On a forgotten conjecture from a famous paper of Erdös
Imre Bárány, Edgardo Roldán-Pensado · 2013
In his paper "On sets of distances of n points", Paul Erdos conjectured that every convex curve contains a point P such that every circle centered at P intersects the curve in at most 2 points. This conjecture is false: If T is an equilateral triangle with boundary T, for any point P on T there is a circle centered at P that intersects T at 4 points. But perhaps the number 2 in Erdos's conjecture can be replaced by some other number.