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**by Ravi Vakil (Stanford University)**

**Award:** Lester R. Ford

**Year of Award:** 2012

**Publication Information:** *The American Mathematical Monthly*, vol. 118, no. 2, January 2011, pp. 116-129

**Summary **(From the Prizes and Awards booklet, MathFest 2012)

A doodle involves starting with a shape (for example a "W") on a piece of paper, and then drawing a curve around it, roughly the set of points within a small constant "distance" from the W. Now repeat the procedure starting with the curve obtained and keep repeating. Do the successive doodles get more and more "circular"?

The author touches on the relevance of these investigations to elementary, and not so elementary, well-known and not so well-known problems in geometry. Along the way the reader gets an informal introduction to linear invariants, winding numbers, differential geometry, Hilbert's third problem, and current research in algebraic and hyperbolic geometry.

**About the Author:** (From the Prizes and Awards booklet, MathFest 2012)

**Ravi Vakil** is a Professor of Mathematics and the Packard University Fellow at Stanford. He is an algebraic geometer, whose work touches on topology, string theory, applied mathematics, combinatorics, number theory, and more. He was a four-time Putnam Fellow while at the University of Toronto. He received his Ph.D. from Harvard, and taught at Princeton and MIT before moving to Stanford. He has received the Dean's Award for Distinguished Teaching, the American Mathematical Society Centennial Fellowship, the Terman fellowship, a Sloan Research Fellowship, the NSF CAREER grant, and the Presidential Early Career Award for Scientists and Engineers. He has also received the Coxeter-James Prize from the Canadian Mathematical Society, and André-Aisenstadt Prize. He was the 2009 Hedrick Lecturer at MathFest, and is a MAA Pólya Lecturer. He is an informal advisor to the website mathoverflow. He works extensively with talented younger mathematicians at all levels, from high school through recent Ph.D. students.

Publication Date:

Wednesday, August 8, 2012