{'fraction_non_alphanumeric': 0.038461538461538464, 'fraction_numerical': 0.029914529914529916, 'mean_word_length': 4.48828125, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Geometry civilized: history, culture and technique , by J. L. Heilbron. Pp. 309. £35. 1998. ISBN 0 19 850078 5 (Oxford University Press).

Geometry civilized: history, culture and technique, by J. L. Heilbron. Pp. 309. £35. 1998. ISBN 0 19 850078 5 (Oxford University Press). As the subtitle indicates, this beautifully produced and sumptuously illustrated book is a multi-layered work. The mathematical canvas consists of a faithful account of Euclid's Elements (Book I-IV and some of VI) but Heilbron embroiders this to make a rich cultural and historical tapestry depicting the place of geometry in the natural and man-made worlds, its traditional role in a liberal education and the pure pleasure of geometrical problem solving. He touches on a wide spectrum of applications from Vedic altars to manhole covers, from native American patterns to Gothic tracery, from the ovals used in the lay-out of St.Peter's Square, Rome to the octagons favoured by Thomas Jefferson in domestic architecture. And he integrates an impressive range of early sources: among many such gobbets, we learn that there is a reference to the 'angle in a semicircle theorem' in Dante's Divine Comedy and that the surprising observation that, in a walk round the Equator, the extra distance your head travels compared with your feet is independent of the size of the Earth, goes back at least as far as a problem posed in 1715.