*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

Comments on Selected Exercises

References

Index

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...