Geometry -- intuition and concepts : imagining, understanding, thinking beyond. an introduction for students / Jost-Hinrich Eschenburg.
This book deals with the geometry of the visual space in all its aspects. As in any branch of mathematics, the aim is to trace the hidden to the obvious; the peculiarity of geometry is that the obvious is sometimes literally before one's eyes. Starting from intuition, spatial concepts are embed...
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Full Text (via Springer) |
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| Format: | eBook |
| Language: | English German |
| Published: |
Wiesbaden, Germany :
Springer,
2022.
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Table of Contents:
- What is geometry
- Parallelism: affine geometry
- From affine geometry to linear algebra
- Definition of affine space
- Parallelism and semiaffine mappings
- Parallel projections
- Affine coordinates and center of gravity
- Incidence: projective geometry
- Central perspective
- Far points and straight lines of projection
- Projective and affine space.-Semi-projective mappings and collineations
- Conic sections and quadrics; homogenization
- The theorems of Desargues and Brianchon
- Duality and polarity; Pascal's theorem
- The double ratio
- Distance: Euclidean geometry
- The Pythagorean theorem
- Isometries of Euclidean space
- Classification of isometries
- Platonic solids
- Symmetry groups of Platonic solids
- Finite rotation groups and crystal groups
- Metric properties of conic sections
- Curvature: differential geometry
- Smoothness
- Fundamental forms and curvatures
- Characterization of spheres and hyperplanes
- Orthogonal hyperface systems
- Angles: conformal geometry
- Conformal mappings
- Inversions
- Conformal and spherical mappings
- The stereographic projection
- The space of spheres
- Angular distance: spherical and hyperbolic geometry. The hyperbolic space. Distance on the sphere and in hyperbolic space. Models of hyperbolic geometry
- Exercises
- Solutions.