英语词汇“Euclidean geometry”造句的方法、技巧、例句及翻译-英语例句辞典

From them, it should be possible to derive a complete system of knowledge embracing every aspect of the natural world, just as one can deduce the whole of Euclidean geometry from five axioms. The Invention of Science 2015-09-17T00:00:00Z

After puzzling over this for some time, Kepler hit on the idea that the number of planets might be related to the number of regular solid figures that can be constructed using Euclidean geometry. The Scientists 2003-10-21T00:00:00Z

These are, in fact, the engineering artifacts of intelligent beings: roads, highways, canals, farmland, city streets—a pattern disclosing the twin human passions for Euclidean geometry and territoriality. Cosmos 1980-01-01T00:00:00Z

Every theorem in Euclidean geometry can be dualized in projective geometry, setting up a whole set of new theorems in the parallel universe of projective geometry. Zero: The Biography of a Dangerous Idea 2000-02-07T00:00:00Z

Wordsworth imagined that Euclidean geometry “wedded soul to soul in purest bond / Of reason, undisturbed by space or time.” ‘Shape’ Makes Geometry Entertaining. Really, It Does. 2021-05-18T04:00:00Z

In this year’s Salon, instead of Bauhaus ideology delivered with strict Euclidean geometry, there’s a high delight quotient. Salon Art + Design, a Fair With Wit, Cheek, History 2018-11-09T05:00:00Z

We refer to this as a flat universe, and the kind of Euclidean geometry you learned in high school applies in this type of universe. Astronomy 2016-10-13T00:00:00Z

Manifolds are objects that on a zoomed-in, ‘local’ scale appear indistinguishable from the plane or higher-dimensional space described by Euclidean geometry. Virtuoso Mathematician Who Reshaped Topology Wins Abel Prize 2022-03-28T04:00:00Z

If we’re supposed to be six feet away from one another, how does a trio of brainy high-schoolers confer on the finer points of Euclidean geometry, DNA chemistry or Medieval history? Perspective | Here’s a tough question: How do you keep ‘It’s Academic’ on the air in a pandemic? 2020-04-28T04:00:00Z

Most of us learn some amount of Euclidean geometry in school. Forget Meters and Feet 2020-02-01T05:00:00Z

Traditional, Euclidean geometry rests on the assumption that parallel lines stay at the same distance from each other forever, neither touching nor drifting apart. Mathematicians create warped worlds in virtual reality 2017-03-20T04:00:00Z

The Euclidean geometry used by Newton and everyone else was not up to this job; fundamentally different and much more challenging mathematics were required. The most beautiful theory 2015-11-25T05:00:00Z

She took science with the physicist Goldowski, but her most profound connection was with the German mathematician Max Dehn, with whom she studied topology, linear algebra and Euclidean geometry. Return to Black Mountain College 2015-10-06T04:00:00Z

As a triangle on the sphere shrinks, its angles get smaller, and its angle sum gets closer and closer to π radians or 180 degrees, the angle sum of a triangle in Euclidean geometry. Grapefruit Math 2015-05-19T04:00:00Z

The intuition we develop in Euclidean geometry does not prepare us well for non-Euclidean geometry. Forget Meters and Feet 2020-02-01T05:00:00Z

Given how little algebra, arithmetic and Euclidean geometry have changed in the past century, the perpetual debates about how we should teach math are more than a bit puzzling. The New Math Strikes Back 2015-02-11T05:00:00Z

But new developments were demonstrating that thinking of them this way yielded insights not easily obtained from traditional Euclidean geometry. Books: ‘Infinitesimal,’ Looks at an Historic Math Battle 2014-04-07T20:44:24Z

Euclidean geometry, codified around 300 BCE by Euclid of Alexandria in one of the most influential textbooks in history, is based on 23 definitions, 5 postulates, and 5 axioms, or “common notions.” Chasing the Parallel Postulate 2014-02-28T13:30:16Z

The second stream of thought confined itself within the circle of ideas of Euclidean geometry. Encyclopaedia Britannica, 11th Edition, Volume 11, Slice 6 "Geodesy" to "Geometry" 2011-09-19T02:00:10.473Z

“I would say that this means Euclidean geometry is probably universal to all human beings,” she said. Observatory: Learning Geometry Without a Protractor 2011-05-23T22:09:10Z

The Euclidean geometry we all learned at school pertains to figures that can be drawn on a plane. Gravity, by George Gamow [Special Archive Article] 2011-03-04T13:45:00.433Z

If classical Euclidean geometry is conceived as a top-down approach with all theorems following by pure logic from a few self-evident axioms, the new approaches can be thought of as bottom-up, inspired by experience. Books: ‘Infinitesimal,’ Looks at an Historic Math Battle 2014-04-07T20:44:24Z

In Euclidean geometry, there are similar triangles that are not congruent. Chasing the Parallel Postulate 2014-02-28T13:30:16Z

Though he still believed in the necessary truth of Euclidean geometry, he confessed that, in Lambert. all his attempted proofs, something remained undemonstrated. Encyclopaedia Britannica, 11th Edition, Volume 11, Slice 6 "Geodesy" to "Geometry" 2011-09-19T02:00:10.473Z

It has to be noted, however, that, when the “squaring” of the circle is especially spoken of, it is almost always tacitly assumed that the restrictions are those of the Euclidean geometry. Encyclopaedia Britannica, 11th Edition, Volume 6, Slice 4 "Cincinnatus" to "Cleruchy"

If these beings say their universe is "plane," there is sense in the statement, because they mean that they can perform the constructions of plane Euclidean geometry with their rods. Relativity: The Special and General Theory

There one of the key figures is Thomas Hobbes, the 17th-century philosopher of authoritarianism, a strong advocate of law, order — and, like the Jesuits, of the top-down hierarchical nature of Euclidean geometry. Books: ‘Infinitesimal,’ Looks at an Historic Math Battle 2014-04-07T20:44:24Z

For example, Euclidean geometry is the only geometry with rectangles. Chasing the Parallel Postulate 2014-02-28T13:30:16Z

Ordinary Euclidean geometry is a descriptive geometry; it becomes a projective geometry when the so-called “points at infinity” are added. Encyclopaedia Britannica, 11th Edition, Volume 11, Slice 6 "Geodesy" to "Geometry" 2011-09-19T02:00:10.473Z

With this, the philosophical status of Euclidean geometry was undermined. Definition & Reality in the General Theory of Political Economy

Under these conditions, the u-curves and v-curves are straight lines in the sense of Euclidean geometry, and they are perpendicular to each other. Relativity: The Special and General Theory

For if contradictions between theory and experience manifest themselves, we should rather decide to change physical laws than to change axiomatic Euclidean geometry. Sidelights on Relativity

In Euclidean geometry we assume definitions of 'points,' 'lines,' 'surfaces,' etc., which are never found in nature, but form the most convenient abstractions for measuring things. Pragmatism

The existence of a natural unit of length is a peculiarity common both to hyperbolic and elliptic geometries, and differentiates them from Euclidean geometry. Encyclopaedia Britannica, 11th Edition, Volume 11, Slice 6 "Geodesy" to "Geometry" 2011-09-19T02:00:10.473Z

Namely, Euclidean geometry already provides us with our system of measurement. Definition & Reality in the General Theory of Political Economy

In Euclidean geometry the sphere is defined as 'the locus of all points which are equidistant from a given point'. Man or Matter

The method of Cartesian coordinates must then be discarded, and replaced by another which does not assume the validity of Euclidean geometry for rigid bodies.* Relativity : the Special and General Theory

Euclidean geometry is reduced to a useful interpretation of the data of experience; it is not theoretically the only one. Pragmatism

In 1799 he announces that Euclidean geometry Gauss. would follow from the assumption that a triangle can be drawn greater than any given triangle. Encyclopaedia Britannica, 11th Edition, Volume 11, Slice 6 "Geodesy" to "Geometry" 2011-09-19T02:00:10.473Z

The Saggio shows that Lobatchewsky’s plane geometry holds in Euclidean geometry on surfaces of constant negative curvature, straight lines being replaced by geodesics. Encyclopaedia Britannica, 11th Edition, Volume 11, Slice 6 "Geodesy" to "Geometry" 2011-09-19T02:00:10.473Z

It is evident that geometrical concepts arising in man's mind in this way must be those of Euclidean geometry. Man or Matter

If these beings say their universe is " plane," there is sense in the statement, because they mean that they can perform the constructions of plane Euclidean geometry with their rods. Relativity : the Special and General Theory

In the sense of Euclidean geometry, a plane is the sum-total of innumerable single points. Man or Matter

单词	Euclidean geometry
例句	Euclidean geometry From them, it should be possible to derive a complete system of knowledge embracing every aspect of the natural world, just as one can deduce the whole of Euclidean geometry from five axioms. The Invention of Science 2015-09-17T00:00:00Z After puzzling over this for some time, Kepler hit on the idea that the number of planets might be related to the number of regular solid figures that can be constructed using Euclidean geometry. The Scientists 2003-10-21T00:00:00Z These are, in fact, the engineering artifacts of intelligent beings: roads, highways, canals, farmland, city streets—a pattern disclosing the twin human passions for Euclidean geometry and territoriality. Cosmos 1980-01-01T00:00:00Z Every theorem in Euclidean geometry can be dualized in projective geometry, setting up a whole set of new theorems in the parallel universe of projective geometry. Zero: The Biography of a Dangerous Idea 2000-02-07T00:00:00Z Wordsworth imagined that Euclidean geometry “wedded soul to soul in purest bond / Of reason, undisturbed by space or time.” ‘Shape’ Makes Geometry Entertaining. Really, It Does. 2021-05-18T04:00:00Z In this year’s Salon, instead of Bauhaus ideology delivered with strict Euclidean geometry, there’s a high delight quotient. Salon Art + Design, a Fair With Wit, Cheek, History 2018-11-09T05:00:00Z We refer to this as a flat universe, and the kind of Euclidean geometry you learned in high school applies in this type of universe. Astronomy 2016-10-13T00:00:00Z Manifolds are objects that on a zoomed-in, ‘local’ scale appear indistinguishable from the plane or higher-dimensional space described by Euclidean geometry. Virtuoso Mathematician Who Reshaped Topology Wins Abel Prize 2022-03-28T04:00:00Z If we’re supposed to be six feet away from one another, how does a trio of brainy high-schoolers confer on the finer points of Euclidean geometry, DNA chemistry or Medieval history? Perspective \| Here’s a tough question: How do you keep ‘It’s Academic’ on the air in a pandemic? 2020-04-28T04:00:00Z Most of us learn some amount of Euclidean geometry in school. Forget Meters and Feet 2020-02-01T05:00:00Z Traditional, Euclidean geometry rests on the assumption that parallel lines stay at the same distance from each other forever, neither touching nor drifting apart. Mathematicians create warped worlds in virtual reality 2017-03-20T04:00:00Z The Euclidean geometry used by Newton and everyone else was not up to this job; fundamentally different and much more challenging mathematics were required. The most beautiful theory 2015-11-25T05:00:00Z She took science with the physicist Goldowski, but her most profound connection was with the German mathematician Max Dehn, with whom she studied topology, linear algebra and Euclidean geometry. Return to Black Mountain College 2015-10-06T04:00:00Z As a triangle on the sphere shrinks, its angles get smaller, and its angle sum gets closer and closer to π radians or 180 degrees, the angle sum of a triangle in Euclidean geometry. Grapefruit Math 2015-05-19T04:00:00Z The intuition we develop in Euclidean geometry does not prepare us well for non-Euclidean geometry. Forget Meters and Feet 2020-02-01T05:00:00Z Given how little algebra, arithmetic and Euclidean geometry have changed in the past century, the perpetual debates about how we should teach math are more than a bit puzzling. The New Math Strikes Back 2015-02-11T05:00:00Z But new developments were demonstrating that thinking of them this way yielded insights not easily obtained from traditional Euclidean geometry. Books: ‘Infinitesimal,’ Looks at an Historic Math Battle 2014-04-07T20:44:24Z Euclidean geometry, codified around 300 BCE by Euclid of Alexandria in one of the most influential textbooks in history, is based on 23 definitions, 5 postulates, and 5 axioms, or “common notions.” Chasing the Parallel Postulate 2014-02-28T13:30:16Z The second stream of thought confined itself within the circle of ideas of Euclidean geometry. Encyclopaedia Britannica, 11th Edition, Volume 11, Slice 6 "Geodesy" to "Geometry" 2011-09-19T02:00:10.473Z “I would say that this means Euclidean geometry is probably universal to all human beings,” she said. Observatory: Learning Geometry Without a Protractor 2011-05-23T22:09:10Z The Euclidean geometry we all learned at school pertains to figures that can be drawn on a plane. Gravity, by George Gamow [Special Archive Article] 2011-03-04T13:45:00.433Z If classical Euclidean geometry is conceived as a top-down approach with all theorems following by pure logic from a few self-evident axioms, the new approaches can be thought of as bottom-up, inspired by experience. Books: ‘Infinitesimal,’ Looks at an Historic Math Battle 2014-04-07T20:44:24Z In Euclidean geometry, there are similar triangles that are not congruent. Chasing the Parallel Postulate 2014-02-28T13:30:16Z Though he still believed in the necessary truth of Euclidean geometry, he confessed that, in Lambert. all his attempted proofs, something remained undemonstrated. Encyclopaedia Britannica, 11th Edition, Volume 11, Slice 6 "Geodesy" to "Geometry" 2011-09-19T02:00:10.473Z It has to be noted, however, that, when the “squaring” of the circle is especially spoken of, it is almost always tacitly assumed that the restrictions are those of the Euclidean geometry. Encyclopaedia Britannica, 11th Edition, Volume 6, Slice 4 "Cincinnatus" to "Cleruchy" If these beings say their universe is "plane," there is sense in the statement, because they mean that they can perform the constructions of plane Euclidean geometry with their rods. Relativity: The Special and General Theory There one of the key figures is Thomas Hobbes, the 17th-century philosopher of authoritarianism, a strong advocate of law, order — and, like the Jesuits, of the top-down hierarchical nature of Euclidean geometry. Books: ‘Infinitesimal,’ Looks at an Historic Math Battle 2014-04-07T20:44:24Z For example, Euclidean geometry is the only geometry with rectangles. Chasing the Parallel Postulate 2014-02-28T13:30:16Z Ordinary Euclidean geometry is a descriptive geometry; it becomes a projective geometry when the so-called “points at infinity” are added. Encyclopaedia Britannica, 11th Edition, Volume 11, Slice 6 "Geodesy" to "Geometry" 2011-09-19T02:00:10.473Z With this, the philosophical status of Euclidean geometry was undermined. Definition & Reality in the General Theory of Political Economy Under these conditions, the u-curves and v-curves are straight lines in the sense of Euclidean geometry, and they are perpendicular to each other. Relativity: The Special and General Theory For if contradictions between theory and experience manifest themselves, we should rather decide to change physical laws than to change axiomatic Euclidean geometry. Sidelights on Relativity In Euclidean geometry we assume definitions of 'points,' 'lines,' 'surfaces,' etc., which are never found in nature, but form the most convenient abstractions for measuring things. Pragmatism The existence of a natural unit of length is a peculiarity common both to hyperbolic and elliptic geometries, and differentiates them from Euclidean geometry. Encyclopaedia Britannica, 11th Edition, Volume 11, Slice 6 "Geodesy" to "Geometry" 2011-09-19T02:00:10.473Z Namely, Euclidean geometry already provides us with our system of measurement. Definition & Reality in the General Theory of Political Economy In Euclidean geometry the sphere is defined as 'the locus of all points which are equidistant from a given point'. Man or Matter The method of Cartesian coordinates must then be discarded, and replaced by another which does not assume the validity of Euclidean geometry for rigid bodies.* Relativity : the Special and General Theory Euclidean geometry is reduced to a useful interpretation of the data of experience; it is not theoretically the only one. Pragmatism In 1799 he announces that Euclidean geometry Gauss. would follow from the assumption that a triangle can be drawn greater than any given triangle. Encyclopaedia Britannica, 11th Edition, Volume 11, Slice 6 "Geodesy" to "Geometry" 2011-09-19T02:00:10.473Z The Saggio shows that Lobatchewsky’s plane geometry holds in Euclidean geometry on surfaces of constant negative curvature, straight lines being replaced by geodesics. Encyclopaedia Britannica, 11th Edition, Volume 11, Slice 6 "Geodesy" to "Geometry" 2011-09-19T02:00:10.473Z It is evident that geometrical concepts arising in man's mind in this way must be those of Euclidean geometry. Man or Matter If these beings say their universe is " plane," there is sense in the statement, because they mean that they can perform the constructions of plane Euclidean geometry with their rods. Relativity : the Special and General Theory In the sense of Euclidean geometry, a plane is the sum-total of innumerable single points. Man or Matter
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