I've been working through The Art and Craft of Problem Solving, and there's been a few problems in it based on Pascal's Triangle. After some hours of scribbling numbers on paper, I got lazy and wrote up a generator for it in Python. The book wants the reader to examine some of the properties of the triangle, so I had my triangle renderer (renderer? ha, it's text!) take a function that'd return a boolean to determine if something should be shown or not. While scribbling odd and even values of the triangle on paper, I noticed that it kind of resembled Sierpinski's triangle, so I started with that.
Now this looked pretty neat to me, so I was thinking of another easy pattern I could look for. Perfect squares came to mind; just check to see if the square root of a number is an integer and you're all setup, right? I tried passing that function into the triangle renderer and beheld an interesting result.
It appeared as if perfect squares formed a kind of parabola past 100 rows of the triangle! What a discovery! Of course, I'm really doubting my naive perfect square test at this point, so I googled up a better one and tried that out. A less interesting result awaited me:
Even though I hadn't made the amazing discovery that perfect squares existed, buried within Pascal's triangle in an almost perfect parabola, I had learned to distrust floating point tests on gigantic integers. So there's that.