Geometry: Plane and Fancy - Undergraduate Texts in Mathematics - David A. Singer - Knjige - Springer-Verlag New York Inc. - 9781461268376 - 28. septembra 2012
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David A. Singer
Geometry: Plane and Fancy - Undergraduate Texts in Mathematics Softcover Reprint of the Original 1st Ed. 1998 edition

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Description for Sales People: GEOMETRY: Plane and Fancy offers students a fascinating tour through parts of geometry they are unlikely to see in the rest of their studies while, at the same time, anchoring their excursions to the well known parallel postulate of Euclid. The author shows how alternatives to Euclid's fifth postulate leads to interesting and different patterns and symmetries. Table of Contents: 1 Euclid and Non-Euclid.- 1.1 The Postulates: What They Are and Why.- 1.2 The Parallel Postulate and Its Descendants.- 1.3 Proving the Parallel Postulate.- 2 Tiling the Plane with Regular Polygons.- 2.1 Isometries and Transformation Groups.- 2.2 Regular and Semiregular Tessellations.- 2.3 Tessellations That Aren t, and Some Fractals.- 2.4 Complex Numbers and the Euclidean Plane.- 3 Geometry of the Hyperbolic Plane.- 3.1 The Poincare disc and Isometries of the Hyperbolic Plane.- 3.2 Tessellations of the Hyperbolic Plane.- 3.3 Complex numbers, Mobius Transformations, and Geometry.- 4 Geometry of the Sphere.- 4.1 Spherical Geometry as Non-Euclidean Geometry.- 4.2 Graphs and Euler s Theorem.- 4.3 Tiling the Sphere: Regular and Semiregular Polyhedra.- 4.4 Lines and Points: The Projective Plane and Its Cousin.- 5 More Geometry of the Sphere.- 5.1 Convex Polyhedra are Rigid: Cauchy s Theorem.- 5.2 Hamilton, Quaternions, and Rotating the Sphere.- 5.3 Curvature of Polyhedra and the Gauss-Bonnet Theorem.- 6 Geometry of Space.- 6.1 A Hint of Riemannian Geometry.- 6.2 What Is Curvature?.- 6.3 From Euclid to Einstein.- References."

Contributor Bio:  Singer, David A Singer-Case Western Reserve University, Cleveland, OH

162 pages, biography

Medij Knjige     Paperback Book   (Knjiga z mehkimi platnicami in lepljenim hrbtom)
Izdano 28. septembra 2012
ISBN13 9781461268376
Založniki Springer-Verlag New York Inc.
Strani 162
Dimenzije 156 × 234 × 9 mm   ·   254 g
Jezik Angleščina  

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Ogled vseh David A. Singer