A shining example of the aesthetics of mathematics. (Illustrations)




The harmonious qualities of the golden ratio—phi—are pleasingly scanned in this history of the number, and, by extension, a historical tour of numbers in general.

Phi—1.6180339887…—is never-ending, never-repeating, irrational, incommensurable, one of those special numbers like pi that confound and delight in the same breath. It has been called the divine proportion for its visual effectiveness and Livio, head of the Science Division/Hubble Space Telescope Institute, is willing to concur with this view, although he is also willing to accept that beauty is in the eye of the beholder and the golden ratio (or golden number, golden section, golden this, golden that) may not be primary in its aesthetic appeal. What he is more concerned with here is the frequency of its occurrence in nature, from the petal arrangements on flowers and leaves on stems (phyllotaxis) to the spiral shells of mollusks (“nature loves logarithmic spirals,” from unicellular foraminifers to the arms of galaxies) to the apple's pentagram, which simply knows no end to its mysterious implications (mystery and surprise are, Livio notes, much of the joy of mathematics). He traces the history of the number, starting with the mists, proceeding through Euclid, the founder of geometry (it threw the Pythagoreans, who liked tidy numbers, into a fit), Francesca, Leonardo, Dürer, Kepler, to Le Corbusier and contemporary mathematicians. He tackles the grander instances where enthusiasts of phi say the number can be found: the pyramids, the Mona Lisa, the Parthenon. What he finds is that, through juggling the numbers, in almost any work of human creation can be found a golden ratio. The nature of the number itself—and others like the Fibonacci series, in which the ratio of successive numbers converges on the golden ratio—beguiles Livio, a keystone to the very meaning of mathematics, concluding that it was both discovered and invented, “a symbolic counterpart of the universe we perceive.” Those with math anxiety beware: this portrait of a number would be adrift without its healthy, if accessible, dose of algebra and geometry.

A shining example of the aesthetics of mathematics. (Illustrations)

Pub Date: Oct. 29, 2002

ISBN: 0-7679-0815-5

Page Count: 320

Publisher: Broadway

Review Posted Online: May 20, 2010

Kirkus Reviews Issue: Sept. 1, 2002

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Stricter than, say, Bergen Evans or W3 ("disinterested" means impartial — period), Strunk is in the last analysis...



Privately published by Strunk of Cornell in 1918 and revised by his student E. B. White in 1959, that "little book" is back again with more White updatings.

Stricter than, say, Bergen Evans or W3 ("disinterested" means impartial — period), Strunk is in the last analysis (whoops — "A bankrupt expression") a unique guide (which means "without like or equal").

Pub Date: May 15, 1972

ISBN: 0205632645

Page Count: 105

Publisher: Macmillan

Review Posted Online: Oct. 28, 2011

Kirkus Reviews Issue: May 1, 1972

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Possibly inspired by the letters Cleary has received as a children's author, this begins with second-grader Leigh Botts' misspelled fan letter to Mr. Henshaw, whose fictitious book itself derives from the old take-off title Forty Ways W. Amuse a Dog. Soon Leigh is in sixth grade and bombarding his still-favorite author with a list of questions to be answered and returned by "next Friday," the day his author report is due. Leigh is disgruntled when Mr. Henshaw's answer comes late, and accompanied by a set of questions for Leigh to answer. He threatens not to, but as "Mom keeps nagging me about your dumb old questions" he finally gets the job done—and through his answers Mr. Henshaw and readers learn that Leigh considers himself "the mediumest boy in school," that his parents have split up, and that he dreams of his truck-driver dad driving him to school "hauling a forty-foot reefer, which would make his outfit add up to eighteen wheels altogether. . . . I guess I wouldn't seem so medium then." Soon Mr. Henshaw recommends keeping a diary (at least partly to get Leigh off his own back) and so the real letters to Mr. Henshaw taper off, with "pretend," unmailed letters (the diary) taking over. . . until Leigh can write "I don't have to pretend to write to Mr. Henshaw anymore. I have learned to say what I think on a piece of paper." Meanwhile Mr. Henshaw offers writing tips, and Leigh, struggling with a story for a school contest, concludes "I think you're right. Maybe I am not ready to write a story." Instead he writes a "true story" about a truck haul with his father in Leigh's real past, and this wins praise from "a real live author" Leigh meets through the school program. Mr. Henshaw has also advised that "a character in a story should solve a problem or change in some way," a standard juvenile-fiction dictum which Cleary herself applies modestly by having Leigh solve his disappearing lunch problem with a burglar-alarmed lunch box—and, more seriously, come to recognize and accept that his father can't be counted on. All of this, in Leigh's simple words, is capably and unobtrusively structured as well as valid and realistic. From the writing tips to the divorced-kid blues, however, it tends to substitute prevailing wisdom for the little jolts of recognition that made the Ramona books so rewarding.

Pub Date: Aug. 22, 1983

ISBN: 143511096X

Page Count: 133

Publisher: Morrow/HarperCollins

Review Posted Online: Oct. 16, 2011

Kirkus Reviews Issue: Aug. 1, 1983

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