min area of a quadrilateral folding an equilateral triangle
Source: 2000 Argentina OMA L3 p6
June 15, 2020
geometrypaperfoldingminarea
Problem Statement
You have an equilateral paper triangle of area and fold it in two, following a straight line that passes through the center of the triangle and does not contain any vertex of the triangle. Thus there remains a quadrilateral in which the two pieces overlap, and three triangles without overlaps. Determine the smallest possible value of the quadrilateral area of the overlay.