The Ellipse Problem of Steinhaus
Given an ellipse with major axis of length and minor axis of length , draw a closed curve with the same perimeter of the ellipse such that encloses an area greater than the area of the ellipse by .
Solution 2. Replace the initial rhombus of area formed by chords with a square having an area of . The difference between the areas is .
 H. Steinhaus, One Hundred Problems in Elementary Mathematics, New York: Basic Books, 1964, p. 18 and pp. 87–88.