Three-Dimensional Geometry and Topology
This book develops some of the extraordinary richness, beauty, and power of geometry in two and three dimensions, and the strong connection of geometry with topology. A strong effort has been made to convey not just denatured formal reasoning (definitions, theorems, and proofs),… Celý popis ↓
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Popis Three-Dimensional Geometry and Topology
Three-Dimensional Geometry and Topology
This book develops some of the extraordinary richness, beauty, and power of geometry in two and three dimensions, and the strong connection of geometry with topology. A strong effort has been made to convey not just denatured formal reasoning (definitions, theorems, and proofs), but a living feeling for the subject. Hyperbolic geometry is the star.
In the 1920s and 1930s the mathematics of two-dimensional spaces was formalized. There are many figures, examples, and exercises of varying difficulty.This book was the origin of a grand scheme developed by Thurston that is now coming to fruition. It was Thurston's goal to do the same for three-dimensional spaces.
To do this, he had to establish the strong connection of geometry to topology--the study of qualitative questions about geometrical structures. The author created a new set of concepts, and the expression
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