The Wallace-Bolyai-Gerwien theorem shows that any two polygons with equal area must admit a dissection into finitely many pieces where one is allowed to arbitrarily rotate and translate the pieces to go from one polygon to the other. The problem about whether a hinged dissection exists remained open until 2007. You can read the paper here, which presents a method which always works to find a hinged dissection.”

From Photos of the Week: 8/17-8/23, one of 35 photos. Australia’s Nathan Hedge rides a wave during the 14th edition of the Billabong Pro Tahiti surf event in Teahupoo, on the French Polynesian island of Tahiti, on August 18, 2014. (Gregory Boissy/AFP/Getty Images)