#theta functions

Equation (1) of www.math.ucla.edu/~wdduke/preprints/mocktheta.pdf reads ∏ 1 ÷ (1−qⁿ). I started expanding the denominator (in crayon) and found the pattern of + − + + − +’s easier to understand in colour.

Here is a sketch of the "combinatorial tetris" that results. I think the colours make the sources of the terms easier to track, and therefore to get a better intuitive feel for the algebra. (Anyone want to make a javascript app of this process?

Doodling with binomial expansion coefficients helped me understand the central limit theorem, Black-Scholes, and the Jones polynomial.