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 ...

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 ...

Everyone learns the number one rule about triangles in high school: the angles of a triangle add up to 180 degrees. But did you know that sometimes they don't? Triangles are much more interesting than ...

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 ...

IN a recent number of NATURE (June 30) there appeared a review of a book by G. Mannoury on the philosophy of mathematics, and the reviewer emphasised a statement of the author to the effect that the ...

Do you think there’s a triangle whose angles measure 41, 76 and 63 degrees? At first, answering this may seem easy. From geometry class we know that the sum of the measures of the interior angles of a ...

In the 1930s, a mathematician by the name of Nicolas Bourbaki was said to frequent the Café Capoulade in Paris, a haven for artists and intellectuals near Luxembourg Gardens. There he wrote an ...

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 ...