Topology

article
A curious collection of bridges

Read about the problem that tickled Euler's curiosity and led to a new branch of mathematics!
problem
Torus patterns

Age

16 to 18

Challenge level

How many different colours would be needed to colour these different patterns on a torus?
problem
Painting by numbers

Age

16 to 18

Challenge level

How many different colours of paint would be needed to paint these pictures by numbers?
problem
The invertible trefoil

Age

14 to 16

Challenge level

When is a knot invertible ?
problem
The bridges of Konigsberg

Age

11 to 18

Challenge level

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

Age

11 to 14

Challenge level

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.
problem
Travelling salesman

Age

11 to 14

Challenge level

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?
problem
Königsberg

Age

11 to 14

Challenge level

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?
problem
Earth shapes

Age

16 to 18

Challenge level

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

Age

11 to 14

Challenge level

This problem is about investigating whether it is possible to start at one vertex of a platonic solid and visit every other vertex once only returning to the vertex you started at.