewrite the given equation in standard form, and then determine the vertex focus and directrix of the parabola. College Algebra with Corequisite Support 2020-09-23T00:00:00Z The graph is a parabola and the graph fails the horizontal line test. College Algebra 2021-12-21T00:00:00Z The y-coordinate of the vertex is the minimum value of a parabola that opens upward. Intermediate Algebra 2020-05-06T00:00:00Z But Newton was the first to propose an exact mathematical form and to use that form to show that the motion of heavenly bodies should be conic sections—circles, ellipses, parabolas, and hyperbolas. College Physics for AP Courses 2015-08-12T00:00:00Z Since a is 2, the parabola opens upward. Elementary Algebra 2020-04-22T00:00:00Z A parabola is all points in a plane that are the same distance from a fixed point and a fixed line. College Algebra with Corequisite Support 2020-09-23T00:00:00Z A nonlinear system could be representative of a parabola and a circle, where the vertex of the parabola meets the circle and the branches also intersect the circle, hence three solutions. College Algebra 2021-12-21T00:00:00Z It is the maximum value of a parabola that opens downward. Intermediate Algebra 2020-05-06T00:00:00Z How can the vertex of a parabola be used in solving real world problems? Precalculus 2021-12-01T00:00:00Z It is the maximum y-value of a parabola that opens downward. Elementary Algebra 2020-04-22T00:00:00Z Our work so far has only dealt with parabolas that open up or down. College Algebra with Corequisite Support 2020-09-23T00:00:00Z A parabola is the set of points in the plane that lie equidistant from a fixed point, the focus, and a fixed line, the directrix. College Algebra 2021-12-21T00:00:00Z This formula is a quadratic function, so its graph is a parabola. Intermediate Algebra 2020-05-06T00:00:00Z We know the path is that of a parabola. Precalculus 2021-12-01T00:00:00Z Since a is positive, the parabola opens upward. Elementary Algebra 2020-04-22T00:00:00Z A parabola is all points in a plane that are the same distance from a fixed point and a fixed line. College Algebra with Corequisite Support 2020-09-23T00:00:00Z If eccentricity is equal to 1, it is a parabola. College Algebra 2021-12-21T00:00:00Z For each of the following exercises, determine if the parabola opens up or down. Intermediate Algebra 2020-05-06T00:00:00Z In Quadratic Functions, we learned about a parabola’s vertex and axis of symmetry. Precalculus 2021-12-01T00:00:00Z This formula is a quadratic equation in the variable t , so its graph is a parabola. Elementary Algebra 2020-04-22T00:00:00Z The graph of quadratic function is called a parabola. College Algebra with Corequisite Support 2020-09-23T00:00:00Z Figure 1.17 Graph of the parabola described by parametric equations in part a. Calculus, Volume 3 2016-03-30T00:00:00Z Explain the process of finding the vertex of a parabola. Intermediate Algebra 2020-05-06T00:00:00Z In the case of a parabola, a represents the distance from the vertex to the focus. Calculus, Vol 2 2016-03-30T00:00:00Z In the following exercises, determine if the parabola opens up or down. Elementary Algebra 2020-04-22T00:00:00Z The line or axis of symmetry of the parabola is the vertical line . College Algebra with Corequisite Support 2020-09-23T00:00:00Z The eccentricity of an ellipse is less than 1, the eccentricity of a parabola is equal to 1, and the eccentricity of a hyperbola is greater than 1. Calculus, Volume 3 2016-03-30T00:00:00Z Describe what effect adding a constant to the function has on the basic parabola. Intermediate Algebra 2020-05-06T00:00:00Z If the plane is parallel to the generating line, the conic section is a parabola. Calculus, Vol 2 2016-03-30T00:00:00Z Determine whether the parabola opens upward or downward. Elementary Algebra 2020-04-22T00:00:00Z Since the graph of a quadratic function is a parabola, the parabola opens upward if a > 0; the parabola opens downward if a < 0. Calculus, Volume 1 2016-03-30T00:00:00Z Figure 1.46 Four parabolas, opening in various directions, along with their equations in standard form. Calculus, Volume 3 2016-03-30T00:00:00Z Once we know this parabola, it will be easy to apply the transformations. Intermediate Algebra 2020-05-06T00:00:00Z Using this diagram in conjunction with the distance formula, we can derive an equation for a parabola. Calculus, Vol 2 2016-03-30T00:00:00Z In the following exercises, determine if the following parabolas open up or down. Elementary Algebra 2020-04-22T00:00:00Z Knowing the fact that the function is quadratic, we also know the graph is a parabola. Calculus, Volume 1 2016-03-30T00:00:00Z It is a hyperbola if e > 1, a parabola if e = 1, or an ellipse if e < 1. Calculus, Volume 3 2016-03-30T00:00:00Z Describe what effect adding a constant to the function has on the basic parabola. Intermediate Algebra 2020-05-06T00:00:00Z Figure 7.45 A typical parabola in which the distance from the focus to the vertex is represented by the variable p. Calculus, Vol 2 2016-03-30T00:00:00Z Graph the following parabolas by using intercepts, the vertex, and the axis of symmetry. Elementary Algebra 2020-04-22T00:00:00Z Since the leading coefficient is negative, the parabola opens downward. Calculus, Volume 1 2016-03-30T00:00:00Z Figure 1.45 A typical parabola in which the distance from the focus to the vertex is represented by the variable p. Calculus, Volume 3 2016-03-30T00:00:00Z The complex solutions tell us the parabola does not intercept the x-axis. Intermediate Algebra 2020-05-06T00:00:00Z Figure 7.46 Four parabolas, opening in various directions, along with their equations in standard form. Calculus, Vol 2 2016-03-30T00:00:00Z In Example 10.43 you will practice graphing a parabola by plotting a few points. Elementary Algebra 2020-04-22T00:00:00Z The function is a parabola with zeros at p = 0 and p = 25, and it is symmetric about the line p = 12.5, so the maximum revenue occurs at a price of p = $12.50 per item. Calculus, Volume 1 2016-03-30T00:00:00Z Figure 1.20 Tangent line to the parabola described by the given parametric equations when t = 2. Calculus, Volume 3 2016-03-30T00:00:00Z The parabola opens upward and is completely above the x-axis—no part of it is below the x-axis. Intermediate Algebra 2020-05-06T00:00:00Z In addition, the equation of a parabola can be written in the general form, though in this form the values of h, k, and p are not immediately recognizable. Calculus, Vol 2 2016-03-30T00:00:00Z When the x2 term is positive, the parabola opens upward, and when the x2 term is negative, the parabola opens downward. Elementary Algebra 2020-04-22T00:00:00Z The base is the region under the parabola y = 1 − x2 in the first quadrant. Calculus, Volume 1 2016-03-30T00:00:00Z We can view these surfaces as three-dimensional extensions of the conic sections we discussed earlier: the ellipse, the parabola, and the hyperbola. Calculus, Volume 3 2016-03-30T00:00:00Z Determine whether the parabola opens to the left or to the right. Intermediate Algebra 2020-05-06T00:00:00Z The graph of this parabola appears as follows. Calculus, Vol 2 2016-03-30T00:00:00Z Since the “a” is negative, the parabola will open downward. Elementary Algebra 2020-04-22T00:00:00Z The base is the region under the parabola y = 1 − x2 and above the x-axis. Calculus, Volume 1 2016-03-30T00:00:00Z The trace is a parabola in this plane and in any plane with the equation y = b. Calculus, Volume 3 2016-03-30T00:00:00Z Let’s practice graphing a parabola by plotting a few points. Intermediate Algebra 2020-05-06T00:00:00Z The dish is aimed directly at the satellite, and a receiver is located at the focus of the parabola. Calculus, Vol 2 2016-03-30T00:00:00Z Since the “a” is positive, the parabola will open upward. Elementary Algebra 2020-04-22T00:00:00Z The x-intercepts are the points at which the parabola crosses the x-axis. Algebra and Trigonometry 2015-02-13T00:00:00Z In planes parallel to the yz-plane, the traces are also parabolas, as we can see in the following figure. Calculus, Volume 3 2016-03-30T00:00:00Z When the quadratic term, is positive, the parabola opens upward, and when the quadratic term is negative, the parabola opens downward. Intermediate Algebra 2020-05-06T00:00:00Z Radio waves coming in from the satellite are reflected off the surface of the parabola to the receiver, which collects and decodes the digital signals. Calculus, Vol 2 2016-03-30T00:00:00Z Do you see that we could fold each parabola in half and that one side would lie on top of the other? Elementary Algebra 2020-04-22T00:00:00Z We can see that the vertex is at Because this parabola opens upward, the axis of symmetry is the vertical line that intersects the parabola at the vertex. Algebra and Trigonometry 2015-02-13T00:00:00Z For example, we can consider the parabola given by the equation x = y2. Calculus, Volume 3 2016-03-30T00:00:00Z Do you see that we could fold each parabola in half and then one side would lie on top of the other? Intermediate Algebra 2020-05-06T00:00:00Z A parabola can also be defined in terms of distances. Calculus, Vol 2 2016-03-30T00:00:00Z We call it the axis of symmetry of the parabola. Elementary Algebra 2020-04-22T00:00:00Z As with the general form, if the parabola opens upward and the vertex is a minimum. Algebra and Trigonometry 2015-02-13T00:00:00Z If v is held constant, then the resulting curve is a vertical parabola. Calculus, Volume 3 2016-03-30T00:00:00Z We can now find the x-intercepts of the two parabolas we looked at. Intermediate Algebra 2020-05-06T00:00:00Z We can also study the cases when the parabola opens down or to the left or the right. Calculus, Vol 2 2016-03-30T00:00:00Z The point on the parabola that is on the axis of symmetry is the lowest or highest point on the parabola, depending on whether the parabola opens upwards or downwards. Elementary Algebra 2020-04-22T00:00:00Z A parabola is a U-shaped curve that can open either up or down. Algebra and Trigonometry 2015-02-13T00:00:00Z Knowing a body in space, the parabolas of certain gestures, the side angles of expressions, the timbre of a wisecrack, the mood of a certain strut lend an illusion of kinship. Commentary: Are Broadway megastars obsolete? Not while Hugh Jackman and Patti LuPone are around 2022-05-02T04:00:00Z Since a is negative, the parabola opens downward. Intermediate Algebra 2020-05-06T00:00:00Z The first equation represents a parabola that opens either up or down. Calculus, Vol 2 2016-03-30T00:00:00Z This point is called the vertex of the parabola. Elementary Algebra 2020-04-22T00:00:00Z The zeros, or intercepts, are the points at which the parabola crosses the axis. Algebra and Trigonometry 2015-02-13T00:00:00Z He attempted a deft lob, conjuring an artful parabola, but his calculations were off, just barely. City Ties Liverpool, Well Aware That One Point May Be Plenty 2022-04-10T04:00:00Z Since the parabola has a maximum, the h-coordinate of the vertex is the maximum value of the quadratic function. Intermediate Algebra 2020-05-06T00:00:00Z The second equation represents a parabola that opens either to the left or to the right. Calculus, Vol 2 2016-03-30T00:00:00Z Finding the coordinates of the intercepts will help us to graph parabolas, too. Elementary Algebra 2020-04-22T00:00:00Z The intercept is the point at which the parabola crosses the axis. Algebra and Trigonometry 2015-02-13T00:00:00Z This was known as the Kuznets curve, a parabola that showed inequality soaring before being slowly brought back to Earth through redistribution. How Many Billionaires Are There, Anyway? 2022-04-07T04:00:00Z The last row of the table shows us when the parabolas never intersect the x-axis. Intermediate Algebra 2020-05-06T00:00:00Z Figure 7.17 Graph of the parabola described by parametric equations in part a. Calculus, Vol 2 2016-03-30T00:00:00Z Let’s find the y-intercepts of the two parabolas shown in the figure below. Elementary Algebra 2020-04-22T00:00:00Z Understand how the graph of a parabola is related to its quadratic function. Algebra and Trigonometry 2015-02-13T00:00:00Z I don’t understand why it makes the curve it does, when it should make a parabola. How a Mathematician Spends His Sundays 2022-01-28T05:00:00Z If k > 0, shift the parabola vertically up k units. Intermediate Algebra 2020-05-06T00:00:00Z Figure 7.20 Tangent line to the parabola described by the given parametric equations when t = 2. Calculus, Vol 2 2016-03-30T00:00:00Z The graphs below show examples of parabolas for these three cases. Elementary Algebra 2020-04-22T00:00:00Z The cross-section of the antenna is in the shape of a parabola, which can be described by a quadratic function. Algebra and Trigonometry 2015-02-13T00:00:00Z When the command "feet down" was yelled - signalling the end of the parabola - "many of us in the blind and low vision crew were able to find our mats," he says. 'It was magical' - meet the first disabled crew to fly in zero-gravity 2021-12-09T05:00:00Z If k < 0, shift the parabola vertically down |k| units. Intermediate Algebra 2020-05-06T00:00:00Z Recall from the definition of a parabola that the distance from any point on the parabola to the focus is equal to the distance from that same point to the directrix. Calculus, Vol 2 2016-03-30T00:00:00Z Since a is −1 , the parabola opens downward. Elementary Algebra 2020-04-22T00:00:00Z If the parabola opens up, the vertex represents the lowest point on the graph, or the minimum value of the quadratic function. Algebra and Trigonometry 2015-02-13T00:00:00Z But what happened on his first parabola was unexpected. How you too can experience weightlessness without having to go to space 2021-10-28T04:00:00Z If h > 0, shift the parabola horizontally left h units. Intermediate Algebra 2020-05-06T00:00:00Z Therefore, by definition, the eccentricity of a parabola must be 1. Calculus, Vol 2 2016-03-30T00:00:00Z That means there is only one x-intercept, and it is the vertex of the parabola. Elementary Algebra 2020-04-22T00:00:00Z If the parabola opens down, the vertex represents the highest point on the graph, or the maximum value. Algebra and Trigonometry 2015-02-13T00:00:00Z Like me, he became more adventurous with each parabola. How you too can experience weightlessness without having to go to space 2021-10-28T04:00:00Z If h < 0, shift the parabola horizontally right |h| units. Intermediate Algebra 2020-05-06T00:00:00Z The graph of this function is a parabola opening to the right. Calculus, Vol 2 2016-03-30T00:00:00Z Since a is 1, the parabola opens upward. Elementary Algebra 2020-04-22T00:00:00Z So the axis of symmetry is This parabola does not cross the axis, so it has no zeros. Algebra and Trigonometry 2015-02-13T00:00:00Z On the next parabola, the pilots went slightly steeper, this time to replicate gravity on the moon, or about one-sixth of what we experience on Earth. How you too can experience weightlessness without having to go to space 2021-10-28T04:00:00Z Determine whether the parabola opens upward, a > 0, or downward, a < 0. Intermediate Algebra 2020-05-06T00:00:00Z This is the equation of a parabola opening upward. Calculus, Vol 2 2016-03-30T00:00:00Z In a math class, a teacher used the arc of a Stephen Curry 3-pointer to explain a parabola. The School That Aspires to Be a Basketball Factory (Not That Kind) 2021-10-05T04:00:00Z We can use the general form of a parabola to find the equation for the axis of symmetry. Algebra and Trigonometry 2015-02-13T00:00:00Z Each time we did a parabola, I got a little bit better, more adventurous, my endeavors only sometimes thwarted by running into others. How you too can experience weightlessness without having to go to space 2021-10-28T04:00:00Z In this chapter, you will learn about conics, including circles, parabolas, ellipses, and hyperbolas. Intermediate Algebra 2020-05-06T00:00:00Z Alexander Calder’s “Four Arches,” in downtown L.A., enormous slashing steel red-orange parabolas 63 feet tall, are still bold and vivacious 45 years after they were installed. What L.A. public art should you look for as you get out and about more? 2021-03-16T04:00:00Z One of them, a beautiful parabola to Scotty Miller in the back corner of the end zone, was thrown as well as a quarterback of any age could hope — 23, 33, 43, doesn’t matter. Analysis | What to know from NFL Week 7: Patriots struggle, Tom Brady soars and Steelers stay perfect 2020-10-26T04:00:00Z If the parabola opens downward, and the vertex is a maximum. Algebra and Trigonometry 2015-02-13T00:00:00Z The kinetic energy of a free electron grows quadratically with its velocity or momentum, resulting in a curve known as a parabola. Atomic forces mapped out by lasers 2020-06-30T04:00:00Z With systems of nonlinear equations, the graphs may be circles, parabolas or hyperbolas and there may be several points of intersection, and so several solutions. Intermediate Algebra 2020-05-06T00:00:00Z In a blink of the eye, her body swings from long diagonals into swooping parabolas, from the fullest extension of a line to the most cavernous curve. 'It's really special': the ballet company shaking up the world of dance 2020-02-19T05:00:00Z A parabola is a symmetrical curve that can describe the path of a projectile, like a thrown football, or the curve of a suspension bridge. This professor’s ‘amazing’ trick makes quadratic equations easier 2020-02-10T05:00:00Z Notice that the horizontal and vertical shifts of the basic graph of the quadratic function determine the location of the vertex of the parabola; the vertex is unaffected by stretches and compressions. Algebra and Trigonometry 2015-02-13T00:00:00Z As a result, the deviation between the free-electron parabola and the flattened band is relatively small. Atomic forces mapped out by lasers 2020-06-30T04:00:00Z Sketch the possible options for intersection of a circle and a parabola. Intermediate Algebra 2020-05-06T00:00:00Z Where are we anyway, in that familiar Pep parabola? Pep Guardiola to set City scheme to the extreme for Anfield summit | Barney Ronay 2019-11-09T05:00:00Z This alternate method for solving quadratic equations uses the fact that parabolas are symmetrical. This professor’s ‘amazing’ trick makes quadratic equations easier 2020-02-10T05:00:00Z Because parabolas have a maximum or a minimum point, the range is restricted. Algebra and Trigonometry 2015-02-13T00:00:00Z When distant in Rye he addressed her in letters as “Dearest Edith,” and, when present, introduced her to his London on the precise parabola of his pompous arm. Dearest Edith 1929-02-23T05:00:00Z A circle and a parabola can intersect in ways that would result in 0, 1, 2, 3, or 4 solutions. Intermediate Algebra 2020-05-06T00:00:00Z There’s an exquisite discussion of his method for expressing the area of a segment of a parabola in terms of the area of a simpler shape made up of straight lines. From counting with stones to artificial intelligence: the story of calculus 2019-04-01T04:00:00Z For example, in the parabola y = x² – 4x – 5 the two solutions when y = 0 are the symmetrical points r and s, where the parabola crosses the x-axis. This professor’s ‘amazing’ trick makes quadratic equations easier 2020-02-10T05:00:00Z Because is negative, the parabola opens downward and has a maximum value. Algebra and Trigonometry 2015-02-13T00:00:00Z At the annual Blossom Kite Festival near the Washington Monument, the sky was speckled with geometric flocks of triangles and boxes, diamonds and deltas, parabolas and disks. Kites and spirits soar on the Mall as D.C. revels in its first nice weekend of spring 2019-03-30T04:00:00Z The fixed point is called the focus, and the fixed line is called the directrix of the parabola. Intermediate Algebra 2020-05-06T00:00:00Z His body is slacker than I expected, a small paunch begins at his waist and settles in a downward parabola to his groin. Bad sex award 2018: the contenders in quotes 2018-11-30T05:00:00Z The midpoint, or average, of r and s is the axis of symmetry of the parabola. This professor’s ‘amazing’ trick makes quadratic equations easier 2020-02-10T05:00:00Z How can the vertex of a parabola be used in solving real-world problems? Algebra and Trigonometry 2015-02-13T00:00:00Z Our bodies in motion are defined by a unified alchemy of speed and direction, as we trace parabolas, lemniscates, trident curves, Poinsot’s spirals, and trajectories that have no mathematical names. How to Control a Machine with Your Brain 2018-11-19T05:00:00Z The highest point is the vertex of the parabola so the y-coordinate of the vertex will be 10. Intermediate Algebra 2020-05-06T00:00:00Z The pitch carved a parabola in the sky and soared over the Green Monster in left field in the seventh inning of a one-run ballgame. Eduardo Nunez becomes an unlikely hero for the Red Sox in Game 1 of the World Series - Los Angeles Times First, a quick review about quadratic equations and parabolas: This professor’s ‘amazing’ trick makes quadratic equations easier 2020-02-10T05:00:00Z Graph parabolas with vertices not at the origin. Algebra and Trigonometry 2015-02-13T00:00:00Z Sunday’s performance may mean nothing at all, a brief spike in a parabola of sullen decline that most assume will culminate in a toxic farewell within the year. Meet Nice José: Mourinho’s radical rebrand seems like a welcome move | Barney Ronay 2018-09-03T04:00:00Z Write the equation of a parabola that opens up or down in standard form and the equation of a parabola that opens left or right in standard form. Intermediate Algebra 2020-05-06T00:00:00Z As we enter Martian gravity, our first parabola, I notice my arms drift up. HP took me on a zero-gravity flight to promote their space printer 2018-02-11T05:00:00Z In other words, this parabola intersects the x-axis when x = –1 and x = 5. This professor’s ‘amazing’ trick makes quadratic equations easier 2020-02-10T05:00:00Z Applications of parabolas are also critical to other areas of science. Algebra and Trigonometry 2015-02-13T00:00:00Z The graph “A Labor U-Turn” in “Women's Work,” by Ana L. Revenga and Ana Maria Munoz Boudet, claims to show a link between female labor force participation and countries' per capita GDP with a parabola. Readers Respond to the September 2017 Issue 2018-01-14T05:00:00Z Provide a sketch of the parabola for each one, label the vertex and axis of symmetry. Intermediate Algebra 2020-05-06T00:00:00Z On another parabola, I pull my legs in toward my chest with a little too much force and find myself somersaulting toward the ceiling of the plane. HP took me on a zero-gravity flight to promote their space printer 2018-02-11T05:00:00Z After a single and an RBI double, Morrow watched a towering parabola rise off the bat of shortstop Carlos Correa. Astros are one win from World Series title after outslugging Dodgers 13-12 in Game 5 2017-10-29T04:00:00Z In this section we will explore the parabola and its uses, including low-cost, energy-efficient solar designs. Algebra and Trigonometry 2015-02-13T00:00:00Z The way the flight works is fairly simple: the plane flies in a series of parabolas, or peaks and valleys. What it feels like to float in zero gravity 2017-09-05T04:00:00Z Explain in your own words, how you can tell from its equation whether a parabola opens up, down, left or right. Intermediate Algebra 2020-05-06T00:00:00Z The plane does parabolas in the sky to create short periods of weightlessness. Want to get rid of space trash? This gecko-inspired robot may do the trick 2017-06-28T04:00:00Z “The pitch he threw that day could most charitably be described as a parabola,” said David Axelrod, the former White House senior adviser. Trump Declines First Pitch on Opening Day, Throwing Ritual a Curveball 2017-04-03T04:00:00Z Now we extend the discussion to include other key features of the parabola. Algebra and Trigonometry 2015-02-13T00:00:00Z The next time Lingard delivered, the ball came on a perfect parabola. West Bromwich Albion frustrate Manchester United the Tony Pulis way 2017-04-01T04:00:00Z There are four conics—the circle, parabola, ellipse, and hyperbola. Intermediate Algebra 2020-05-06T00:00:00Z After filming the State Theater, whose structural supports soar above its roof in concrete parabolas like those of a suspension bridge, Echo Delta and Ghost took a taxi to the city’s Central district. Using Stealth, and Drones, to Document a Fading Hong Kong 2017-02-07T05:00:00Z Abbs handles the parabola of this real life story with tremendous assurance. Readers’ books of the year 2016 2016-12-31T05:00:00Z By definition, the distance from the focus to any point on the parabola is equal to the distance from to the directrix. Algebra and Trigonometry 2015-02-13T00:00:00Z Instead, Nan and his team designed a system that pulls a roughly 300-meter-diameter section of FAST’s spherical reflector into a subtle parabola, while positioning receivers along the parabola’s axis. World’s largest radio telescope will search for dark matter, listen for aliens 2016-09-26T04:00:00Z We define a parabola as all points in a plane that are the same distance from a fixed point and a fixed line. Intermediate Algebra 2020-05-06T00:00:00Z Try buying or making your own parabola if you're trying to catch something super specific from farther away. The sounds in your backyard are unique, go record them 2016-08-28T04:00:00Z And it sticks in an annoyingly obvious piece of product placement, where one of the characters not only prominently chows down on Pringles, but praises the irresistibility of their "salty parabolas." Ghostbusters' cast is what saves it from the reboot doldrums 2016-07-13T04:00:00Z When given a standard equation for a parabola centered at the origin, we can easily identify the key features to graph the parabola. Algebra and Trigonometry 2015-02-13T00:00:00Z The actuators tug the dish into a parabola by pulling on tie-down cables connected to the dish’s supporting mesh. World’s largest radio telescope will search for dark matter, listen for aliens 2016-09-26T04:00:00Z The fixed point is called the focus, and the fixed line is called the directrix of the parabola. Intermediate Algebra 2020-05-06T00:00:00Z It’s so tempting to try to quantify the sweetness of their play: Geometrists sketch the parabola of Stephen Curry’s shot, and gangs of statisticians evaluate their records and probabilities of repeating as NBA champions. The Golden State Warriors can’t be defined by numbers alone 2016-04-20T04:00:00Z Each parabola will generate 20 to 25 seconds of weightlessness as passengers pass through the top of the arc. Swiss group buys Airbus jet for zero-gravity flights 2016-04-12T04:00:00Z We can also use the calculations in reverse to write an equation for a parabola when given its key features. Algebra and Trigonometry 2015-02-13T00:00:00Z Radio telescope dishes are typically parabolic because that shape focuses waves from astronomical objects in line with the parabola’s axis to a point above the dish. World’s largest radio telescope will search for dark matter, listen for aliens 2016-09-26T04:00:00Z Previously, we learned to graph vertical parabolas from the general form or the standard form using properties. Intermediate Algebra 2020-05-06T00:00:00Z Finally, with the crowd at full roar, Curry launched the ball from several steps beyond the three-point line, and its parabola toward the basket seemed to last forever. What Happened When Venture Capitalists Took Over the Golden State Warriors 2016-03-30T04:00:00Z You just grip a club attached to the robot, known as RoboGolfPro, and the German-designed training machine guides you through the ideal parabola of an effective windup. This robotic training machine fits his golf game to a T 2016-03-16T04:00:00Z When rays of light parallel to the parabola’s axis of symmetry are directed toward any surface of the mirror, the light is reflected directly to the focus. Algebra and Trigonometry 2015-02-13T00:00:00Z The position of the parabola can be shifted in real time, so that the parabolic axis always aims at a cosmic object of interest as Earth rotates, just as a steerable radio telescope does. World’s largest radio telescope will search for dark matter, listen for aliens 2016-09-26T04:00:00Z The graphs show what the parabolas look like when they open up or down. Intermediate Algebra 2020-05-06T00:00:00Z “Galileo’s observation that all falling objects trace a parabola is one of the most wonderful discoveries in all of science,” physicist Lee Smolin writes in his book “Time Reborn.” A brief history of gravity, gravitational waves and LIGO 2016-02-11T05:00:00Z But throwing a rock over the fence to hit a target close to the barrier is far more difficult, requiring a narrow, perfect parabola, delivered with incredible precision or incredible luck. A barrage of rocks and then bullets: When the Border Patrol kills Mexican teens 2015-12-15T05:00:00Z Because the igniter is located at the focus of the parabola, the reflected rays cause the object to burn in just seconds. Algebra and Trigonometry 2015-02-13T00:00:00Z Almost every tee shot is a giant, soaring parabola with 30 yards of curve, and the shot he hit to win the 2012 Masters made an almost 90 degree curve from the trees. How He Hit That: Bubba Watson's fairway bunker slash: The Loop 2013-10-16T04:00:00Z To graph a parabola from these forms, we used the following steps. Intermediate Algebra 2020-05-06T00:00:00Z When air resistance is very low, a projectile moves in the shape of a parabola—a type of mathematical curve. The Physics of Baseball: How Far Can You Throw? 2015-05-28T04:00:00Z When Curry dribbles, the ball orbits around his legs and behind his back, then goes whistling off in unexpected directions via no-look passes or in pinpoint parabolas that find the bottom of the net. Golden State Vs. the Playoff Grind 2015-05-12T04:00:00Z If the equation of a parabola is written in standard form and is positive and the directrix is a vertical line, then what can we conclude about its graph? Algebra and Trigonometry 2015-02-13T00:00:00Z In “Red Army,” the swirling, interlocking parabolas of Soviet hockey live again. 'Red Army' Hockey Documentary Begins Limited Run This Week 2014-11-12T05:00:00Z The next example reviews the method of graphing a parabola from the general form of its equation. Intermediate Algebra 2020-05-06T00:00:00Z So instead of measuring it as a right triangle, Wallenda's engineers measured it as a parabola. As a math problem, Wallenda wire walk was complicated 2014-11-06T05:00:00Z You shouldn’t teach the area of the parabola unless a student knows how to estimate the full four-year cost of college attendance. How to Ditch the Common Core and Teach Kids Real Skills 2014-11-05T05:00:00Z If the equation of a parabola is written in standard form and is negative and the directrix is a horizontal line, then what can we conclude about its graph? Algebra and Trigonometry 2015-02-13T00:00:00Z The drag coefficient is coded into the game’s software to simulate air resistance, which greatly affects the pace at which an object rises and falls in the shape of a parabola. Getting on the Ball: How the FIFA 14 Soccer Video Game Finally Got Its Physics Right 2013-09-27T15:15:04.687Z Since a is −1, the parabola opens downward. Intermediate Algebra 2020-05-06T00:00:00Z “They are large parabolas,” says Bill Stewart, managing partner at SSA Acoustics, which is based in Seattle. The Science of Sound: How Seattle Got So Loud 2013-09-17T10:50:22Z Holding umbrella-shaped parabola microphones, they were told to record Anthony's interactions and send the tape directly to Dolan himself. In London, Carmelo Anthony praises Knicks owner 2013-01-16T17:51:09Z For the following exercises, determine whether the given equation is a parabola. Algebra and Trigonometry 2015-02-13T00:00:00Z When rotating, the forces of nature keep the thin layer of liquid mercury in the shape of a parabola. Liquid Mirror Telescope Technology Finally Going Mainstream 2012-12-30T08:29:35Z We are now going to look at horizontal parabolas. Intermediate Algebra 2020-05-06T00:00:00Z A “vast majority” of the children of the older mice were “completely normal,” he said, which meant their score fell under the upside-down parabola of the curve. Opinion: Why Fathers Really Matter 2012-09-08T21:03:01Z No one cares about parabolas, which is why half the class is playing Angry Birds under their desk. Surviving math class by doodling — video 2012-08-31T01:03:43Z For the following exercises, graph the parabola, labeling the focus and the directrix. Algebra and Trigonometry 2015-02-13T00:00:00Z But shaping parabolas is just one of many tasks facing engineers like Mr. Miller. Wood Takes a Thrilling Turn in Roller Coaster Design 2012-07-02T20:02:33Z These parabolas open either to the left or to the right. Intermediate Algebra 2020-05-06T00:00:00Z Across a mound of thrown-up sand one of the lanterns cast a short parabola of shadow. Mushroom Town 2012-04-21T02:00:25.923Z If wound around a parabola, the pitch would vary at every point in its diameter and thread. Modern Machine-Shop Practice, Volumes I and II 2012-03-23T02:00:33.140Z For the following exercises, determine the equation for the parabola from its graph. Algebra and Trigonometry 2015-02-13T00:00:00Z By the principles of optics, all the rays from a star that strike a concave mirror will be reflected to the geometric focal point, provided a section of that mirror is a parabola. Astronomy: The Science of the Heavenly Bodies 2012-03-17T02:01:02.630Z If we interchange the x and y in our previous equations for parabolas, we get the equations for the parabolas that open to the left or to the right. Intermediate Algebra 2020-05-06T00:00:00Z The epithets hyperbolic and parabolic are of course derived from the conic hyperbola and parabola respectively. Encyclopaedia Britannica, 11th Edition, Volume 7, Slice 8 "Cube" to "Daguerre, Louis" 2012-01-31T03:00:17.257Z Parabol′ic, -al, like a parable or a parabola: expressed by a parable: belonging to, or of the form of, a parabola.—adv. Chambers's Twentieth Century Dictionary (part 3 of 4: N-R) 2012-01-30T03:00:13.887Z For the following exercises, the vertex and endpoints of the latus rectum of a parabola are given. Algebra and Trigonometry 2015-02-13T00:00:00Z The flying gentleman soared softly into a parabola, coming down with a crash, while a pistol fell from his hand. Parson Kelly 2012-01-28T03:00:30.303Z The graphs show what the parabolas look like when they to the left or to the right. Intermediate Algebra 2020-05-06T00:00:00Z The nature of the two kinds of branches is best understood by considering them as projections, in the same way as we in effect consider the hyperbola and the parabola as projections of the ellipse. Encyclopaedia Britannica, 11th Edition, Volume 7, Slice 8 "Cube" to "Daguerre, Louis" 2012-01-31T03:00:17.257Z The curve, therefore, connecting height of aerial with sending distance for given arrangements is a portion of a parabola. Hertzian Wave Wireless Telegraphy 2012-01-09T03:00:20.570Z For the following exercises, write the equation of the parabola using the given information. Algebra and Trigonometry 2015-02-13T00:00:00Z The white body caromed sharply off a couple of projecting ledges, and then, gathering momentum, began to describe a great parabola which promised to carry it right to the foot of the cliff. Down the Columbia 2011-12-10T03:00:16.583Z Looking at these parabolas, do their graphs represent a function? Intermediate Algebra 2020-05-06T00:00:00Z The five divergent parabolas are curves each of them symmetrical with regard to an axis. Encyclopaedia Britannica, 11th Edition, Volume 7, Slice 8 "Cube" to "Daguerre, Louis" 2012-01-31T03:00:17.257Z In the most improved form these were made to that peculiar curve known as a parabola. Marvels of Scientific Invention An Interesting Account in Non-technical Language of the Invention of Guns, Torpedoes, Submarine Mines, Up-to-date Smelting, Freezing, Colour Photography, and many other recent Discoveries of Science 2011-11-19T03:00:24.517Z For the following exercises, write the equation of the parabola in standard form, and give the vertex, focus, and equation of the directrix. Algebra and Trigonometry 2015-02-13T00:00:00Z We looked aloft and saw in mid-air a solid shot from the Matterhorn describing its proper parabola, and finally splitting into fragments as it smote one of the rocky towers in front. The Ascent of the Matterhorn 2011-11-19T03:00:23.233Z To graph the parabola we need more points. Intermediate Algebra 2020-05-06T00:00:00Z Thus the fireplace end of the room lay in a sort of irregular parabola of illumination. In Accordance with the Evidence 2011-11-06T02:00:12.393Z In mortar fire, the theoretical trajectory of the projectile la a parabola, as shown in Fig. Dropping Bombs from Flying Machines 2011-10-13T12:15:03.687Z For the following exercises, graph the parabola, labeling the vertex, focus, and directrix. Algebra and Trigonometry 2015-02-13T00:00:00Z It is natural, therefore, that circle, ellipse, parabola, and hyperbola should all be looked upon as lines. The Teaching of Geometry 2011-10-12T02:00:52.133Z To box lists the steps for graphing a parabola in the standard form x = a⎛y − k⎞2 + h. Intermediate Algebra 2020-05-06T00:00:00Z The axis of a curved line is formed by a right line dividing the curve into two symmetrical parts, as in the parabola, ellipse, and hyperbola:—pl. Chambers's Twentieth Century Dictionary (part 1 of 4: A-D) 2011-10-11T02:01:08.990Z Neglecting atmospheric resistance, the ascending and descending halves of the parabola: are equal and symmetrical. Dropping Bombs from Flying Machines 2011-10-13T12:15:03.687Z A parabola is formed by slicing the plane through the top or bottom of the double-cone, whereas a hyperbola is formed when the plane slices both the top and bottom of the cone. Algebra and Trigonometry 2015-02-13T00:00:00Z While these conic sections are not studied in elementary geometry, the terms should be known for general information, particularly the ellipse and parabola. The Teaching of Geometry 2011-10-12T02:00:52.133Z Since a = 2, the parabola opens to the right. Intermediate Algebra 2020-05-06T00:00:00Z From the line-pair we pass through an infinity of hyperbolas to the parabola, and thence through an infinity of ellipses to the circle. Encyclopaedia Britannica, 11th Edition, Volume 11, Slice 6 "Geodesy" to "Geometry" 2011-09-19T02:00:10.473Z He smote the red-skin warrior so earnestly on the ear that Mr. Brannigan described a parabola and dented a papier-mache rock with his hundred and seventy pounds of muscular body. The Sin of Monsieur Pettipon and other humorous tales 2011-09-17T02:00:25.067Z The standard form of a parabola with vertex and the y-axis as its axis of symmetry can be used to graph the parabola. Algebra and Trigonometry 2015-02-13T00:00:00Z Most comets seem to move in parabolas, and a body thrown into the air would take a parabolic path if it were not for the resistance of the atmosphere. The Teaching of Geometry 2011-10-12T02:00:52.133Z Since a = 2, the parabola opens to the right. Intermediate Algebra 2020-05-06T00:00:00Z The parabola has one focus within it, and another, the “caecus focus,” which may be imagined to be at infinity on the axis within or without the curve. Encyclopaedia Britannica, 11th Edition, Volume 11, Slice 6 "Geodesy" to "Geometry" 2011-09-19T02:00:10.473Z A Scout rose from the trench and aimed his rifle, when the blood-dripping rag described a rapid parabola and was sticking flaccidly on the soldier's khaki, the handle quivering behind. Caybigan 2011-08-31T02:01:21.780Z When given the focus and directrix of a parabola, we can write its equation in standard form. Algebra and Trigonometry 2015-02-13T00:00:00Z Individual sprays and fronds, projecting from the mass in parabolas with flamboyant abandon and poise, were as rigid as metallic and enamelled shapes. The Sea and the Jungle 2011-08-30T02:00:30.350Z To find the value of a use one of the other points on the parabola. Intermediate Algebra 2020-05-06T00:00:00Z As a special case we get, by taking the line at infinity: Through four points of which none is at infinity either two or no parabolas may be drawn. Encyclopaedia Britannica, 11th Edition, Volume 11, Slice 6 "Geodesy" to "Geometry" 2011-09-19T02:00:10.473Z Hamlet darted the bus at the curves; then softly padded round like an angel: then off again for the next parabola. Sea and Sardinia 2011-08-28T02:00:30.857Z The standard form of a parabola with vertex and axis of symmetry parallel to the y-axis can be used to graph the parabola. Algebra and Trigonometry 2015-02-13T00:00:00Z The toughest thing to do is stay invested during the various parabolas and sit through the corrections.” Gold Futures Plunge Most in 18 Months 2011-08-24T19:36:01Z Explain how to find the intercepts of a parabola. Intermediate Algebra 2020-05-06T00:00:00Z All diameters of a parabola are parallel, the pole to the line at infinity being the point where the curve touches the line at infinity. Encyclopaedia Britannica, 11th Edition, Volume 11, Slice 6 "Geodesy" to "Geometry" 2011-09-19T02:00:10.473Z See, his hand springs from his hip, and describes an exact segment of a circle—no, a parabola, I suppose—every time, so as to make the seed spread itself equally. Greene Ferne Farm 2011-08-14T02:00:22.210Z Real-world situations can be modeled using the standard equations of parabolas. Algebra and Trigonometry 2015-02-13T00:00:00Z When these eyes of Rotifers are not readily conspicuous, they must be sought for by opaque illumination, or by the dark-ground method which, especially with the parabola, is successful in bringing them out. Marvels of Pond-life A Year's Microscopic Recreations 2011-08-01T02:00:12.067Z We want to know when the parabola is below the x-axis. Intermediate Algebra 2020-05-06T00:00:00Z A parabola has one axis, if we define an axis as a diameter perpendicular to the chords which it bisects. Encyclopaedia Britannica, 11th Edition, Volume 11, Slice 6 "Geodesy" to "Geometry" 2011-09-19T02:00:10.473Z Not a flyer in the game such parabolas could claim, At the place where the old cleek broke! Verse and Worse 2011-07-12T02:00:34.607Z They include an ellipse, a circle, a hyperbola, and a parabola. Algebra and Trigonometry 2015-02-13T00:00:00Z Birds were given different colors, squawks and abilities such as extra density, acceleration and the power to lay explosive eggs in the air before winging off their parabolas from the counterforce of laying eggs. Audacious Birds 2011-06-29T22:00:00Z In the last example, the parabola opened upward and in the next example, it opens downward. Intermediate Algebra 2020-05-06T00:00:00Z For the parabola, too, follow some metrical properties. Encyclopaedia Britannica, 11th Edition, Volume 11, Slice 6 "Geodesy" to "Geometry" 2011-09-19T02:00:10.473Z The machine rolled forward, the propellers beat the air, and the Racing Star rose on a smooth parabola. Airship Andy or The Luck of a Brave Boy 2011-06-13T02:00:31.130Z For the following exercises, graph the parabola, labeling vertex, focus, and directrix. Algebra and Trigonometry 2015-02-13T00:00:00Z He demonstrated that a projectile follows the path of a parabola, instead of a straight line, and that it descends a vertical distance which is proportional to the square of the time taken to fall. Our Legal Heritage June 2011 (Sixth) Edition 2011-06-03T02:00:23.737Z In both cases, we are looking for the part of the parabola that is below the x-axis but note how the position of the parabola affects the solution. Intermediate Algebra 2020-05-06T00:00:00Z But a diameter cuts the parabola once at infinity. Encyclopaedia Britannica, 11th Edition, Volume 11, Slice 6 "Geodesy" to "Geometry" 2011-09-19T02:00:10.473Z Over the front of the stockade something flew through the darkness, its parabola marked by a string of sparks that spluttered behind it. The Snow-Burner 2011-05-17T02:00:21.527Z If it is a parabola, label the vertex, focus, and directrix. Algebra and Trigonometry 2015-02-13T00:00:00Z The directrix of a parabola is a line perpendicular to the axis produced, and at a distance from the vertex equal to the distance of the vertex from the focus. The New Gresham Encyclopedia Volume 4, Part 1: Deposition to Eberswalde 2011-04-14T02:00:57.977Z Since a = 2, the parabola opens to the right. Intermediate Algebra 2020-05-06T00:00:00Z Hence— The segment PM which joins the middle point M of a chord of a parabola to the pole P of the chord is bisected by the parabola at A. Fig. Encyclopaedia Britannica, 11th Edition, Volume 11, Slice 6 "Geodesy" to "Geometry" 2011-09-19T02:00:10.473Z Readers are invited to submit your own pictures of these starchy parabolas in whatever exotic locations you happen to find them. How to explain the popularity of Pringles? 2011-03-23T00:55:00Z The graph of a quadratic function is a parabola. Algebra and Trigonometry 2015-02-13T00:00:00Z He discovered a simpler method of quadrating parabolas than that of Archimedes, and a method of finding the greatest and the smallest ordinates of curved lines analogous to that of the then unknown differential calculus. Encyclopaedia Britannica, 11th Edition, Volume 10, Slice 3 "Fenton, Edward" to "Finistere" 2011-03-14T03:01:00.580Z Since a = −1, the parabola opens to the left. Intermediate Algebra 2020-05-06T00:00:00Z In a parabola the vertex lies halfway between directrix and focus. Encyclopaedia Britannica, 11th Edition, Volume 11, Slice 6 "Geodesy" to "Geometry" 2011-09-19T02:00:10.473Z I'll just as soon say that the parabola and the ellipsis are the same," said the Dominie; "or that the diameter is not the longest line that can be drawn in the circle. The Shepherd's Calendar Volume I (of II) 2011-03-05T03:00:28.153Z Standard or vertex form is useful to easily identify the vertex of a parabola. Algebra and Trigonometry 2015-02-13T00:00:00Z If the observer inside the chamber draws a line through the spots, it will look to him like a parabola bending toward the floor. Gravity, by George Gamow [Special Archive Article] 2011-03-04T13:45:00.433Z In Table 11.1, we see the relationship between the equation in standard form and the properties of the parabola. Intermediate Algebra 2020-05-06T00:00:00Z In case of the parabola this becomes— The line joining any point on a parabola to the focus and the diameter through the point, are equally inclined to the tangent and normal at that point. Encyclopaedia Britannica, 11th Edition, Volume 11, Slice 6 "Geodesy" to "Geometry" 2011-09-19T02:00:10.473Z Crawling over shell-torn ground, slow work at the best, is rendered slower by the frequent waits necessary while rockets flare overhead and Verrey lights describe brilliant parabolas in unexpected directions. The Revellers 2011-02-26T03:00:50.133Z Then we choose points to test both inside and outside the parabola. Algebra and Trigonometry 2015-02-13T00:00:00Z The vertical filament through the centroid of any cross-section becomes a cubical parabola, as shown in fig. Encyclopaedia Britannica, 11th Edition, Volume 9, Slice 2 "Ehud" to "Electroscope" 2011-01-29T03:00:23.777Z In the next example, we notice the a is negative and so the parabola opens to the left. Intermediate Algebra 2020-05-06T00:00:00Z In case of the parabola there is but one axis. Encyclopaedia Britannica, 11th Edition, Volume 11, Slice 6 "Geodesy" to "Geometry" 2011-09-19T02:00:10.473Z Then, with splendid judgment, he threw the lasso in a lateral parabola that landed its end across the rail of the bridge, where it was promptly made fast by the first officer. His Unknown Wife 2011-01-27T03:00:38.763Z Many of the orbits she determined were made up of parabolas, and her ability to combine different types of math enabled an unprecedented level of precision. Algebra and Trigonometry 2015-02-13T00:00:00Z His work "On the Quadrature," that is the finding of the area of a segment of the parabola, is probably his most significant contribution to mathematical knowledge. Education: How Old The New 2011-01-14T03:00:54.370Z Since a = −4, the parabola opens to the left. Intermediate Algebra 2020-05-06T00:00:00Z Hence the theorem— The tangents to a parabola cut each other proportionally. Encyclopaedia Britannica, 11th Edition, Volume 11, Slice 6 "Geodesy" to "Geometry" 2011-09-19T02:00:10.473Z The fact that comet orbits are parabolas, or differ but little from them, explains at once the temporary character and speedy disappearance of these bodies. A Text-Book of Astronomy 2011-01-05T03:00:57.347Z Set the two expressions for equal to each other and solve for to derive the equation of the parabola. Algebra and Trigonometry 2015-02-13T00:00:00Z After making this tool according to Mr. Nasmyth's pattern, father found it applicable to metal specula only, and unsuitable to glass inasmuch as it would not parabolize, or work in the figure of a parabola. The Life of Roger Langdon Told by himself. With additions by his daughter Ellen. [With a preface by H. Clifton Lambert.] 2010-12-21T22:55:56.210Z It is not uncommon for bridges to be constructed using parabolas as we will see in the next example. Intermediate Algebra 2020-05-06T00:00:00Z The surface is thus generated by a variable hyperbola moving parallel to itself along the parabolas as directrices. Encyclopaedia Britannica, 11th Edition, Volume 11, Slice 6 "Geodesy" to "Geometry" 2011-09-19T02:00:10.473Z If the comet of 1668 had moved in a parabola instead of the ellipse supposed above, how many years would have been required to reach its present distance from the sun? A Text-Book of Astronomy 2011-01-05T03:00:57.347Z The equations of parabolas with vertex are when the x-axis is the axis of symmetry and when the y-axis is the axis of symmetry. Algebra and Trigonometry 2015-02-13T00:00:00Z He set the torch down on the table, where it made a vivid flat parabola of light, and took an envelope from his pocket. The Tower of Oblivion 2010-12-20T17:11:53.787Z Lessons include the role of parabolas in punting, how defenders instinctively use the Pythagorean theorem to prevent touchdowns and why the shape of a football - a prolate spheroid - helps quarterbacks throw spirals. Videos demonstrate some of the science behind football 2010-11-15T22:26:03Z The precise flight of a football, as it leaves the quarterback’s hand, is dissected in special slow-motion to show how the principles of a parabola work. Teaching Science With Football 2010-09-07T22:42:00Z Astronomers, therefore, consider meteors as well as comets to have the parabola and the elongated ellipse as their characteristic orbits. A Text-Book of Astronomy 2011-01-05T03:00:57.347Z For the following exercises, find the equation of the parabola given information about its graph. Algebra and Trigonometry 2015-02-13T00:00:00Z In a wry account, Roach herself braves motion sickness on NASA’s “Vomit Comet,” a C-9 transport plane modified to fly in parabolas — the only means of experiencing weightlessness outside of orbit. Book Review - Packing for Mars - By Mary Roach 2010-08-07T22:41:00Z After a stomach-ripping second or so of rapid descent his parachute billows and in a gentle, expert parabola he floats away from the jutting brickwork and eases towards the drop zone. Base jumping is absurdly dangerous ? so why do it? 2010-08-06T07:00:00Z The arching curve above — technically known as a “parabola”— is the signature of the squaring function x 2 operating behind the scenes. Power Tools 2010-03-28T23:57:00Z Because comet orbits are nearly parabolas, it used to be assumed that they were exactly parabolic, and this carried with it the conclusion that comets have their origin outside the solar system. A Text-Book of Astronomy 2011-01-05T03:00:57.347Z On a schematic, the equation of the parabola is given as At what coordinates should you place the light bulb? Algebra and Trigonometry 2015-02-13T00:00:00Z But over the parabola’s crest and during the half-minute journey downward, fliers “rise up off the floor like spooks from a grave.” Book Review - Packing for Mars - By Mary Roach 2010-08-07T22:41:00Z If you're planning to participate in this national sit-in, you can drastically enhance the viewing experience by pondering the parabola. In basketball, shooting angle has a big effect on the chances of scoring 2010-03-16T04:00:00Z For a parabola, n = 2; for a constant, n = 0. Power Tools 2010-03-28T23:57:00Z It is, in fact, a part of a parabola, which, as we shall see later, is a kind of orbit in which comets and some other heavenly bodies move. A Text-Book of Astronomy 2011-01-05T03:00:57.347Z This means that it can be formed by rotating a parabola around its axis of symmetry. Algebra and Trigonometry 2015-02-13T00:00:00Z But Reisinger is reluctant to draw a simple parabola of artistic merit in Israel, where the descent begins as Israel becomes enmeshed, from 1967 onwards, in the occupation. Primary colours 2010-03-15T12:25:00Z But they reach their apex in basketball, where field goals and free throws demand precision control of parabolas. In basketball, shooting angle has a big effect on the chances of scoring 2010-03-16T04:00:00Z He is good on people, observing one man’s “flowery nose” and “grenadine complexion,” another’s “white parabola” of a mustache, yet another’s “precarious nail-bitten superiority.” Books of The Times: A Look at the Snarled Past of Armenians and Turks 2010-03-02T22:19:00Z Phil Weber, a D’Antoni assistant, saw something else: Lee was “a yanker” — meaning he yanked his wrist back too far on his windup, shooting line drives instead of parabolas. 2010-01-10T00:51:00Z Find the equation of the parabola, and determine the height of the arch 40 feet from the center. Algebra and Trigonometry 2015-02-13T00:00:00Z A body moving in a parabola or hyperbola would recede indefinitely from its centre of motion and never return to it. Encyclopaedia Britannica, 11th Edition, Volume 2, Slice 7 "Arundel, Thomas" to "Athens" Well, there are many different parabolas that will do the job, and the choice varies according to player height, personal preference and position on the court. In basketball, shooting angle has a big effect on the chances of scoring 2010-03-16T04:00:00Z Young Lord Dereham was no light weight, and his lordship’s wriggling carcass had described sufficient parabola to clear coping-stones set ten feet above the pavement. The Great Mogul If the air-resistance be neglected, it can be shown that the trajectory is a parabola. The New Gresham Encyclopedia. Vol. 1 Part 3 Atrebates to Bedlis The graph of is a parabola facing downward, as shown in Figure 4. Algebra and Trigonometry 2015-02-13T00:00:00Z Michael would linger on his journey home through the mellow streets of Kensington, writing with his bicycle wheels lazy parabolas and curves in the dust of each quiet road. Sinister Street, vol. 1 And while you're at it, take a moment to remember Menaechmus, the geometer who first described the parabola in the 4th century B.C. In basketball, shooting angle has a big effect on the chances of scoring 2010-03-16T04:00:00Z The parabola would narrow the beam to little more than its initial diameter and would concentrate the energy more than is required. The Year When Stardust Fell Bent nearly double by the blow, the enemy Cro-Magnard was lifted completely from his feet and propelled into space, his already unconscious body tracing a perfect parabola to death on the ground sixty feet below. The Return of Tharn The graph is a parabola with vertex at the point opening to the right. Algebra and Trigonometry 2015-02-13T00:00:00Z During their walk Utrilla, with incredible geometrical skill, cut a series of circles, ellipses, parabolas, and other incomprehensible and erratic curves, the focus of which was constantly our friends. Maximina "A Creole," thought Ruis; and raising his right hand to the left side of his broad-brimmed hat, he made it describe a magnificent parabola through the air, and as he replaced it, bowed. A Transient Guest and Other Episodes A comet is visible only in a small arc of its orbit near perihelion, differing but slightly 760 from the arc of a parabola. Encyclopaedia Britannica, 11th Edition, Volume 6, Slice 7 "Columbus" to "Condottiere" Sadu, soaring in a majestic parabola, overshot his mark and landed a full two yards beyond. The Return of Tharn As values of become negative, they trace out the lower half of the parabola. Algebra and Trigonometry 2015-02-13T00:00:00Z He described a perfect parabola and landed on his head and shoulders on the ground. Frances of the Ranges The Old Ranchman's Treasure This curve—called the parabola—is that of all projected or bounding objects. Modern Painters, Volume IV (of V) A few comets are known to revolve in orbits with a regular period, while, in the case of others, no evidence is afforded by observation that the orbit deviates from a parabola. Encyclopaedia Britannica, 11th Edition, Volume 6, Slice 7 "Columbus" to "Condottiere" The power of these reflectors, however, was comparatively small, from the reflecting surface being composed of numerous pieces, in each of which only one point coincided with the curve of the parabola. Smeaton and Lighthouses A Popular Biography, with an Historical Introduction and Sequel We can see that the solution set consists of all points inside the parabola, but not on the graph itself. Algebra and Trigonometry 2015-02-13T00:00:00Z Among his mathematical investigations must not be omitted the quadrature of the parabola. History of the Intellectual Development of Europe, Volume I (of 2) Revised Edition There are also colourless phosphorous rockets that describe a wide parabola in their flight. Cavalry of the Clouds In this case the motion of the sun through space renders it almost infinitely improbable that the orbit would have been so nearly a parabola as all such orbits are actually found to be. Encyclopaedia Britannica, 11th Edition, Volume 6, Slice 7 "Columbus" to "Condottiere" His parabola starts at the seventeenth century, rises to its maximum somewhere about the Johnsonian period, continues with scarcely abated vigour as far as Thackeray and Carlyle, declines towards Trollope and—ends. An Ocean Tramp If we sketch lines tangent to the parabola at the endpoints of the latus rectum, these lines intersect on the axis of symmetry, as shown in Figure 6. Algebra and Trigonometry 2015-02-13T00:00:00Z At night fiery parabolas blazed their course against the sky, up from the outer hills, sweeping down on Las Campanas or La Cruz. The Missourian His big foot described an upward arc, and Jake a parabola, ending in a drop that almost took him through an open hatch into the depth of the hold. The Cup of Fury A Novel of Cities and Shipyards From each one a small black cigar-shaped object was released and fell in a long parabola toward the earth. Astounding Stories, February, 1931 I feel, “inside,” as children say, that my parabola will be finished before I can win to the burning heart of the man. An Ocean Tramp Because we will graph a parabola with a focus at the origin. Algebra and Trigonometry 2015-02-13T00:00:00Z Well, to-morrow we must begin polishing, or rather I must, to turn our glass from a spherical-curved mirror into a parabola.” The Vast Abyss The Story of Tom Blount, his Uncles and his Cousin Sam Observations on a comet moving in an extremely eccentric ellipse, which are possible only when it is comparatively near perihelion, must fail to distinguish its orbit from a parabola. Essays: Scientific, Political, & Speculative, Vol. I There was a hollow in the wall, a great parabola, deep and wide, and it was lined throughout with beaten gold. Astounding Stories of Super-Science, June, 1930 They can get no further, because their mental parabola is complete. An Ocean Tramp If it is a parabola, label the vertex, focus, and directrix. Algebra and Trigonometry 2015-02-13T00:00:00Z No, boy; because it is the step towards making an ellipse, or, as they call it when shaped for a reflecting telescope, a parabola. The Vast Abyss The Story of Tom Blount, his Uncles and his Cousin Sam Evidently, then, it is not safe to class it as a parabola because of inability to detect the elements of an ellipse. Essays: Scientific, Political, & Speculative, Vol. I The priests were now upon the dais—the rocky platform, divided by the great, glowing parabola of light. Astounding Stories of Super-Science, June, 1930 The steamer was plowing straight to the westward, cutting the waves so keenly that a thin parabola of water continually curved over in front of her from the knife-like prow. Adrift on the Pacific A Boys [sic] Story of the Sea and its Perils It isn’t a parabola and it isn’t an ellipse. Astounding Stories of Super-Science, March 1930 “Oh,” said Tom, who only knew parabolas from a cursory acquaintance with them through an old Greek friend called Euclid. The Vast Abyss The Story of Tom Blount, his Uncles and his Cousin Sam Consequently, anything coming to the Sun from a great distance must have one exact amount of proper motion to produce a parabola: all other amounts would give hyperbolas or ellipses. Essays: Scientific, Political, & Speculative, Vol. I The next time, he flew to the peak in a zipping parabola that was as the course of a rocket. The Trimming of Goosie Each of them is an opened parabola of such spread that their beams will cover an area ten yards in diameter at fifty miles above the earth. Astounding Stories of Super-Science July 1930 As a matter of fact the path of a projectile in vacuo is only approximately a parabola. Pioneers of Science Boomerang: a thin piece of wood, having the shape of a parabola, about eighteen inches or two feet long from point to point, the curve being on the thin side. Austral English A dictionary of Australasian words, phrases and usages with those aboriginal-Australian and Maori words which have become incorporated in the language, and the commoner scientific words that have had their origin in Australasia Ellipses and hyperbolas have countless varieties of forms, but there is only one form of parabola; or, to speak literally, all parabolas are similar, while there are infinitely numerous dissimilar ellipses and dissimilar hyperbolas. Essays: Scientific, Political, & Speculative, Vol. I At the beginning of the ninth section of the parabola, the wanderer breaks red and white roses from the rosebush and sticks them in his hat. Hidden Symbolism of Alchemy and the Occult Arts He dropped upon the imprudent mouse, in describing what is called in geometry a parabola, and seized it by the nose, to prevent it from crying out. The Story of a Cat Its actual path will be a curve, which in this case is a parabola. Pioneers of Science The theory of gravitation, though it admits the parabola as a possible orbit for a comet, does not assert that the path must necessarily be of this type. The Story of the Heavens By continuing this process, the ellipse passes insensibly into a parabola; and, ultimately, by still further diminishing the angle, into an hyperbola. Essays: Scientific, Political, & Speculative, Vol. I And my uniform-case, of which he never let go, described a very beautiful parabola, and then came down upon the weigh-bridge, as the swiple of an uplifted flail comes down upon grain…. Jonah and Co. The bullet hit the neck of the glass bowl, a trifle below the burner, the latter describing a parabola in the air and falling into the ruin of the bowl. 'Firebrand' Trevison It is now thought possible that it may not be quite a parabola, but an ellipse so elongated that it will not return till 2255. Pioneers of Science There is a certain beautiful curve known to geometricians by the name of the parabola. The Story of the Heavens It will always be erratic, peculiar, unsettled; and this conclusion substantiates our previous proposition with regard to the condition of a social system represented by a parabola. The Romance of Mathematics Being the Original Researches of a Lady Professor of Girtham College in Polemical Science, with some Account of the Social Properties of a Conic; Equations to Brain Waves; Social Forces; and the Laws of Political Motion. But he never mentions how very nearly Cluvier agrees with the Greek: they only differ by 1 divided by 3n2, where n is the infinite number of parts of which a parabola is composed. A Budget of Paradoxes, Volume II Then describing a beautiful parabola, he descended, and striking the water, sent the spray flying in every direction, while the body went to the bottom. Camp-fire and Wigwam A small, spent, but accurately directed obus, came in a parabola from over behind the roofs, and floated by the ambulance and thudded against the yellow brick of the stately hall. Young Hilda at the Wars It will here be only necessary to point to the connection which exists between the parabola and the ellipse. The Story of the Heavens If a parabola roll on another parabola, their vertices coinciding, the focus of the first traces out the directrix of the second. The Romance of Mathematics Being the Original Researches of a Lady Professor of Girtham College in Polemical Science, with some Account of the Social Properties of a Conic; Equations to Brain Waves; Social Forces; and the Laws of Political Motion. He looked at Stover in sleepy reproachfulness, and then slid around the counter in the shortest parabola possible. The Varmint The original parabola is converted into an ellipse, if the imprudent adventurer in returning to the Sun passes near some great planet, such as Jupiter, Saturn, Uranus, or Neptune, and suffers its attraction. Astronomy for Amateurs She places a finger upon her mouth, and, describing an immense parabola, topples over into the abyss. The Temptation of St. Antony or A Revelation of the Soul In 1681 Doerfel, a clergyman of Saxony, proved that the great comet then recently observed moved in a parabola, in the focus of which the sun was situated. The Story of the Heavens Or, on the other hand, in our chart of nations, must we describe that troublesome country as a rotating parabola, or complex figure, altogether outside our more favoured State? The Romance of Mathematics Being the Original Researches of a Lady Professor of Girtham College in Polemical Science, with some Account of the Social Properties of a Conic; Equations to Brain Waves; Social Forces; and the Laws of Political Motion. Some shooting stars slipped suddenly, describing on the sky, as it were, the parabola of an enormous rocket. Bouvard and Pécuchet A Tragi-comic Novel of Bourgeois Life He heard Captain Downs's astonished oath when he dove over that worthy mariner's head, a human comet in a twenty-foot parabola. Blow The Man Down A Romance Of The Coast - 1916 Is the orbit that of an ellipse, or a circle, or a parabola? Aether and Gravitation The fact that the comet moves in an ellipse or in a parabola proves that the two bodies act and react on each other in obedience to the law of universal gravitation. The Story of the Heavens You will remember that a Republican State is represented by a parabola. The Romance of Mathematics Being the Original Researches of a Lady Professor of Girtham College in Polemical Science, with some Account of the Social Properties of a Conic; Equations to Brain Waves; Social Forces; and the Laws of Political Motion. In the Middle Ages the word "Word" came to mean the Word of God with such distinctness that the romance languages adopted parabola, or derivatives from it, for "word." Folkways A Study of the Sociological Importance of Usages, Manners, Customs, Mores, and Morals The solar furnace was a rough parabola of mirrors used to focus the sun's heat on anything that it was desirable to heat. All Day September Two shadowy forms, that were groundlings at another time, took wings and flew in a neat parabola over the windscreen, striking the metal surface of the road with a single thud. Men of Affairs This comet followed a path which could not be certainly distinguished from a parabola, though there is no doubt that it might have been a very elongated ellipse. The Story of the Heavens I have already, in my previous lecture, touched upon the social properties of the parabola, and examined the constitution of erratic curves and eccentric nations. The Romance of Mathematics Being the Original Researches of a Lady Professor of Girtham College in Polemical Science, with some Account of the Social Properties of a Conic; Equations to Brain Waves; Social Forces; and the Laws of Political Motion. To draw a parabola mechanically: In Figure 84 C D is the width and H J the height of the curve. Mechanical Drawing Self-Taught Walky, as though shot from a catapult, described a parabola over his horse's head and landed with a crash on all fours directly under Josephus' nose. How Janice Day Won The distinctive feature of his Vera quadratura is his use of an infinite converging series, a plan that Archimedes used with the parabola. A Budget of Paradoxes, Volume I The characteristic feature of the movement in a parabola may be thus described. The Story of the Heavens For instance, in the case of the parabola, the distance of any particle from the directrix is equal to its distance from the focus. The Romance of Mathematics Being the Original Researches of a Lady Professor of Girtham College in Polemical Science, with some Account of the Social Properties of a Conic; Equations to Brain Waves; Social Forces; and the Laws of Political Motion. At any convenient distance above J fasten a straight-edge A B, setting it parallel to the base C D of the parabola. Mechanical Drawing Self-Taught He reached the height of the 'parabola,' and is now about to descend. Debts of Honor As she spoke, a shot rose high in air and ended its parabola in the heart of the doomed city. The New England Magazine, Volume 1, No. 1, January 1886 Bay State Monthly, Volume 4, No. 1, January, 1886 Menaechmus, a pupil of Eudoxus, was the discoverer of the conic sections, two of which, the parabola and the hyperbola, he used for solving the problem of the two mean proportionals. The Legacy of Greece Essays By: Gilbert Murray, W. R. Inge, J. Burnet, Sir T. L. Heath, D'arcy W. Thompson, Charles Singer, R. W. Livingston, A. Toynbee, A. E. Zimmern, Percy Gardner, Sir Reginald Blomfield In most instances, comets move in space, about the sun, in ellipses so very lengthened, that their paths seem to be parabolas as long as the cloudy bodies are visible in the sky. Chambers's Edinburgh Journal, No. 450 Volume 18, New Series, August 14, 1852 It swung into the air in a slow, lazy parabola, came down and dropped into the lake. Tarrano the Conqueror “Are you aware that a ship sailing describes a parabola round the globe?” Mr. Midshipman Easy Speaking in parabolas like, what I say is, that the t’other gun’s worth twopence up there, but down here it ’ll be worth a hundred pound or more. Syd Belton The Boy who would not go to Sea A parabola of light had suddenly shot out athwart the soft black night. The Madigans In a beautiful parabola, Garth's sword sailed out into the water, and he dropped to the sand to nurse his right wrist. Out Around Rigel This parabola is the curve of maximum moments for a travelling load uniform per ft. run. Encyclopaedia Britannica, 11th Edition, Volume 4, Part 3 "Brescia" to "Bulgaria" The focus of the parabola is here for the first time indicated, a circumstance which has escaped the notice of scientific historians. The Private Diary of Dr. John Dee And the Catalog of His Library of Manuscripts It enters at the narrowest part of the ground, farthest from the house, makes a long parabola, and turns again into the street close beside the dwelling. The Amateur Garden The word transcendental is like a parabola, in that there is no knowing where its meaning ends. What is Darwinism? Nicholas Tartaglia first showed that the course of a projectile was a parabola, and that the maximum range of a gun would be at an angle of 45 degrees. The Age of the Reformation The curve of the main arch is a parabola. Encyclopaedia Britannica, 11th Edition, Volume 4, Part 3 "Brescia" to "Bulgaria" The segments being put in horizontally instead of square with the lagging, gave circles instead of parabolas, making them much easier to lay out, and giving a form which was amply stiff. Transactions of the American Society of Civil Engineers, Vol. LXX, Dec. 1910 A Concrete Water Tower, Paper No. 1173 Traced on paper, the course of the tug would be a tight parabola. Space Tug As she advanced, deeply bowing to right and left, parabolas of light exhaled from her coronet like falling stars. King John of Jingalo The Story of a Monarch in Difficulties The dark mass which an aviator sees approaching when he is over the battlefield proves to be a fifteen-inch shell at the top of its parabola which passes ten feet over his head. My Second Year of the War The three lightly dotted parabolas are the curves of maximum moment for each of the loads taken separately. Encyclopaedia Britannica, 11th Edition, Volume 4, Part 3 "Brescia" to "Bulgaria" A point moves uniformly in describing a parabola, for it constantly fulfils the formula of the curve. Theodicy Essays on the Goodness of God, the Freedom of Man and the Origin of Evil What little I do see of its trajectory is disheartening, though: the wind whips it away on an almost horizontal parabola, off towards Boston. Eastern Standard Tribe Consider now a central conic, that is, one which is not a parabola and the center of which is therefore at a finite distance. An Elementary Course in Synthetic Projective Geometry On the shelf was a slate scrabbled all over with geometrical figures, and one of these figures was a parabola with two tangents drawn touching. The Romance of the Coast Now, except for very short bridges and very unequal loads, a parabola can be found which includes the curve of maximum moments. Encyclopaedia Britannica, 11th Edition, Volume 4, Part 3 "Brescia" to "Bulgaria" Language studies have their unique terms: nominative, comma, plot; mathematics has its: tangent, sum, parabola, etc. Sequential Problem Solving A Student Handbook with Checklists for Successful Critical Thinking So we watch anxiously while the shell—a long time in flight—follows its allotted parabola. Four Months Besieged The Story of Ladysmith Given the tangent at the vertex of a parabola, and two other tangents, to find the focus. An Elementary Course in Synthetic Projective Geometry "Well," said the Captain, a little bumptiously, "a parabola is a curve of the second order, formed by the intersection of a cone by a plane parallel to one of its sides." All Around the Moon Let we be the load per ft. run which would produce the maximum moments represented by this parabola. Encyclopaedia Britannica, 11th Edition, Volume 4, Part 3 "Brescia" to "Bulgaria" I heard the scream of the projectile, saw it describing its flaring parabola in my direction, and with my last energies dived to avoid it. Under the Dragon Flag My Experiences in the Chino-Japanese War A steel fragment came sailing over in a wide parabola and struck the foot of a man standing in the breakfast queue. Combed Out Thus the focus of the ellipse was discovered some five hundred years before the focus of the parabola! An Elementary Course in Synthetic Projective Geometry Then let the Eye of Science and her parabolas and hyperbolas, and conjugates, and asymptotes, and the rest of the confounded nonsensical farrago, all go to pot! All Around the Moon He squirted a brown parabola of tobacco juice, parenthetically, into the wood-box behind the stove, right on top of the cat that had some kittens in there. Tramping on Life An Autobiographical Narrative Again a tiny arrow traveled towards them in a graceful parabola. The Wings of the Morning Buck eyed them gravely, hat and arm describing parabolas with increasing frequency as they approached Fiftieth Street, slackening as the colourful pageant grew less brilliant, thinned, and faded into the park mists. Half Portions The center of the parabola is at infinity, and therefore all its diameters are parallel, for the pole of a tangent line is the point of contact. An Elementary Course in Synthetic Projective Geometry "Exactly so," chimed in M'Nicholl; "it must describe and keep on describing either a parabola or a hyperbola." All Around the Moon You describe the curve known as a parabola, and skin your own nose on the icy crust of the snow. Bog-Myrtle and Peat Tales Chiefly of Galloway Gathered from the Years 1889 to 1895 There was a dead silence of suspense among the crowd as the ball described a lofty parabola. The Firm of Girdlestone One was for the hyperbola, the other for the parabola. The Moon-Voyage There is one diameter, however, which is at right angles to its conjugate system of chords, and this one is called the axis of the parabola. An Elementary Course in Synthetic Projective Geometry "I want merely to convince him that it is a parabola!" All Around the Moon The back of the piebald changed from an ugly humped line to a decidedly sharp parabola and the horse left the ground with all four feet. The Night Horseman But a slight tremble of the hand he held acknowledged the intruding sharpness, and then the red parabola rose from the golden bowl. Paul Faber, Surgeon The projectile immediately rose with rapidity, described a majestic parabola, attained a height of about a thousand feet, and then with a graceful curve fell into the waves. The Moon-Voyage The parabola is thus identified with the curve of the same name studied in treatises on analytic geometry. An Elementary Course in Synthetic Projective Geometry Through the dark curtain of the sky in a parabola rising from the German trenches swept the brilliant sputter of red light of a German flare. My Year of the War Including an Account of Experiences with the Troops in France and the Record of a Visit to the Grand Fleet Which is Here Given for the First Time in its Complete Form There was a whang, a whistle—and the ink bottle hurtled in a beautiful parabola over Greenwich Street. By Advice of Counsel He who has undertaken to describe the parabola of a projectile, cannot be satisfied with tracing its gradual rise and determining its culmination. Renaissance in Italy Volume 3 The Fine Arts "Yes," answered Barbicane, "with some speed it will describe a parabola, and with greater speed an hyperbola." The Moon-Voyage |
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