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Here's Looking at Euclid
A Surprising Excursion Through the Astonishing World of Math
By Alex Bellos
Free Press, 291 pages, $33
'THE rules for blindfolded solving are as follows: The timer starts when the cube is shown to the competitor. He must then study it, and put on a blindfold. When he thinks it is solved he tells the judge to stop the stopwatch."
Yes, it's the '70s sensation Rubik's Cube, and so-called "speedcubing" competitions take place around the world.
The urge to puzzle and to seek patterns and to reckon, whether the setting is academic, recreational or commercial -- that's math in its broadest terms.
Alex Bellos enjoyed both math and writing while growing up in Britain. After earning a degree in philosophy and mathematics at Oxford University, he pursued journalism, writing for newspapers such as The Guardian.
Some 20 years after leaving his formal math studies, Bellos decided to revisit it, but this time "free to wander down avenues just because they sounded curious and interesting."
And the result is Here's Looking at Euclid, a book that rises well above the quality of the fairly unsatisfying pun used for its title (but only in the North American release; in the U.K., it's Alex's Adventures in Numberland).
Actually, Bellos did more than wander; he globetrotted. Every chapter sees him visiting people and places, including an Indian ashram, a Japanese after-school lightning calculation club, and even the home of an ebullient numerologist.
Each of the dozen largely free-standing chapters explores one general area of math, touching on historical background, and illustrating the central ideas with stories, examples and drawings. The book is full of interesting excursions, oddball factoids, and some gently rendered non-trivial mathematical ideas, and so, ultimately, quite fun.
A reader who expects math exposure to elicit bad reactions -- abdominal secretions, chest poundings and such -- should not shy away; this book is for the most part a relaxing read.
Bellos keeps things moving along edutainingly, and enjoyment is available even if one skims the more mind-stretching bits.
And for the other kind of reader, having a pencil and paper handy is certainly not necessary, but may add to the enjoyment now and again.
Some of the topics will be familiar to those who have spent some time with math history, such as the Law of Pythagoras (including some nice instances of proofs suggested by diagrams), Euclid's Elements (and the eventual arrival of non-Euclidian geometries), and the discovery of zero (a crucial advance, originating with ancient Indians, later brought by Persian and Arab scholars to Roman Alexandria).
These stories bear repeating; they are essential to the story of human intellectual and cultural development.
There's a fascinating chapter about research into how the brain deals with number and quantity, and the attempt to tease out what's instinctual from what's culturally transmitted.
Clues are provided by tribes whose language has no words for numbers beyond the first few (as if we could only say "one, two, many"), by babies whose gaze can indicate whether they notice an apparent violation of some basic arithmetic fact, and from reaction times and success rates of animals, including non-human primates, faced with arithmetic-related decisions.
Here are a few more topics:
-- Bases other than 10: the case for reconsidering our loyalty to the number of fingers we have, and some people who practise alternative lifestyles.
-- Pi through the ages, and folks who design computers to determine it with ever increasing accuracy: we're currently at around 2.7 trillion decimal places.
-- Popular puzzles, from magic squares to Sudoku.
-- The origins of probability theory: brainy fellows looking to win big in gambling houses
-- The Golden Ratio, long familiar to architects and art history types, but lately of interest to zoologists and botanists.
And in case you were wondering: the world record for blindfolded speedcubing? About 48 seconds.
Winnipegger Neil Schipper has worked as an R&D engineer and a math and science teacher.