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There are **28** NRICH Mathematical resources connected to **Topology**, you may find related items under Decision mathematics and combinatorics.

Article
Primary curriculum
Secondary curriculum
### A Curious Collection of Bridges

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

Age 11 to 18

Game
Primary curriculum
Secondary curriculum
### Colouring Curves Game

In this game, try not to colour two adjacent regions the same colour. Can you work out a strategy?

Age 7 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Torus Patterns

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

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Painting by Numbers

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

Age 16 to 18

Challenge Level

Article
Primary curriculum
Secondary curriculum
### Symmetric Tangles

The tangles created by the twists and turns of the Conway rope trick are surprisingly symmetrical. Here's why!

Age 14 to 16

Article
Primary curriculum
Secondary curriculum
### Tangles

A personal investigation of Conway's Rational Tangles. What were the interesting questions that needed to be asked, and where did they lead?

Age 11 to 16

General
Primary curriculum
Secondary curriculum
### Making Maths: Make a Magic Circle

Make a mobius band and investigate its properties.

Age 7 to 11

Challenge Level

General
Primary curriculum
Secondary curriculum
### Making Maths: Walking Through a Playing Card?

It might seem impossible but it is possible. How can you cut a playing card to make a hole big enough to walk through?

Age 7 to 14

Challenge Level

Article
Primary curriculum
Secondary curriculum
### Going Places with Mathematicians

This article looks at the importance in mathematics of representing places and spaces mathematics. Many famous mathematicians have spent time working on problems that involve moving and mapping things.

Age 7 to 14

Article
Primary curriculum
Secondary curriculum
### Bands and Bridges: Bringing Topology Back

Lyndon Baker describes how the Mobius strip and Euler's law can introduce pupils to the idea of topology.

Age 7 to 14

Article
Primary curriculum
Secondary curriculum
### More on Mazes

There is a long tradition of creating mazes throughout history and across the world. This article gives details of mazes you can visit and those that you can tackle on paper.

Age 7 to 14

Article
Primary curriculum
Secondary curriculum
### The Konigsberg Bridge Problem

This article for pupils describes the famous Konigsberg Bridge problem.

Age 7 to 14

Article
Primary curriculum
Secondary curriculum
### The Development of Spatial and Geometric Thinking: 5 to 18

This is the first article in a series which aim to provide some insight into the way spatial thinking develops in children, and draw on a range of reported research. The focus of this article is the work of Piaget and Inhelder.

Age 5 to 16

Article
Primary curriculum
Secondary curriculum
### A-maze-ing

Did you know that ancient traditional mazes often tell a story? Remembering the story helps you to draw the maze.

Age 7 to 14

Problem
Primary curriculum
Secondary curriculum
### The Bridges of Konigsberg

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

Age 11 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Tourism

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.

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Travelling Salesman

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?

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### KÃ¶nigsberg

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?

Age 11 to 14

Challenge Level

Article
Primary curriculum
Secondary curriculum
### Impossible Polyhedra

Is it possible to make an irregular polyhedron using only polygons of, say, six, seven and eight sides? The answer (rather surprisingly) is 'no', but how do we prove a statement like this?

Age 16 to 18

Article
Primary curriculum
Secondary curriculum
### Euler's Formula and Topology

Here is a proof of Euler's formula in the plane and on a sphere together with projects to explore cases of the formula for a polygon with holes, for the torus and other solids with holes and the relationship between Euler's formula and angle deficiency of polyhedra.

Age 16 to 18

Problem
Primary curriculum
Secondary curriculum
### Earth Shapes

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

Age 16 to 18

Challenge Level

Article
Primary curriculum
Secondary curriculum
### Links and Knots

Some puzzles requiring no knowledge of knot theory, just a careful inspection of the patterns. A glimpse of the classification of knots, prime knots, crossing numbers and knot arithmetic.

Age 14 to 18

Article
Primary curriculum
Secondary curriculum
### Where Do We Get Our Feet Wet?

Professor Korner has generously supported school mathematics for more than 30 years and has been a good friend to NRICH since it started.

Age 16 to 18

Article
Primary curriculum
Secondary curriculum
### Geometry and Gravity 2

This is the second of two articles and discusses problems relating to the curvature of space, shortest distances on surfaces, triangulations of surfaces and representation by graphs.

Age 11 to 18

Article
Primary curriculum
Secondary curriculum
### Geometry and Gravity 1

This article (the first of two) contains ideas for investigations. Space-time, the curvature of space and topology are introduced with some fascinating problems to explore.

Age 11 to 18

Problem
Primary curriculum
Secondary curriculum
### Icosian Game

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.

Age 11 to 14

Challenge Level