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The Golden Ratio by Mario Livio, Broadway Books, $24.95, ISBN 0767908155, Reviewed by Ben Longstaff

THERE isn’t room here to define phi, the remarkable number at the heart of The Golden Ratio, but that’s probably just as well. In Livio’s book, you’ll find as many ways to pin down this number as there are intriguing instances of where it crops up.

Livio, a theoretical astrophysicist, is engagingly enthusiastic about his theme, yet he keeps a cool head and avoids the excesses of the number zealots that he scorns. It’s hard not to feel inspired and even unsettled by the hidden order Livio reveals, and there are plenty of leads if you’re bitten by the phi bug.