Einstein Tile

In News

• Recently  Mathematicians have discovered  an “einstein tile”

About

• An “einstein tile” – a shape that could be singularly used to create a non-repeating (aperiodic) pattern on an infinitely large plane. Here, “einstein” is a play on German ein stein or “one stone” – not to be confused with Albert Einstein, the famous German physicist.
• A periodic tiles are a set of tile-types whos copies can form Patterns without repition
• In 1961, mathematician Hao Wang conjectured that aperiodic tilings were impossible. But his student, Robert Berger, disputed this, finding a set 104 tiles, which when arranged together will never form a repeating pattern.
• In the 1970s, Nobel prize-winning physicist Roger Penrose found a set of only two tiles that could be arranged together in a non-repeating pattern ad infinitum. This is now known as Penrose tiling and has been used in artwork across the world.
• But since Penrose’s discovery, mathematicians have been looking for the “holy grail” of aperiodic tiling – a single shape or monotile which can fill a space up to infinity without ever repeating the pattern it creates.
• Mathematicians call this the einstein problem in geometry. This problem has stumped mathematicians for decades and many felt that there was simply no answer to this problem.
• The recent discovery named “the hat” answers this problem.

Applications: 

• aperiodic tiling will help physicists and chemists understand the structure and behaviour of quasicrystals, structures in which the atoms are ordered but do not have a repeating pattern
• The newly discovered tile might become  a springboard for innovative art.

Source: IE