November 2014
Intermediate to advanced
326 pages
7h 46m
English
Content preview from From Mathematics to Generic Programming
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4. Euclid’s Algorithm
The whole structure of number theory rests on a single foundation,namely the algorithm for finding the greatest common divisor.Dirichlet, Lectures on Number Theory
In the previous chapter, we met Pythagoras and the secretive order he founded to study astronomy, geometry, number theory, and music. While the Pythagoreans’ failure to find a common measure of the side and the diagonal of a square ended the dream of reducing the world to numbers, the idea of a greatest common measure (GCM) turned out to be an important one for mathematics—and eventually for programming. In this chapter, we’ll introduce an ancient algorithm for GCM that we’ll be exploring throughout the rest of the book.
4.1 Athens and Alexandria
To set the stage ...
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I'm always learning. So when I got on to O'Reilly, I was like a kid in a candy store. There are playlists. There are answers. There's on-demand training. It's worth its weight in gold, in terms of what it allows me to do.