Euclid's window. The story of geometry from parallel lines to hyperspace (Q2726644)

This enjoyably written book gives a history of geometry linked around five particular people, with others discussed as appropriate. The five are: Euclid (axiomatization), Descartes (use of coordinates), Gauss (non-Euclidean geometries), Einstein (relativity), and Witten (string theory). As one might guess from this list, there is a subversive attempt going on to think of all of geometry as a subset of mathematical physics. There is nothing inherently wrong in this, but the general reader for whom this book is intended will not know that there is much greater richness in geometry than is found here. As a history of how the idea of geometry and space have come into modern theoretical physics, it is quite good.NEWLINENEWLINENEWLINEMy only other complaint concerns some of the slangy use of language: for example, on p. 98, ``What should we think of Ptolemy? Did he live in an intelligence-free zone? Should we picture him racing to his friends, exclaiming, `Eureka! I found a new form of proof: the circular argument.' '' Or p. 87, concerning Galileo's Dialogue concerning the two chief world systems: ``It was a cute piece involving three talking heads in a dialogue about astronomy. Definitely Off-Broadway.'' I wonder what someone who doesn't know about modern American culture will think about such things.NEWLINENEWLINENEWLINENevertheless, it is a pleasure to see extensive discussion of some of the innovations of Gauss, Riemann, and Beltrami in a general book!