Topology

What if the Earth's shape was a cube or a cone or a pyramid or a saddle ... See some curious worlds here.

Can you cross each of the seven bridges that join the north and south of the river to the two islands, once and once only, without retracing your steps?

A Hamiltonian circuit is a continuous path in a graph that passes through each of the vertices exactly once and returns to the start. How many Hamiltonian circuits can you find in these graphs?

If you can copy a network without lifting your pen off the paper and without drawing any line twice, then it is traversable. Decide which of these diagrams are traversable.

Investigate how networks can be used to solve a problem for the 18th Century inhabitants of Konigsberg.

When is a knot invertible ?

How many different colours of paint would be needed to paint these pictures by numbers?

How many different colours would be needed to colour these different patterns on a torus?