For each point on the lemniscate, the area of a squircle sector and a lemniscate arc length obey l = 2√2 a, with an elementary calculus proof.
Topics in Complex Function Theory – Elliptic Functions and Uniformization Theory, Volume 1, Wiley
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An Elementary Proof of a Remarkable Relation Between the Squircle and Lemniscate
For each point on the lemniscate, the area of a squircle sector and a lemniscate arc length obey l = 2√2 a, with an elementary calculus proof.