62 Frequencies + 1 Line = π

BEHIND THE WORK

Can rotating circles write π?

A block-pi outline is sampled as complex points pⱼ = xⱼ + iyⱼ. A discrete Fourier transform measures the coefficient cₖ of each frequency from k = −31 to 31. Adding the 63 complex terms reconstructs the outline: 62 terms rotate while k = 0 fixes the center. The video shows the nine largest epicycles; the residual arm connects their partial sum to the exact endpoint drawn by all terms.

Artismathic turns equations into visual art—one function at a time.

Music: 'Eternal Garden' by Dan Henig

#MathArt #FourierSeries #Pi