There are plenty of interesting plots that use various ways to plot the integer occurrences of a^2 + b^2 = c^2 such as making ordered pairs (a,b) and doing that for all such that a^2 + b^2 < [a really big number] and very interesting patterns are noted. My thought is plotting a polar analog. Consider the legs of a right triangle a and b, use tangent to find the angle theta that is opposite of b, then knowing the value for c (because it is a pythagorean triple) plot it in polar form (theta, radius) where theta is can be easily found and the radius is c. I am new to mathematica, and am trying to get it to work with little success yet. I will continue to try. I am posting it if anyone else wants to take a crack at it. Sorry for any lack of clarity in my explanation above; I am in a hurry want to post this before I leave. Thoughts, advice, criticism, all are welcome!