Hyperbolic Functions

Name: Hyperbolic Functions | With Configuration Theorems and Equivalent and Equidecomposable Figures
Brand: Dover Publications
Price: 12.99 EUR
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With Configuration Theorems and Equivalent and Equidecomposable Figures

V. G. Shervatov(Autor*in)

Dover Publications (Verlag)

Erschienen am 7. November 2013

327 Seiten

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Cover
Title Page
Copyright Page
Hyperbolic Functions
Contents
Chapter 1. The Hyperbolic Rotation
1. Homothetic transformations
2. Strains
3. The hyperbola
4. The hyperbolic rotation
5. Properties of the hyperbola
Chapter 2. Hyperbolic Functions
6. The unit hyperbola and its equation
7. The hyperbolic functions
8. Identities between hyperbolic functions
Chapter 3. Natural Logarithms
9. Logarithms and the hyperbola
10. The base e of natural logarithms
11. Analytic expressions for the hyperbolic functions
12. Infinite series expansions for ea, sinh t, cosh t
13. Euler's formulas
Configuration Theorems
Contents
Introduction
1. What is a configuration theorem?
2. Example of a configuration theorem
Chapter 1. Central Projection and Ideal Elements
3. Central projection in the plane
ideal elements
4. Elimination of exceptional cases
5. Basic theorems about projective lines
6. Central projection in space
Chapter 2. The Theorem of Pappus and Pascal
7. The Pappus-Pascal theorem
8. Introduction to the proof of the Pappus-Pascal theorem
9. Completion of the proof of the Pappus-Pascal theorem
10. Brianchon's theorem
Chapter 3. Desargues's Theorem
11. Desargues's theorem
12. Alternative proofs of Desargues's theorem
13. The converse of Desargues's theorem
Chapter 4. Some Properties of Polygons
14. Some properties of quadrilaterals
15. Some properties of pentagons
16. More properties of quadrilaterals
Chapter 5. Problems
17. Inaccessible points or lines
18. Constructions involving inaccessible points or lines
19. Problems for solution by the reader
Chapter 6. The Algebraic Meaning of Configuration Theorems
20. Algebraic identities as configuration theorems
21. Schematic notation for configuratiod theorems
Bibliography
Equivalent and Equidecomposable Figures
Contents
Chapter 1. The Bolyai-Gerwin Theorem
Equidecomposability of Polygons
1. Decomposition method
2. The Bolyai-Gerwin theorem
3. Complementation method
Chapter 2. The Hadwiger-Glur Theorem
4. Motions
5. The Hadwiger-Glur theorem
Chapter 3. Equidecomposability and the Concept of Additive Invariants
6. The additive invariant Jl(M)
7. T-equidecomposability
8. Properties of the invariant Jl(M)
9. Centrally symmetric polygons
Chapter 4. Equidecomposability and the Concept of Groups
10. Groups
11. Groups of motions
12. A property of the group S (optional)
Chapter 5. The Theorems of Dehn and Hadwiger for Polyhedra
13. Equidecomposable polyhedra
14. The theorem of Hadwiger
15. The theorem of Dehn
16. Proof of the theorem of Hadwiger
17. n-dimensional polyhedra
Chapter 6. Methods for Calculating Volumes
18. The method of limits
19. Equivalence of the decomposition and complementation methods (optional)
Appendix
1. Necessary and sufficient conditions for the equidecomposability of polyhedra
2. G-equidecomposability of polyhedra
Bibliography

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