Constructing a regular quadrilateral (square) and circle of equal area was proved impossible in Euclidean geometry in 1882. Hyperbolic geometry, however, allows this construction. In this article, we complete the story, providing and proving a construction for squaring the circle in elliptic geometry. We also find the same additional requirements as the hyperbolic case: only certain angle sizes work for the squares and only certain radius sizes work for the circles; and the square and circle constructions do not rely on each other.
Mike McDaniel, Professor of Mathematics, Aquinas College
Davis, Noah and Jansens, Kyle
"Squaring the Circle in Elliptic Geometry,"
Rose-Hulman Undergraduate Mathematics Journal: Vol. 18
, Article 1.
Available at: https://scholar.rose-hulman.edu/rhumj/vol18/iss2/1