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Voltaire's Riddle: Micromégas and the Measure of All Things
Catalog Code: DOL-39
377 pp., Hardbound, 2010
List Price: $58.95
Member Price: $47.95
Series: Dolciani Mathematical Expositions
Voltaire's Riddle is a new translation of Voltaire's Micromégas, the story of a very tall visitor from another planet who encounters an Arctic expedition testing Newton's theories about gravity. The ensuing dialogue ranges from measurements of the very small and very large to the human tendency to make war. At the end of the extended conversation, the visitor offers up a book with the answers to everything. The riddle is why the book is blank.
Andrew Simoson tells the story and describes the underlying mathematics. Topics encompass trajectories of comets, the flattening Earth at the poles, Maupertuis's pursuit problem, Dürer's possible use of trochoids, and the precession of the equinoxes. Requiring readers to have only a bit of knowledge of linear algebra, vector calculus, and differential equations, the book concludes with possible answers to questions that Voltaire poses.
IV. Newton's Polar Ellipse
Excerpt(p. 163): Dürer's Hypocycloid
Albrecht Dürer, the great Renaissance German artist, is credited with being the first to introduce the hypocycloid curve along with the more general family of trochoid curves, as presented in his 1525 four-volume geometry treatise, The Art of Measurement with Compass and Straightedge, one of the first printed mathematical texts to appear in German. In this chapter, we characterize the hypocycloid geometrically. We then characterize it algebraically as a system of parametric equations, and dynamically as a differential equation. Finally we show that the hypocycloid is a solution to a minor variation of one of the most famous of mathematical riddles. But first we ask a natural question:
Did Dürer use the trochoid in his woodcuts?
Dürer argues at length that "geometry is that without which no one can either be or become a master artist" . . . . If he truly believed what he said, we have a measure of hope of finding abstract curves in his artwork.
Andrew Simoson (King College, Bristol, Tenn.) won the MAA's 2007 Chauvenet Prize for his article "The Gravity of Hades" and the 2008 George Polya Award for "Pursuit Curves for the Man in the Moone." He has chaired his college's mathematics and physics department for 30 years.
This is a largely delightful text weaving together Voltaire’s famous satire, history, science, and mathematics. Continued...