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 ...

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 ...

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 ...

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, ...

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 ...

Even the most brilliant innovators get their inspiration from somewhere. For the Dutch graphic artist M.C. Escher, such a creative impetus came from a particular illustration in a 1957 mathematical ...

Virtual reality can take you to some far-out places — mountaintops, distant cities and even fantastical game worlds. A team of artists and mathematicians is now adding to that list: universes where ...