Periodic table of shapes
7 March 2011
Imperial mathematicians are creating their own version of the periodic table that will provide a vast directory of all the possible shapes in the universe across three, four and five dimensions, linking shapes together in the same way as the periodic table links groups of chemical elements.
The three-year project, announced on 16 February, should provide a resource that mathematicians, physicists and other scientists can use for calculations and research in a range of areas, including computer vision, number theory and theoretical physics.
The researchers, from Imperial and institutions in Australia, Japan and Russia, are aiming to identify all the shapes across three, four and five dimensions that cannot be divided into other shapes.
Project leader, Professor Alessio Corti (Mathematics), explained: “We think we may find vast numbers of these shapes, so you probably won’t be able to stick our table on your wall, but we expect it to be a very useful tool.”
Professor Corti’s colleague on the project, Dr Tom Coates (Mathematics), has created a computer modelling programme that should enable the researchers to pinpoint the basic building blocks for these multi-dimensional shapes from a pool of hundreds of millions of shapes. The researchers will be using this programme to identify shapes that can be defined by algebraic equations and that cannot be divided any further. The researchers calculate that there are around 500 million shapes that can be defined algebraically in four dimensions and they anticipate that they will find a few thousand building blocks from which all these shapes are made.
— Laura Gallagher, Communications and Development