The team created these images when analysing special 3-dimensional shapes known as Fano varieties - the mathematical name for the 'building block' shapes they're looking for. These will be the 'elements' in their 'periodic table of shapes'.
Credit: Imperial College London
LONDON: Mathematicians have embarked on a three-year project to create 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 new table 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 periodic table is one of the most important tools in chemistry. Our work aims to create a directory that lists all the geometric building blocks and breaks down each one’s properties using relatively simple equations,” said project leader Alessio Corti, from the Department of Mathematics at Imperial College London.
Describing the 'flow' of building blocks
The researchers, from Imperial College London, the Computational Algebra Group at the University of Sydney and institutions in Japan and Russia, are aiming to identify all the shapes across three, four and five dimensions that cannot be divided into other shapes.
Through differential equations - a type of mathematical equation that expresses a relationship between functions and their derivatives - the building block shapes are able to be described in terms of their 'flow'.
Italian mathematician, Gino Fano, used a technique during the 1930's to find nine two-dimensional atomic shapes. The current approach, invented by Corti and his colleague Vasily Golyshev, is based on ideas from string theory to find atomic shapes in higher dimensions.
"We are searching for special shapes, called Fano varieties, that are the 'elements' in our 'periodic table of shapes'," said the team on their blog.
Exploring other dimensions
Corti's team will be analysing shapes that involve dimensions that cannot be ‘seen’ in a conventional sense in the physical world.
In addition to the three dimensions of length, width and depth found in a three-dimensional shape, the scientists will explore shapes that involve other dimensions.
For example, the space-time described by Einstein’s Theory of Relativity has four dimensions – the three spatial dimensions, plus time. String theorists believe that the Universe is made up of many additional hidden dimensions that cannot be seen.
