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Library tiling inspired by work of Nobel prize-winner Sir Roger Penrose

All calculations must be done by hand, which would put off most people, but the tiles were invented purely for fun by Sir Roger

'Ingenious' Professor Sir Roger Penrose, alumnus and Honorary Fellow of St John's, has just won a Nobel Prize for Physics for his research on the formation of black holes, but did you know that he also designed a mathematical tiling system?

Known as Penrose tiling, it shows what is known as fivefold symmetry and an example of the tiling decorates the floor at the entrance to the Library at St John's. 

Library floor - Penrose tiling
Penrose tiling under the main door inside the entrance of the Working Library

Sir Roger jointly won the 2020 Nobel Prize in Physics for the discovery that black hole formation is a robust prediction of the general theory of relativity. 

According to the Nobel Prize website: “Penrose used ingenious mathematical methods in his proof that black holes are a direct consequence of Albert Einstein’s general theory of relativity.” 

Einstein himself did not believe that black holes really existed. But in January 1965, ten years after Einstein’s death, Penrose proved that black holes really can form and described them in detail. His ground-breaking article, published in January 1965, continues to be viewed as the most important contribution to the general theory of relativity since Einstein.

In 1974, Sir Roger designed a mathematical tiling system based on his work with black holes, known as Penrose tiling. Penrose tilings are examples of tilings that do not repeat themselves, or ‘aperiodic tilings’. They use just two different shapes of tiles to cover an entire plane, or flat surface area, without creating a pattern that repeats, producing infinitely changing patterns. The tiles were invented purely for fun by Sir Roger. 

Penrose tilings
An example of Penrose tiling, showing rhombuses of two different shapes

Penrose tilings have applications in mathematics, from quasicrystals – crystals whose pattern of atomic arrangement does not repeat itself, unlike most crystals – to the manufacture of toilet paper. The latter resulted in a law suit when in 1997 Sir Roger realised that Kleenex was using a form of his rhomboid design on its quilted toilet tissue without his permission.

As well as tilings, Sir Roger also invented the Penrose Staircase along with his father, the geneticist L.S Penrose, also an alumnus of St John's, which was made famous in a lithograph by Escher and depicts a staircase that appears to climb forever but goes round on itself in a circle. Sir Roger's use of mathematics is not confined to his work - one of his hobbies is solving and devising geometrical puzzles.

The tiling in the Working Library is a good example of Penrose tiling, but it was originally placed there as a type of pun, as the older part of the building, dating from 1888, forms part of the Penrose building, and was named after its architect, Francis Cramer Penrose, and not Sir Roger Penrose.

Dr Peter Goddard, mathematical physicist, Fellow and former Master of St John’s, said: “The older part of the 'working library' building dates from 1888 and forms part of the Penrose building, named after its architect, Francis Cramer Penrose (1817-1903). As far as I am aware, FC Penrose is not known to be related to Roger.

"I was a member of the College committee superintending the building of the new Library and, along with Dr Howard Hughes, Fellow and Supervisor in Physics at St John's, suggested it would be both appropriate and fun to acknowledge Roger’s connection with the College by putting the tiling there. Fun because it might in future years lead to harmless confusion between the two Penroses if anybody remembered!”

The Penrose tilings can be viewed under the main door inside the entrance of the Working Library, Chapel Court. The pattern is used to decorate the walls of buildings at Miami University, and there is also paving at the Mathematical Insitute (Wiles Building) at the University of Oxford University, where Sir Roger is now Emeritus Professor at the Mathematical Institute. 

Published: 13/10/2020

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