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Eighteen Essays in Non-Euclidean Geometry
, 2019This book consists of a series of self-contained essays on non-Euclidean geometry in a broad sense, including the classical geometries of constant curvature (spherical and hyperbolic), de Sitter, anti-de Sitter, co-Euclidean, co-Minkowski geometries ...
Vincent Alberge, A. Papadopoulos
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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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A Euclidean Model for Euclidean Geometry
The American Mathematical Monthly, 1989(1989). A Euclidean Model for Euclidean Geometry. The American Mathematical Monthly: Vol. 96, No. 1, pp. 43-49.
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Is the Geometry of Space Euclidean or Non-Euclidean? [PDF]
, 2011 Is space Euclidean or non-Euclidean? This question was much discussed around 1900, and we look at Poincare’s surprising answer that it will be impossible to tell. This is derived from his philosophy of conventionalism, which is conveyed through extensive extracts from his popular essays.
Jeremy Gray, Jeremy Gray
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, 2015
tributed to the Alexandrian Greek mathematician Euclid, which he described in his textbook on geometry: the Elements. Euclid’s method consists in assuming a small set of intuitively appealing axioms, and deducing many other propositions (theorems) from ...
Richard J. Cochrane, A. Mcgettigan
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tributed to the Alexandrian Greek mathematician Euclid, which he described in his textbook on geometry: the Elements. Euclid’s method consists in assuming a small set of intuitively appealing axioms, and deducing many other propositions (theorems) from ...
Richard J. Cochrane, A. Mcgettigan
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Euclidean and Non-Euclidean Geometries
2014Ancient mathematics was motivated by very practical reasoning. What we now call land management and commerce were the overriding considerations, and calculational questions grew out of those transactions. As a result, many of the ideas considered involved meshing rectangles and triangles, their areas, and their relative proportions.
Steven G. Krantz, Harold R. Parks
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1966
Publisher Summary This chapter focuses on Euclidean geometry. Two triangles are congruent if there is a rigid motion of the plane which carries one triangle exactly onto the other. Corresponding angles of congruent triangles are equal, corresponding sides have the same length, the areas enclosed are equal, and so on.
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Publisher Summary This chapter focuses on Euclidean geometry. Two triangles are congruent if there is a rigid motion of the plane which carries one triangle exactly onto the other. Corresponding angles of congruent triangles are equal, corresponding sides have the same length, the areas enclosed are equal, and so on.
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Exploring Advanced Euclidean Geometry with GeoGebra
, 2013A quick review of elementary Euclidean geometry 1. The elements of GeoGebra 2. The classical triangle centers 3. Advanced techniques in GeoGebra 4. Circumscribed, inscribed, and escribed circles 5. The medial and orthic triangles 6. Quadrilaterals 7. The
G. Venema
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2001
In affine geometry it is possible to deal with ratios of vectors and barycenters of points, but there is no way to express the notion of length of a line segment or to talk about orthogonality of vectors. A Euclidean structure allows us to deal with metric notions such as orthogonality and length (or distance).
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In affine geometry it is possible to deal with ratios of vectors and barycenters of points, but there is no way to express the notion of length of a line segment or to talk about orthogonality of vectors. A Euclidean structure allows us to deal with metric notions such as orthogonality and length (or distance).
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