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A Tail of Two Palindromes

by Edward R. Burger

Year of Award: 2006

Award: Lester R. Ford

Publication Information: The American Mathematical Monthly, vol. 112, (2005), pp. 311-321

Summary: (From MAA Online) In this paper, written in a lively literary style, the question of determining when a real quadratic irrational is a linear fractional transformation of its conjugate is addressed. The surprising answer involves pairs of palindromes and continued fractions. A necessary and sufficient condition for a quadratic to have integral trace is also presented.

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About the Author: [from The American Mathematical Monthly, (2005)] Edward R. Burger was the host of the 1980s radio show “Ed’s Place” on WCNI 91.1 FM at Connecticut College. In the late 1980s he performed stand-up comedy at The Laff Stop located near the University of Texas at Austin and was an independent contractor for Jay Leno. At Williams College, while not hosting “The Off Hour” on WCFM 91.9 FM, Burger is professor of mathematics and chair of his department. He has also authored a number of articles, books, and videos. Despite his antics, Burger has been honored on several occasions by the MAA: he received the 2001 Deborah and Franklin Tepper Haimo Award for Distinguished Teaching; he was named the 2001–2003 Polya Lecturer; and he was awarded the 2004 Chauvenet Prize.


Subject classification(s): Algebra and Number Theory | Number Theory | Index
Publication Date: 
Wednesday, October 22, 2008