This challenge invites you to create your own picture using just straight lines. Can you identify shapes with the same number of sides and decorate them in the same way?

This practical activity challenges you to create symmetrical designs by cutting a square into strips.

How can you make a curve from straight strips of paper?

This is a simple paper-folding activity that gives an intriguing result which you can then investigate further.

Make new patterns from simple turning instructions. You can have a go using pencil and paper or with a floor robot.

Nearly all of us have made table patterns on hundred squares, that is 10 by 10 grids. This problem looks at the patterns on differently sized square grids.

Here is a chance to create some attractive images by rotating shapes through multiples of 90 degrees, or 30 degrees, or 72 degrees or...

Here is a chance to create some Celtic knots and explore the mathematics behind them.

In abstract and computer generated art, a real object can be represented by a simplified set of lines. Can you create a picture using mathematical instructions?

Anamorphic art is used to create intriguing illusions - can you work out how it is done?

How can you represent the curvature of a cylinder on a flat piece of paper?

Use functions to create minimalist versions of works of art.

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?

This tricky problem required you to try lots of things out and make sense of your findings. Why not read these solutions?

This problem generated concise statements of general rules based on clearly presented evidence.

Several people thought that this problem clearly had no solution, although it did! Why not see how Steve tackled the problem to gain insights into the behaviour of functions and turning points?

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

Jennifer Piggott and Steve Hewson write about an area of teaching and learning mathematics that has been engaging their interest recently. As they explain, the word ‘trick’ can be applied to mathematical activity in many ways.

In this article, Rachel Melrose describes what happens when she mixed mathematics with art.

Proofs that there are only seven frieze patterns involve complicated group theory. The symmetries of a cylinder provide an easier approach.