36 has long been one of my favorite numbers, but faced with this carnival, it was hard to figure out why. It’s a square number that’s a product of two squares, but that’s not too rare. (Why?) It’s the 6th perfect square and the sum of the first six odds, but that’s not too remarkable. (Why?) It’s the 8th triangular number, but not a Sierpinski step or anything… wait! It’s a square triangular number? How common is that? 1, 36, then…?