How many different colours would be needed to colour these
different patterns on a torus?
A personal investigation of Conway's Rational Tangles. What were
the interesting questions that needed to be asked, and where did
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.
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. . . .
The tangles created by the twists and turns of the Conway rope
trick are surprisingly symmetrical. Here's why!
What if the Earth's shape was a cube or a cone or a pyramid or a
saddle ... See some curious worlds here.
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. . . .
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.
A review of the website http://www.bangor.ac.uk/cpm/exhib/
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?
How many different colours of paint would be needed to paint these
pictures by numbers?
When is a knot invertible ?
Professor Korner has generously supported school mathematics for more than 30 years and has been a good friend to NRICH since it started.
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.