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 19, 2010
Kirkus Reviews Issue: Sept. 1, 2002
An enjoyable slice of 20th-century music journalism almost certain to provide something for most readers, no matter one’s...
Music journalist and musician Wald (Talking 'Bout Your Mama: The Dozens, Snaps, and the Deep Roots of Rap, 2014, etc.) focuses on one evening in music history to explain the evolution of contemporary music, especially folk, blues, and rock.
The date of that evening is July 25, 1965, at the Newport Folk Festival, where there was an unbelievably unexpected occurrence: singer/songwriter Bob Dylan, already a living legend in his early 20s, overriding the acoustic music that made him famous in favor of electronically based music, causing reactions ranging from adoration to intense resentment among other musicians, DJs, and record buyers. Dylan has told his own stories (those stories vary because that’s Dylan’s character), and plenty of other music journalists have explored the Dylan phenomenon. What sets Wald's book apart is his laser focus on that one date. The detailed recounting of what did and did not occur on stage and in the audience that night contains contradictory evidence sorted skillfully by the author. He offers a wealth of context; in fact, his account of Dylan's stage appearance does not arrive until 250 pages in. The author cites dozens of sources, well-known and otherwise, but the key storylines, other than Dylan, involve acoustic folk music guru Pete Seeger and the rich history of the Newport festival, a history that had created expectations smashed by Dylan. Furthermore, the appearances on the pages by other musicians—e.g., Joan Baez, the Weaver, Peter, Paul, and Mary, Dave Van Ronk, and Gordon Lightfoot—give the book enough of an expansive feel. Wald's personal knowledge seems encyclopedic, and his endnotes show how he ranged far beyond personal knowledge to produce the book.
An enjoyable slice of 20th-century music journalism almost certain to provide something for most readers, no matter one’s personal feelings about Dylan's music or persona.Pub Date: July 25, 2015
ISBN: 978-0-06-236668-9
Page Count: 368
Publisher: Dey Street/HarperCollins
Review Posted Online: May 15, 2015
Kirkus Reviews Issue: June 1, 2015
BOOK REVIEW
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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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