The Ellipse Problem of Steinhaus

solution 1

solution 2

a

b

rotate 1

translate

rotate 2

Given an ellipse with major axis of length

2a

and minor axis of length

2b

, draw a closed curve

C

with the same perimeter of the ellipse such that

C

encloses an area greater than the area of the ellipse by

2

(a-b)

.