Exponentials Reiterated

Year of Award: 1982

Award: Lester R. Ford, also the Chauvent Prize in 1984

Publication Information: The American Mathematical Monthly, vol. 88, 1981, pp. 235-252

Summary: Starting from the question, "When is $$x^y$$ less than $$y^x$$?" this article touches on Bernoulli's work in integral solutions, algebraic numbers, some noteworthy facts about the non-commutativity of $$x^y$$, iterated exponentiation, and even an application to biochemistry.

About the Author: (from The American Mathematical Monthly, vol. 88, (1981)) R. Arthur Knoebel received his Ph.D. under the direction of Alfred Foster at the University of California, Berkeley, in 1965. Since then he has been at New Mexico State University. His interests are in general algebraic systems and theoretical computer science. He became interested in the commutativity of powers when he was an undergraduate in Physics, and his interest was renewed when he accidentally came across Varner’s article.

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R. Arthur Knoebel
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R. Arthur Knoebel
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Wednesday, September 24, 2008
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Starting from the question, "When is $$x^y$$ less than $$y^x$$?" this article touches on Bernoulli's work in integral solutions, algebraic numbers, some noteworthy facts about the non-commutativity of $$x^y$$, iterated exponentiation, and even an application to biochemistry.