Mathematicians Find Perfect Shape

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There is often a criticism leveled at mathematicians that much of their work has limited real world applications.   Mathematicians can often spend years pondering complex equations and defining complicated proofs to see their work greeted with a sigh of ‘so what’ from their non-mathematician colleagues.

However the latest discover in the realm of geometry will actually have a host of real-life applications which could affect all of us.  The discovery is that of a pentagon which can actually completely tile a floor without overlapping or leaving any gaps.


It’s the result of work by three Washington based maths researchers working together in a field often referred to as ’tiling the plane’, this discovery is only the 15th type of non-regular pentagon which has ever been discovered.  The news has caused great excitement in the maths world, one colleague described it as the equivalence of discovering a new atomic particle for physicists.

The scientists responsible include Professor Casey Mann, his wife Jennifer Mcloud-Mann and an undergraduate researcher David Von Derau.  There are more details on their websites and on the Washington University site although you may need an American IP address to access.

So why a Pentagon?

While a  triangle and square can be arranged to tile in virtually limitless sizes and structures.  It has been proven mathematically that any irregular convex, polygon which has more than six sides  cannot.  This has led to the challenge of creating non traditional pentagons to be used in tiling, a difficult and complex task.  It was nearly a hundred years ago in 1918 that a German mathematician discovered that you can in fact use pentagons to tile.  Not many have been discovered so far though, a San Diego housewife discovered five of them and this is only the 15th and the first one for over thirty years.

These particular mathematicians specialize in this area of tiling and knot theory (an equally practical related area).  They did however begin to doubt that any other shapes could be found, computer models were used to research possibilities which were then investigated by the mathematicians themselves.

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