John von Neumann once claimed, "with 4 parameters, I can fit an elephant, and with 5, I can make him wiggle his trunk."
\[x(t)=\displaystyle\sum_{k=0}^\infty\left(A_k^x\cos(kt)+B_k^x\sin(kt) \right)\]
\[y(t)=\displaystyle\sum_{k=0}^\infty\left(A_k^y\cos(kt)+B_k^y\sin(kt) \right)\]
Here's a paper proving that von Neumann's claim is valid! 🔗 https://aapt.scitation.org/doi/10.1119/1.3254017
#Neumann #JohnVonNeumann #VonNeumann #FourierSeries #parameters #complexparameters #parametrization #mathematics #maths
Drawing an elephant with four complex parameters

We define four complex numbers representing the parameters needed to specify an elephantine shape. The real and imaginary parts of these complex numbers are the coefficients of a Fourier coordinate...

American Association of Physics Teachers