2 papers
math.HO2026
Generalizations of the Squircle-Lemniscate Relation and Keplerian Dynamics
Zbigniew Fiedorowicz, Muthu Veerappan Ramalingam
This paper establishes a generalized relationship between the arc length of sinusoidal spirals \(r^n=\cos(nθ)\) and the area of generalized Lamé curves defined by \(x^{2n}+y^{2n}…
math.HO2026
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 , aka squircle, and the arc length of the lemniscate $(x^2+y^2…