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non-euclidean geometries bernard lavenda [pdf]

Perspective Relativity: An Odyssey in non-Euclidean Geometries by Bernard H Lavenda

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Perspective Relativity: An Odyssey in non-Euclidean Geometries written by Bernard H Lavenda .
This textbook is the last of a three volume set describing a very personal arc of thought that begins with earth measurement (that is, geo-metry), passes through the topology of 2-dimensional surfaces, and ends with space-time measurement (that is, geochronometry, where Einstein identifies gravity with the curvature of space-time). The volumes are (1) The Geometry of the 2- Dimensional Spaces; (2) The Topology of 2-Dimensional Spaces; and (3) An Introduction to Non Euclidean Geometry and Curvature.
Volume 3 gives a general introduction to hyperbolic non-Euclidean geometry in all dimensions, with an introduction to all of the standard models and their relationships to one another. It explains why the models are called hyperbolic. It discusses the ways in which this geometry differs from Euclidean geometry. It calculates the shortest paths in this geometry (the geodesics). It explains some of the reasons why this geometry is studied. Following the introduction to non-Euclidean geometry, Volume 3 approaches curvature in dimension 2 in a way that does not begin with the Gauss map. Instead, it begins with a natural metricinvariant definition of curvature that measures in an obvious way the difficulty of flattening a surface into the plane without distorting lengths and areas. It ends with the Gauss map and a proof of Gauss’s Theorema Egregium. This approach, which is backward to the classical approach, is intuitive; but it entails difficulties in proving that certain limits exist.
Bernard H Lavenda

Book Detail :-
Title: Perspective Relativity: An Odyssey in non-Euclidean Geometries
Edition:
Author(s): Bernard H Lavenda
Publisher: World Scientific
Series:
Year: 2012
Pages: 694
Type: PDF
Language: English
ISBN: 978-981-4340-48-9,981-4340-48-0
Country: US
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The author Bernard Howard Lavenda (born 1945) is a retired professor of chemical physics at the University of Camerino and expert on irreversible thermodynamics. He has contributed to many areas of physics, including that of Brownian motion, and in the establishment of the statistical basis of thermodynamics, and non-Euclidean geometrical theories of relativity. He was the scientific coordinator of the "European Thermodynamics Network" in the European Commission Program of Human Capital and Mobility. He was also a proponent for the establishment of, and scientific director of, a National (Italian) Centre for Thermodynamics, and has acted as scientific consultant to companies such as the ENI Group, where he helped to found TEMA, a consulting firm for SNAM Progetti, ENEA (Italian National Agency for New Technologies, Energy and the Environment), and the Solar Energy Research Institute in Golden, Colorado. He has had over 130 scientific papers published in international journals, some critical of the new fashions and modes in theoretical physics.
Professor Lavenda currently lives in Trevignano Romano near Rome, is married with two adult children and two grandchildren, for whom his textbook "A New Perspective on Thermodynamics" is dedicated.

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Book Contents :- Perspective Relativity: An Odyssey in non-Euclidean Geometries written by Bernard H Lavenda cover the following topics.
List of Figures
1. Introduction
2. Which Geometry?
3. A Brief History of Light, Electromagnetism and Gravity
5. The Origins of Mass
6. Thermodynamics of Relativity
7. General Relativity in a Non-Euclidean Geometrical Setting
8. Relativity of Hyperbolic Space
9. Nonequivalence of Gravitation and Acceleration
10. Aberration and Radiation Pressure in the Klein and Poincaré Models
11. The Inertia of Polarization
References
Index

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