How To Use Euclidean geometry In A Sentence
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Other topics to interest Carslaw throughout his career, which we have not touched on above, included an interest in non-euclidean geometry, Green's functions and the history of Napier's logarithms.
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In Euclidean geometry, light travels on straight lines.
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It is also mathematics, of course, but Euclidean geometry is by no means the only conceivable mathematical geometry.
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It follows from Kant's view that we know a priori that non-Euclidean geometry cannot be applied in physics.
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This appendix proved to be one of the foundations of non-Euclidean geometry; it was a mathematical landmark worth far more than anything else in the book.
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Each innovation destined to dwarf the one extensive accomplishment of the Greeks - Euclidean geometry.
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Although spatial intuition or observation remains the source of the axioms of Euclidean geometry, in Hilbert's writing the role of intuition and observation is explicitly limited to motivation and is heuristic.
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One minute you're learning that Sir Issac Newton chuckled only once in his life (scoffing at Euclidean geometry) and that the term for such people who don't laugh is 'agelast'; the next that the apparently nonsensical elephant jokes that were popular in the Sixties are believed to be racist in origin; the next how Bertrand Russell put down a heckler during one of his lectures on logic.
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Why do I refer to Euclidean geometry as a physical theory rather than a branch of mathematics?
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She believed that in order to get students excited about mathematics, it was essential to teach the revolutionary aspects of such fields as Galois theory of groups, non-Euclidean geometry, and modern logic.
Lillian R. Lieber.
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However, this revelation did not bring about the destruction of Euclidean geometry, it simply added to it.
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Some of his work on physical topics relates to his non-euclidean geometry for he examined how the gravitational potential as given by Newton would have to be modified in a space of negative curvature.
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This had the remarkable corollary that non-euclidean geometry was consistent if and only if euclidean geometry was consistent.
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Something that exists nowhere and exists along the lines of Euclidean geometry, judging by what I understand of it, cannot exist.
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Saccheri then studied the hypothesis of the acute angle and derived many theorems of non-Euclidean geometry without realising what he was doing.
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At this time thinking was dominated by Kant who had stated that Euclidean geometry is the inevitable necessity of thought.
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The work of Bolyai and Lobachevsky are comparable in that sense, that they both challenge axiomatic assumptions, but their postulates are of Euclidean geometry.
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For example, recall that in Euclidean geometry the sum of the angles of any triangle is always 1800.
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However, this revelation did not bring about the destruction of Euclidean geometry, it simply added to it.
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Thus, for example, the notions of Euclidean geometry are invariant under similarity transformations, those of affine geometry under affine transformations, and those of topology under bicontinuous transformations.
Logical Constants
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For example, in Euclidean geometry, the relevant invariants are embodied in quantities that are not altered by geometric transformations such as rotations, dilations, and reflections.
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Euclidean geometry studies Euclidean-space-structure, topology studies topological structures, and so on.
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Much of his career is spent working on physics and non-euclidean geometry.
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In particular he made contributions of major importance in the theory of polytopes, non-euclidean geometry, group theory and combinatorics.
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Why do I refer to Euclidean geometry as a physical theory rather than a branch of mathematics?
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The second chapter presents a development of absolute and Euclidean geometry based on Hilbert's axioms.
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Euclidean geometry, Fibonacci numbers, the digits of pi, the notion of algorithms, concepts of infinity, fractals, and other ideas furnished the mathematical underpinnings.
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His interest in mathematics was stimulated during his school years in Izmir by a teacher who encouraged him to solve problems in euclidean geometry.
