• Recently Mathematicians have discovered an “einstein tile”
• 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.

Aperiodic tiles

• Aperiodic tiles are a set of tile-types whose copies can form Patterns without repetition.
• History
  • 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.
• The recent discovery named “the hat” is a 13-sided shape which has presented a deceptively simple solution.
• The hat comprises eight copies of a 60°–90°–120°–90° kite, glued edge-to-edge, and can be generalised to an infinite family of tiles with the same aperiodic property.
• 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.