Mark Gritter (markgritter) wrote,
Mark Gritter
markgritter

GCD

"Best Writing on Mathematics 2011" is a mixed bag; some neat articles on art, Escher, and Rubik's Cube. When it turned to mathematics education and philosophy of mathematics--- areas I consider myself at least somewhat interested in--- I started skipping through, because the articles were close to unreadable. (But not uniformly so.)

One of the interesting ideas I came away with, was mentioned peripherally (so much so that I can't find the exact reference.) Basically, the Euclidean Algorithm requires just repeated subtraction and ordering. So you can apply it to mathematical structures other than the integers (and the reals, as Euclid did.) Wikipedia mentions a batch of applications in this area: polynomials, gaussian integers, noncommutative rings. You can even turn it around from "this is an algorithm to calculate Greatest Common Denominator" to "GCD is defined to be whatever the algorithm produces" and show that it behaves like GCD ought to.
Tags: books, mathematics
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