## Parametric Spiral Ball Animation with GeoGebra 5

###### This is that neat thing I said I was working on in GeoGebra 5.  I wanted to come up with a mathematical model that described this metal mixing ball. After playing around with some formulas and testing out properties, I chose some constants for a, n, and d for the base image.  For each frame p, GeoGebra took a “screen capture” of the curve after all t units in the domain [-π, π] were mapped.  This is the formula I came up with:

$latex \begin{bmatrix}\bold{x}\\ \bold{y}\\ \bold{z} \end{bmatrix}=\begin{bmatrix}a\cdot \sqrt{1-t^{2}}\cos(n(t-\frac{p\pi}{d}))\\ a\cdot \sqrt{1-t^{2}}\sin(n(t-\frac{p\pi}{d}))\\ a\cdot t \end{bmatrix}$ such that $-\pi\leq t\leq\pi$ and $a,n,p,d\in\mathbb{Z^{\textrm{+}}}$.