###### 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 and .

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