Editorial Mir Moscu | 1978 | 80 páginas | PDF | 13 Mb
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Se da a conocer al lector los fundamentos principales de la geometría no euclidiana de Lobachevski. Las geometrías de Euclides y Lobachevski tienen mucho de común; en ellas sólo con diferentes las definiciones, los teoremas y las fórmulas ligadas al axioma del paralelismo. Para comprender qué es lo que suscitó esta diferencia se debe examinar cómo surgieron y desarrollaron las nociones geométricas fundamentales.
Lobachevskian Geometry (Little Mathematics Library)
Mir |1982 | 73 páginas | djvu | 633 kb
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The aim of this book is to acquaint the reader with the fundamentals of Lobachevsky's non-Euclidean geometry.
The famous Russian mathematician N. I. Lobachevsky was an outstanding thinker, to whom is credited one of the greatest mathematical discoveries, the construction of an original geometric system distinct from Euclid's geometry. The reader will find brief biography of N. I. Lobachevsky in Sec. I.
The famous Russian mathematician N. I. Lobachevsky was an outstanding thinker, to whom is credited one of the greatest mathematical discoveries, the construction of an original geometric system distinct from Euclid's geometry. The reader will find brief biography of N. I. Lobachevsky in Sec. I.
Euclidean and Lobachevskian geometries have much in common, differing only in their definitions, theorems and formulas as regards the parallel-postulate. To clarify the reasons for these differences we must consider how the basic geometric concepts originated and developed, which is done in Sec. 2.
Apart from a knowledge of school plane geometry and trigonometry reading our pamphlet calls for a knowledge of the transformation known as inversion, the most important features of which are reviewed in Sec. 3.
We hope that the reader will be able to grasp its principles with profit to himself and without great difficulty, since it, and Sec. 10, play very important, though ancillary, role in our exposition.
Contents are as under:
Author’s Note 7
1. A Brief Essay on the Life and Work of N. I. Lobachevsky 9
2. On the Origin of Axioms and Their Role in Geometry 11
3. Inversion 21
4. Map of a Lobachevskian Plane 29
5. A Circle in a Lobachevskian Plane 42
6. Equidistant Curve 46
7. Horocycle 47
8. Selected Theorems of Lobachevskian Geometry 49
9. Supplementary Remarks 52
10. On Natural Logarithms and Hyperbolic Functions 53
11. Measurement of Segments of Hyperbolic Straight Lines 57
12 Basic Formulas of Hyperbolic Trigonometry 60
13. The Lengths of Certain Plane Curves in Lobachevskian Geometry 64
Conclusion 68
1. A Brief Essay on the Life and Work of N. I. Lobachevsky 9
2. On the Origin of Axioms and Their Role in Geometry 11
3. Inversion 21
4. Map of a Lobachevskian Plane 29
5. A Circle in a Lobachevskian Plane 42
6. Equidistant Curve 46
7. Horocycle 47
8. Selected Theorems of Lobachevskian Geometry 49
9. Supplementary Remarks 52
10. On Natural Logarithms and Hyperbolic Functions 53
11. Measurement of Segments of Hyperbolic Straight Lines 57
12 Basic Formulas of Hyperbolic Trigonometry 60
13. The Lengths of Certain Plane Curves in Lobachevskian Geometry 64
Conclusion 68
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