Tessellations aren’t just eye-catching patterns—they can be used to crack complex mathematical problems. By repeatedly ...

Euclidean geometry is the kind you were taught at school, the world of sines and cosines, and the square on the hypotenuse ...

Researchers uncover the mathematical structure behind mesmerizing tiling patterns, linking their visual appeal to the ...

Mathematicians often comment on the beauty of their chosen discipline. For the non-mathematicians among us, that can be hard to visualise. But in Prof Caroline Series’s field of hyperbolic geometry, ...

Hyperbolic space is a Pringle-like alternative to flat, Euclidean geometry where the normal rules don’t apply: angles of a triangle add up to less than 180 degrees and Euclid’s parallel postulate, ...

Atomic interactions in everyday solids and liquids are so complex that some of these materials’ properties continue to elude physicists’ understanding. Solving the problems mathematically is beyond ...

One hypothesis about the shape of the universe is that the universe is in the space of Euclidean geometry and flat. In Euclidean geometry, it is assumed that straight lines extend everywhere, planes ...