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Discovered by William Chapple in 1746, the Poristic family is a set ofvariable-perimeter triangles with common Incircle and Circumcircle. Bydefinition, the family has constant Inradius-to-Circumradius ratio.Interestingly, this invariance also holds for the family of 3-periodics in theElliptic Billiard, though here Inradius and Circumradius are variable andperimeters are constant. Indeed, we show one family is mapped onto the othervia a varying similarity transform. This implies that any scale-free quantitiesand invariants observed in one family must hold on the other.

Related by Similiarity: Poristic Triangles and 3-Periodics in the Elliptic Billiard