Geometry

About two months ago I saw on television a program about the impossible geometry that Dutch artist M.C. Escher used in his drawings. There was a professor (I didn't catch his name) from the Israeli Technion who showed that this geometry is possible from a certain viewing direction. Today I found another work of the same Prof, Gershon Elber, and this time he deals with other objects. The one that interested me was the Hexagram. He shows how it can be built from two Penrose triangles. I was amazed when I saw the TV program and again when I saw this website!

The Penrose triangle is an impossible object. Oscar Reutersvard, a Swedish artist, was the first to create it (1934) but it's called after Roger Penrose, a mathematician who devised it independently in the 1950s.

Escher's work has a strong mathematical component and many of his optical illusions are based on impossible objects like the Necker cube and the Penrose triangle.