Green flag and enjoy these geometric curiosities! First, the actual Basel construction for N=2,4,8,16,32 are shown and then these constructs are applied to sides of regular polygons (triangle, square, pentagon, etc.)
Song: "In this shirt" by Irrepressibles. These constructions were inspired by a video on YouTube by 3Blue1Brown where he explains how it is possible to prove that the sum of reciprocal squares is pi^2/6 (known as the Basel problem which Euler solved in 1734) using very clever geometric constructions and the property of light that its strength is proportional to the reciprocal square of the distance between the observer and the light source. Video: Why is pi here? And why is it squared? A geometric answer to the Basel problem https://youtu.be/d-o3eB9sfls?si=OuZH1qYWxp_x2xnS
