An Elementary Proof of a Remarkable Relation Between the Squircle and Lemniscate

Zbigniew Fiedorowicz, Muthu Veerappan Ramalingam

It is well known that there is a somewhat mysterious relation between the area of the quartic Fermat curve $x^4+y^4=1$, aka squircle, and the arc length of the lemniscate $(x^2+y^2…