Can you combine simple observations and mathematical thinking to show that atoms exist?
The mathematics of knot theory says that a simple loop and a trefoil are fundamentally different knots. But is that all there is to the question?
The Menger Sponge, a well-studied fractal, was first described in the 1920s. The fractal is cube-like, yet its cross section is quite surprising. What happens when it is sliced on a diagonal plane?
George Hart describes in this video how to create physical models of mathematical objects, surveying some examples of surfaces and polytopes.
A video explaining how some seemingly complex patterns on sea shells can be created by simple, one-dimensional, two-state cellular automata.
A video illustrating the beautiful geometry behind symmetrical linkages of regular polygons.
A sculpture project built entirely with right angles combines math and art in subtle and surprising ways.