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There are 28 NRICH Mathematical resources connected to Topology, you may find related items under Decision Mathematics and Combinatorics.

Broad Topics > Decision Mathematics and Combinatorics > Topology

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A Curious Collection of Bridges

Age 11 to 18

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

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Colouring Curves Game

Age 7 to 14 Challenge Level:

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

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Torus Patterns

Age 16 to 18 Challenge Level:

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

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Painting by Numbers

Age 16 to 18 Challenge Level:

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

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The Invertible Trefoil

Age 14 to 16 Challenge Level:

When is a knot invertible ?

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Symmetric Tangles

Age 14 to 16

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

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Tangles

Age 11 to 16

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

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Making Maths: Make a Magic Circle

Age 7 to 11 Challenge Level:

Make a mobius band and investigate its properties.

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Making Maths: Walking Through a Playing Card?

Age 7 to 14 Challenge Level:

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

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Going Places with Mathematicians

Age 7 to 14

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. . . .

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Bands and Bridges: Bringing Topology Back

Age 7 to 14

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

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The Art of Celtic Knots

Age 7 to 11

This article gives a taste of the mathematics of Celtic knots.

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More on Mazes

Age 7 to 14

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.

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The Königsberg Bridge Problem

Age 7 to 14

This article for pupils describes the famous Konigsberg Bridge problem.

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The Development of Spatial and Geometric Thinking: 5 to 18

Age 5 to 16

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. . . .

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A-maze-ing

Age 7 to 14

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

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Konigsberg Plus

Age 11 to 14 Challenge Level:

Euler discussed whether or not it was possible to stroll around Koenigsberg crossing each of its seven bridges exactly once. Experiment with different numbers of islands and bridges.

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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.

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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?

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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?

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Impossible Polyhedra

Age 16 to 18

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?

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Euler's Formula and Topology

Age 16 to 18

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. . . .

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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.

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Links and Knots

Age 14 to 18

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.

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Where Do We Get Our Feet Wet?

Age 16 to 18

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

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Geometry and Gravity 2

Age 11 to 18

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.

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Geometry and Gravity 1

Age 11 to 18

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.

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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.