Topology

Puzzles

• complete.graphs.on.torusShow how to draw the complete graphs K6 and K7 on a torus, with no two edges crossing. New
• euler.formulaA polyhedron with F faces, V vertices and E edges satisfies F + V = E + 2. New
• fixed.pointA man hikes up a mountain, and starts hiking at 2:00 in the afternoon on a Friday.
• hairy.ballShow that a "hairy coconut" in an odd number of dimensions cannot be combed: if n is odd, there is no... New
• horseshoesHow do you get the ring off the wire puzzle called "Horseshoes" or "Handcuffs"? New
• poincare.conjectureWhat is the exact statement of the Poincare conjecture, and where does it stand (fake R^4s, the case n = 3)? New
• wobbly.tableCan a four-legged table standing on an uneven (but smooth) floor always be turned so that all four legs... New