Results 281 to 290 of about 211,344 (325)
Three-dimensional motion-capture of the heart uncovers signatures of human health and disease
Schiratti P +8 more
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, 1989 Surprisingly, the geometry of curved surfaces throws light on the geometry of the plane. More than 2000 years after Euclid formulated axioms for plane geometry, differential geometry showed that the parallel axiom does not follow from the other axioms of Euclid.
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Some of the next articles are maybe not open access.
2021
Four-dimensional theories match Virtual Reality because here time and space are configured through mutable lines. Since the discovery of non-Euclidean geometry, linearity has been submitted to a profound crisis. Mathematicians showed that there are not one but several geometries.
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Four-dimensional theories match Virtual Reality because here time and space are configured through mutable lines. Since the discovery of non-Euclidean geometry, linearity has been submitted to a profound crisis. Mathematicians showed that there are not one but several geometries.
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1999
This book includes: Introduction; The parallel postulate: A blot on Euclid?; The parallel postulate: 1663-1826; Lobachevskii and Bolyai; Criticisms; Reconsidering non-Euclidean geometry; and, Further reading.
Jeremy Gray +2 more
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This book includes: Introduction; The parallel postulate: A blot on Euclid?; The parallel postulate: 1663-1826; Lobachevskii and Bolyai; Criticisms; Reconsidering non-Euclidean geometry; and, Further reading.
Jeremy Gray +2 more
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1997
Euclid’s Elements is dull, long-winded, and does not make explicit the fact that two circles can intersect, that a circle has an outside and an inside, that triangles can be turned over, and other assumptions essential to his system. By modern standards Bertrand Russell could call Euclid’s fourth proposition a ”tissue of nonsense” and declare it a ...
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Euclid’s Elements is dull, long-winded, and does not make explicit the fact that two circles can intersect, that a circle has an outside and an inside, that triangles can be turned over, and other assumptions essential to his system. By modern standards Bertrand Russell could call Euclid’s fourth proposition a ”tissue of nonsense” and declare it a ...
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2020
One of the new frontiers in geometry opened up by calculus was the study of curvature. The concept of curvature is particularly interesting for surfaces, because it can be defined intrinsically. The intrinsic curvature, or Gaussian curvature as it is known, is unaltered by bending the surface, so it can be defined without reference to the surrounding ...
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One of the new frontiers in geometry opened up by calculus was the study of curvature. The concept of curvature is particularly interesting for surfaces, because it can be defined intrinsically. The intrinsic curvature, or Gaussian curvature as it is known, is unaltered by bending the surface, so it can be defined without reference to the surrounding ...
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, 2011 In this chapter we discuss the non-Euclidean geometry of curved surfaces, using the sphere as our primary example. We find that all the information about the geometry of the surface is contained in the expression for the distance between two nearby points in some coordinate system, called the metric. For example, the distance between two distant points
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1984
It is unlikely that Euclid ever held his five postulates to be self-evident. Mathematicians sharing the Aristotelian conviction that only manifest truths may be admitted without proof in geometry usually did not find the fifth postulate quite so obvious as the other four.
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It is unlikely that Euclid ever held his five postulates to be self-evident. Mathematicians sharing the Aristotelian conviction that only manifest truths may be admitted without proof in geometry usually did not find the fifth postulate quite so obvious as the other four.
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The Mathematics Teacher, 1922
About 2200 years ago there was published in Greek one of the most remarkable books of all times, Euclid's “Elements of Geometry”. It contains a systematic exposition of the leading propositions of elementary geometry and the elementary theory of numbers. It was at once adopted by the Greeks as the standard text book on pure mathematics.
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About 2200 years ago there was published in Greek one of the most remarkable books of all times, Euclid's “Elements of Geometry”. It contains a systematic exposition of the leading propositions of elementary geometry and the elementary theory of numbers. It was at once adopted by the Greeks as the standard text book on pure mathematics.
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Investigating A Non-Euclidean Geometry
The Mathematical Gazette, 1982In this article we describe how a group of third year mathematics students of the University of Rome who were following a mathematics education option explored some of the properties of hyperbolic plane geometry before preparing a unit on non-Euclidean geometry to be used with sixth-formers at the Liceo Virgilio, Rome.
Lucilla Cannizzaro, Mauro Carosi
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