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Gauss, Landen, Ramanujan, the Arithmetic-Geometric Mean, Ellipses, \(\pi\) and the Ladies Diary

by Gert Almkvist and Bruce Berndt

Year of Award: 1989

Award: Lester R. Ford

Publication Information: The American Mathematical Monthly, vol. 95, 1988, pp. 585-608

Summary: This article explains the arithmetic-geometric mean (first discovered by Lagrange) and describes some of its major properties, many of which are due to Gauss.

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About the Authors: (from The American Mathematical Monthly, vol. 95 (1988))

Gert Almkvist received his Ph.D. at the University of California in 1966 and has been at Lund since 1967. His main interests are algebraic K-theory, invariant theory, and elliptic functions

Bruce Berndt received his A.B. degree from Albion College, Albion, Michigan in 1961 and his Ph.D. from the University of Wisconsin, Madison, in 1966. Since 1977, he has devoted all of his research efforts to proving the hitherto unproven results in Ramanujan’s notebooks. His book, Ramanujan’s Notebooks, Part I (Springer-Verlag, 1985), is the first of either three or four volumes to be published on this project.


Subject classification(s): Mathematics History
Publication Date: 
Tuesday, September 23, 2008