The maths behind 'impossible' never-repeating patterns

Remember the graph paper you used at school, the kind that's covered with tiny squares? It's the perfect illustration of what mathematicians call a "periodic tiling of space", with shapes covering an entire area with no overlap ...

Working group seeks new algorithms for an old problem

Symmetry appears readily in nature: on the petals of a sunflower or the spires of a snowflake. But not all symmetries are alike. Flip a square horizontally, vertically, or diagonally – these are reflectional symmetries ...

A necklace of fractional vortices

Researchers at Chalmers University of Technology have arrived at how what is known as time-reversal symmetry can break in one class of superconducting material. The results have been published in the highly ranked Nature ...

Patterns are math we love to look at

Why do humans love to look at patterns? I can only guess, but I've written a whole book about new mathematical ways to make them. In Creating Symmetry, The Artful Mathematics of Wallpaper Patterns, I include a comprehensive ...

Magic and symmetry in mathematics

We live in a three-dimensional world. Despite the many benefits this presents, it also makes for a complicated math problem, according to Northeastern associate professor of mathematics Ivan Loseu. The best a path to a solution, ...

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