Einstein Tile

  • 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.
Print Friendly, PDF & Email

© 2023 Civilstap Himachal Design & Development