Hyperbolic geometry originated in the 19th century, when mathematicians questioned the necessity of the parallel postulate in Euclidean geometry and discovered the hyperbolic plane ℍ², which satisfied ...

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

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 ...

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 ...

Mathematics Magazine presents articles and notes on undergraduate mathematical topics in a lively expository style that appeals to students and faculty throughout the undergraduate years. The journal ...

Geometry boasts a rich and captivating history within the realm of mathematics. In its early development, it was deeply rooted in practical observation used to describe essential concepts such as ...

This originally appeared in the July/August issue of Discover magazine as "Your Hyperbolic Mind." Support our science journalism by becoming a subscriber. The human brain is both a marvel and a ...

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, ...