# Voltaire's Riddle: Micromegas and the Measure of All Things

### By Andrew Simoson

Catalog Code: DOL-39
ISBN: 978-0-88385-345-0
377 pp., Hardbound, 2010
List Price: $63.95 Member Price:$51.95
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.

Highlights:

• This tale, written in 1752, still broadens the horizons, both mathematical and historical, of anyone who reads it.
• It covers numerous mathematical topics.
• Each chapter ends with exercises to aid understanding.

Introduction
Vignette I. A Dinner Invitation
I. The Annotated Micromégas
Vignette II. Here Be Giants!
II. The Micro and the Mega
Vignette III. The Bastille
III. Fragments from Flatland
Vignette IV. A want-to-be mathematician
IV. Newton's Polar Ellipse
Vignette V. A Bourgeois Poet in the Temple of Taste
V. A Mandarin Orange or a Lemon?
Vignette VI. The Zodiac
VI. Hipparchus's Twist
Vignette VII. Love Triangles
VII. Dürer's hypocycloid
Vignette VIII. Maupertuis's Hole
VIII. Newton's Other Ellipse
Vignette IX. The Man in the Moon
IX. Maupertuis's Pursuit Problem
Vignette X. Voltaire and the Almighty
X. Solomon's Π
Vignette XI. Laputa and Gargantua
XI. Moon Pie
Vignette XII. A Last Curtain Call
XII. Riddle Resolutions
Appendix
Cast of Characters
References
Index

### Excerpt: Dürer's Hypocycloid (P. 163)

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.