MMO 206 Moscow MO 1951 find a closed planar curve without self-intersections
Source:
August 7, 2019
geometrycombinatoricscurve
Problem Statement
Consider a curve with the following property: inside the curve one can move an inscribed equilateral triangle so that each vertex of the triangle moves along the curve and draws the whole curve. Clearly, every circle possesses the property. Find a closed planar curve without self-intersections, that has the property but is not a circle.