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Geometry: Plane and Fancy

BuchKartoniert, Paperback
162 Seiten
Englisch
Springererschienen am28.09.2012Softcover reprint of the original 1st ed. 1998
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.mehr
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EUR53,49
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Produkt

KlappentextGEOMETRY: 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.
Zusammenfassung
This book offers students a fascinating tour through parts of geometry they are unlikely to see in the rest of their studies.

Lively exposition and off-beat approach.

Covers many topics in geometry not found in other introductions to the subject.

No calculus is assumed; book written at an elementary level.

Interesting problems are nicely scattered throughout.
Details
ISBN/GTIN978-1-4612-6837-6
ProduktartBuch
EinbandartKartoniert, Paperback
Verlag
Erscheinungsjahr2012
Erscheinungsdatum28.09.2012
AuflageSoftcover reprint of the original 1st ed. 1998
ReiheUndergraduate Texts in Mathematics
Seiten162 Seiten
SpracheEnglisch
Gewicht278 g
IllustrationenX, 162 p.
Artikel-Nr.19020756

Inhalt/Kritik

Inhaltsverzeichnis
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 Poincaré disc and Isometries of the Hyperbolic Plane.- 3.2 Tessellations of the Hyperbolic Plane.- 3.3 Complex numbers, Möbius 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.mehr

Autor

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.
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