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 ...

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 ...

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 ...

Molten metal solidifies into a new kind of glass

(Phys.org) —When a molten material cools quickly, parts of it may have enough time to grow into orderly crystals. But if the cooling rate is too fast for the entire melt to crystallize, the remaining material ends up in ...

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