Problem 9 deals with one of the more interesting things I learned in high school geometry: Pythagorean triples. In high school, I just memorized the 2 most common ones (3, 4, 5 and 5, 12, 13) and thought to myself: Wouldn't it be cool if I could generate all of these?
But that was in the before time; Wikipedia didn't exist and my text book wasn't cool enough to dwell on them. At any rate, now I know Euclid's formula for generating Pythagorean triples: 
Here's the script I used to solve the actual problem:
"""Solves Problem 9 from Project Euler."""
import operator
def triples(upper_bound):
"""Generator for Pythagorean Triples (represented as tuples).
Uses Euclid's formula to generate Pythagorean Triples
(see http://en.wikipedia.org/wiki/Pythagorean_triple#Generating_a_triple).
"""
for m in xrange(2, upper_bound):
for n in xrange(1, m):
yield m ** 2 - n ** 2, 2 * m * n, m ** 2 + n ** 2
# Only uncomment if the triples we get from the original Euclid's are insufficient.
# for k in xrange(1, upper_bound):
# yield k * (m ** 2 - n ** 2), k * (2 * m * n), k * (m ** 2 + n ** 2)
def problem_9():
"""Finds the product of the Pythagorean Triple where a + b + c = 1000."""
for triple in triples(1000):
if sum(triple) == 1000:
return reduce(operator.mul, triple)
return 0
if __name__ == '__main__':
print problem_9()
Back to flipping out...
