Euclid's Window: The Story of Geometry from Parallel Lines to Hyperspace Amazon.com Review "How do you know where you are?" asks Leonard Mlodinow in his charming mathematical history, Euclid's Window. This question and others about space and time grew out of simple observations of the environment by a select group of thinkers whose lives and brains Mlodinow dissects. Starting with Euclid, geometry has flowed out over the centuries, describing the universe, and, Mlodinow argues, making modern civilization possible. This is not just a history of geometry--it's a timeline of reason and abstraction, with all the major players present: Euclid, Descartes, Gauss, Einstein, and Witten, each represented by a minibiography.  Lots of examples pepper the narrative to help readers achieve their own "eureka!" And it's impossible not to be staggered at the mathematical feats of these geniuses, accomplished as many of them were in the absence of anything but observation and intense thought. Each story builds satisfactorily on the last, until at the end of this delightful book, one has a sense of having climbed a peak of understanding. A working knowledge of basic geometry is helpful but not essential for enjoying Euclid's Window, and Mlodinow's chatty style lends itself remarkably well to explaining these deep and revolutionary concepts. --Adam Fisher  From Booklist Mlodinow's spry account of geometry stresses the stature of the greatest math book of all time, Euclid's Elements. Although the three-dimensional space he described in it doesn't truly represent the shape of nature, Euclid compensated by codifying an attitude essential to rational thinking--to wit, distrust intuition and therefore don't accept unjustified assumptions. Unfortunately, Euclid himself made one unjustified assumption, the parallel postulate, which worked fine in the flat-Earth mathematical world that existed until Carl Friedrich Gauss dismantled it in the nineteenth century. Gauss invented a new geometry of curved or hyperbolic space, a feat that Mlodinow honors in such amusing asides as his remark on Kant's defense of Euclid: "Gauss did not dismiss Kant's work out of hand. He read it, then dismissed it." Such japes lighten and popularize Mlodinow's approach to the further demolition of Euclid by Gauss' student Georg Riemann, whose work critically contributed to the theory of general relativity. Mlodinow's lively exposition concludes with string theorists' claim that geometry possesses no fewer than 11 dimensions. Gilbert TaylorCopyright © American Library Association. All rights reserved               See all Product description