Finding Pythagorean triples

For this tutorial you may need to read the Wikipedia page about Pythagorean triple (for more information on Pythagorean triple visit http://en.wikipedia.org/wiki/Pythagorean_triple). Pythagorean triples are closely related to the Pythagorean Theorem, which you probably have learned about in high school geometry.

Pythagorean triples represent the three sides of a right triangle, and therefore, obey the Pythagorean Theorem. Let's find the Pythagorean triple that has a components sum of 1000. We will do this using Euclid's formula:

In this example we will see some universal functions in action.

How to do it...

The Euclid's formula defines indices m and n.

1. Create m and n arrays.

   We will create arrays to hold these indices:

   m = numpy.arange(33)
   n = numpy.arange(33)

2. Calculate a, b, and c of the Pythagorean triple.

   The second step is to calculate a, b, and c of the Pythagorean triple using Euclid's formula. Use the outer function to get the Cartesian products, difference, and...