There is an elaborately carved ancient gate, often considered the most beautiful in Japan, that is completely symmetrical except for a tiny design flaw. The story goes that the artist fashioned one ...

To most people, “symmetry” means the bilateral symmetry exhibited by, say, a butterfly, or the human face. That is, if you take a picture of a butterfly and draw a straight line down the middle of the ...

To begin to understand what mathematicians and physicists see in the abstract structures of symmetries, let’s start with a familiar shape. We are fond of saying things are symmetric, but what does ...