## Rendering a 3D shape with Python

A friend wanted to 3D-print a shape to demonstrate using calculus to find the volume of solids of known cross-section. The shape he wanted was a graph of $sin(x)$ vs $x^2$, where each vertical slice of the intersection was a square. Here's the graph, with $y_1 = sin(x)$ and $y_2 = x^2$. The blue lines show the edge of each square. He couldn't figure out how to do this in a CAD program (I'm not even sure if it's possible), so he asked me if I could write some code to render it.

This post was written in literate Python. Download buildshape.py and run it yourself!

## Multinomial Probability Mass Function in TI-BASIC

Another TI-BASIC challenge proposed to me by the same person who asked me last time was to calculate the probability mass function of a multinomial distribution. The formula is:

$$\frac{n!}{x_1 \cdots x_k} p_1^{x_1}\cdots p_k^{x\_k} \mbox{ where } n = \sum\_{i=1}^k x_i$$
The naïve way of calculating this is to read $x\_1$ and $p\_1$ through $x\_k$ and $p\_k$ and then crunch the numbers. However, this necessitates a list to keep track of all the numbers and an extra loop at the end to crunch them. Since we don't actually need the numbers, there's an easier way.