Any convex pentagon has a uniquely determined ellipse that touches all of its sides from the inside!
For a quadrilateral, is seems that there's basically one "degree of freedom" – you can squish and stretch it!
For a triangle, there's two degrees of freedom: Rotation and squishyness (aka eccentricity).
One way to construct a pentagon's inellipse involves a pentagram, so here's a witchy diagram for the three types of shapes.
#mathober2026 #math #geometry
