Einstein Tile: New shape answers a 50-year-old geometry mystery

Source: The post is based on the article “New shape answers a 50-year-old geometry mystery” published in The Hindu on 2nd April 2023

What is the News?

A group of four scientists have discovered an entirely new shape which has 13 sides and has named it “the hat”. It is the first ‘Einstein’ tile to have been found.

What is Einstein Tile?

It is a shape that could be singularly used to create a non-repeating (aperiodic) pattern on an infinitely large plane.

A set of tile types is considered to be aperiodic if copies of these tiles can only form patterns without repetition.

Note: The name bears no connection to Albert Einstein but means ‘one stone’ in German.

What is the significance of this discovery?

The discovery has answered a long-standing question in the field of plane geometry where one tries to tile a plane in different ways. While several ways tiling exists in nature and the real world (think bathroom tiles or the hexagons of honeycomb), these are periodic and have a translation symmetry–the size, shape and angle remain the same, only the location changes.

What are the applications of this discovery?

First, 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.

Second, the newly discovered tile might be a springboard for innovative art.