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The Ellipse Problem of Steinhaus

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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 .

Contributed by: Izidor Hafner (January 2015)
Open content licensed under CC BY-NC-SA

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Solution 2. Replace the initial rhombus of area formed by chords with a square having an area of . The difference between the areas is .

Reference

[1] H. Steinhaus, One Hundred Problems in Elementary Mathematics, New York: Basic Books, 1964, p. 18 and pp. 87–88.

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