In the Search for Beauty - Unravelling Non-Euclidean Geometry
This is a popular book that chronicles the historical attempts to prove the fifth postulate of Euclid on parallel lines that led eventually to the creation of non-Euclidean geometry. To absorb the mathematical content of the book, the reader should be familiar with the foundations of Euclidean geometry at the high school level. But besides the mathematics, the book is also devoted to stories about the people, brilliant mathematicians starting from Pythagoras and Euclid and terminating with Gauss, Lobachevsky and Klein. For two thousand years, mathematicians tried to prove the fifth postulate (whose formulation seemed to them too complicated to be a real postulate and not a theorem, hence the title In the Search for Beauty). But in the 19th century, they realized that such proof was impossible, and this led to a revolution in mathematics and then in physics. The two final chapters are devoted to Einstein and his general relativity which revealed to us that the geometry of the world we live in is not Euclidean.
Also included is an historical essay on Omar Khayyam, who was not only a poet, but also a brilliant astronomer and mathematician.Contents:Before Euclid — Prehistoric TimesEuclidThe Fifth PostulateThe Age of Proofs. The BeginningOmar KhayyamThe Age of Proofs (Continued)Non-Euclidean Geometry. The SolutionNikolai Ivanovich LobachevskyNon-Euclidean Geometry. Some IllustrationsNew Ideas. Riemann. Non-ContradictorinessAn Unexpected Finale. The General Theory of RelativityEinstein Readership: All students, historians and researchers interested in mathematical physics.Key Features:Presents a very clear description of the foundations of Euclidean and non-Euclidean geometry written in simple terms and accessible to any reader with a high school certificateA unique concise narration about the history of mathematics and not just mathematicsAccompanied by witty funny pictures, which can help the reader better absorb the contents