Patterns in a2 + b2 = c2 (March 2002)
There are an infinite number of integral solutions to the Pythagorean formula a2 + b2 = c2. Here's a plot of the integral solutions for a < 300 and b < 200.
As you can see, there are clear patterns in the distribution. This month, I'm suggesting that you look for the patterns. Explore freely. To help you out, here's another plot. This time with some lines to guide your eyes.
Are there fundamental relationships underlying these lines? If so, what are they?
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