The Elements Of Non-Euclidean Geometry by Julian Lowell Coolidge
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About this book :-
This text attempt to prove the parallel axiom by means of the other usual assumptions is now seldom undertaken, and those who do undertake it, are considered in the class with circle-squarers and searchers for perpetual motion– sad by-products of the creative activity of modern science. The book explores a type of geometry that differs from the traditional Euclidean geometry most people learn in school. In Euclidean geometry, parallel lines never meet. However, in non-Euclidean geometry, this rule doesn't always apply. Coolidge examines two main types: Hyperbolic Geometry: Here, through a point not on a given line, there are infinitely many lines that do not intersect the given line.
Elliptic Geometry: In this system, all lines eventually intersect. These alternative geometries challenge our usual understanding of space and have applications in various fields, including physics and art.
Book Detail :-
This book has following details information.
Title:
The Elements Of Non-Euclidean Geometry by Julian Lowell Coolidge
Publisher:
Palala Press
Year:
2008
Pages:
322
Type:
PDF
Language:
English
ISBN-10 #:
1436561086
ISBN-13 #:
978-1436561082
License:
0266497802
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About Author :-
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Book Contents :-
This book has following table of contents.
1. FOUNDATION FOR METRICAL GEOMETRY IN A LIMITED REGION
2. CONGRUENT TRANSFORMATIONS
3. THE THREE HYPOTHESES
4. THE INTRODUCTION OF TRIGONOMETRIC FORMULAE
5. ANALYTIC FORMULAE
6. CONSISTENCY AND SIGNIFICANCE OF THE AXIOMS
7. THE GEOMETRIC AND ANALYTIC EXTENSION OF SPACE
8. THE GROUPS OF CONGRUENT TRANSFORMATIONS
9. POINT, LINE, AND PLANE TREATED ANALYTICALLY
10. THE HIGHER LINE GEOMETRY
11. THE CIRCLE AND THE SPHERE
12. CONIC SECTIONS
13. QUADRIC SURFACES
14. AREAS AND VOLUMES
15. INTRODUCTION TO DIFFERENTIAL GEOMETRY
16. DIFFERENTIAL LINE-GEOMETRY
17. MULTIPLY CONNECTED SPACES
18. THE PROJECTIVE BASIS OF NON-EUCLIDEAN GEOMETRY
19. THE DIFFERENTIAL BASIS FOR EUCLIDEAN AND NON-EUCLIDEAN GEOMETRY
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