Our paper "Pythagorean triples: The hyperbolic view" establishes the simple computation (c + b)/a, written in lowest terms as n/m, for determining the parameters n and m that identify the Pythagorean triple (a, b, c) as (2mn, n2 - m2, n2 + m2) (use half of these entries if a is odd). For example (8, 15, 17) has parameters n = 4 and m = 1. Until recently we had not seen this result in print elsewhere! It is spelled out in Jekuthiel Ginsburg's short note, The generators of a Pythagorean triangle, Scripta Math. 11 (1945), p. 188.R. A. Beauregard
University of Rhode Island, beau@math.uri.edu
January 1997 Issue
The author of the short elementary proof of the Fundamental Theorem of Algebra on page 58 credits the proof to a fellow graduate student. Please inform your readers that a slightly improved version of the same proof can be found in Walter Rudin's classic Principles of Mathematical Analysis, 2nd edition, 1964, page 170. Let's give credit to one of the best writers of analysis textbooks. Of course, the proof may have appeared even earlier than 1964.Steve Friedberg
Illinois State University
The "folk proof" of the Fundamental Theorem of Algebra by Uwe Mayer (page 58) is well worth highlighting. However, it previously appeared in print as "An Easy Proof of the Fundamental Theorem of Algebra," by Charles Fefferman, in the American Mathematical Monthly, 74:7 (1967) 839.
David Callan
University of Wisconsin, callan@stat.wisc.edu
Regarding Dennis Gittinger's "Can You Sum This Familiar Series?", page 393, you might like to note that essentially the same observation was made by L.P. Knight in a recent issue of Mathematical Spectrum, 29 (1996/7) 13.D.G. Rogers
University of Hawaii, steve@math.ilstu.edu
On page 142 of the March issue my Algebra II students found an error. Line 12 should read cuberoot(2+11i) + cuberoot(2 - 11i).I gave the class this example as originally written and told them to prove that it equaled four. They couldn't, because it doesn't equal four, but the amended version above does, and the proof is a nice exercise for algebra students.
Lawrence S. Braden
St. Paul's School
Concord, NH 03301