From four-dimensional hexagons to the mind-bending amplituhedron, geometrical shapes are wilder than we learn at school - and they are a crucial tool for understanding reality
Can you imagine the imprint a four-dimensional hexagon might leave as it passes through your three-dimensional kitchen table? Probably not, but some people can.
This story is part of our Concepts Special, in which we reveal how experts think about some of the most mind-blowing ideas in science.For most of us, geometry conjures up thoughts of pencils, rulers, triangles and circles. It means those complicated questions you got asked at school involving parallel lines and angles. But as Boole Stott’s story shows, researchers have been taking geometry way beyond this for some time.
For theoretical physicists, extra dimensions seem to be a necessary part of any full description of the universe, with some proposing that our reality is a “projection” from a higher dimension, for instance. This may sound outlandish, but if physicists make certain simplifying assumptions related to this idea, it suddenly makes it possible to carry out calculations to do with fundamental particles and black holes that are otherwise impossible.
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