Euclidean and non-euclidean geometries. Development and History

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Авторы: Marvin .Jay Greenberg

Издательство: University of California, Santa Cruz

Год: 1995

Кол-во страниц: 502

Формат: pdf

Размер: 18 Мб

Язык: english

This book presents the discovery of non-Euclidean geometry and the subsequent reformulation of the foundations of Euclidean geometry as a suspense story. The mystery of why Euclid's parallel postulate could not be proved remained unsolved for over two thousand years, until the discovery of non-Euclidean geometry and its Euclidean models revealed the impossibility of any such proof. This discovery shattered the traditional conception of geometry as the true description of physical space. Mainly through the influence ofDavid Hilbert's Grundlagen der Geometrie, a new conception emerged in which the existence of many equally consistent geometries was acknowledged, each being a purely formal logical discipline that mayor may not be useful for modeling physical reality. Albert Einstein stated that without this new conception of geometry, he would not have been able to develop the theory of relativity (see Einstein, 1921, Chapter I). The philosopher Hilary Putnam stated that "the overthrow of Euclidean geometry is the most important event in the history of science for the epistemologist" (1977, p. x). Chapter 8 of this book reveals the philosophical confusion that persists to this day.