Just as the sphere offered an alternative to a flat Earth, other three-dimensional shapes offer alternatives to “ordinary” infinite space. We can ask two separate but interrelated questions about the ...

A Fight to Fix Geometry’s Foundations Results about three-dimensional contact manifolds frequently come back to spheres. If you glue a contact sphere onto another contact manifold, such as a 3D ...

Regular geometrical shapes are such a common feature in human civilizations that we often don’t realize that they are not ...

The egg has been called the "perfect shape." Analysis of all egg shapes used four geometric figures: sphere, ellipsoid, ovoid, and pyriform (conical or pear-shaped), with a mathematical formula ...

Our world is made up of elegant shapes — there's the square, the rectangle, the sphere, the prism and many more. But sometimes, these shapes don't quite fit nature's game board. Sometimes ...