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

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

In our mind’s eye, the universe seems to go on forever. But using geometry we can explore a variety of three-dimensional shapes that offer alternatives to “ordinary” infinite space. When you gaze out ...

Margaret Wertheim gave a talk for the Australian Mathematical Sciences Institute at their 2016 annual Summer School. We have built a world of largely straight lines – the houses we live in, the ...

“The treatise itself, therefore, contains only twenty-four pagesthe most extraordinary two dozen pages in the whole history of thought!” “How different with BolyaiJnos and Lobachvski, who claimed at ...

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, ...