Euclid's Window: The Story of Geometry from Parallel Lines to Hyperspace (Penguin Press Science)

Leads us on a journey through five revolutions in geometry, from the Greek concept of parallel lines to the notions of hyperspace. This title reveals how simple questions anyone might ask about space in the living room or in some other galaxy have been the hidden engine of science's highest achievements.

In his charming mathematical history, Euclid's Window Leonard Mlodinow asks "How do you know where you are?" 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 mini-biography.

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 upon 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