The Penrose Unilluminable Room
In the early 1950s, Ernst Straus asked if a single candle could illuminate an entire room made with mirrored walls, no matter what the shape of the room. In 1958, a young Roger Penrose used the properties of the ellipse to make a room that would always have dark regions, regardless of the position of the candle. In this Demonstration, the locator is the candle, and regions of the room are white (lit) or gray (dark). The red points are the foci of the half ellipses at the top and bottom of the room.