Jun 20, 2011
Tarski's circle-squaring problem is the challenge, posed by Alfred Tarski in 1925, to take a disc in the plane, cut it into finitely many pieces, and reassemble the pieces so as to get a square of equal area. This was proven to be possible by Miklós Laczkovich in 1990; the decomposition makes heavy use of the axiom of choice and is therefore non-constructive. By approximating the circle with even-sided polygons, "paper and scissor" dissections become possible. Shown above is the dissection of a icosagon into a square. Read more.
