Compound transformations

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Mathematical Patchwork

Jenny Murray describes the mathematical processes behind making patchwork in this article for students.
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Grouping Transformations

An introduction to groups using transformations, following on from the October 2006 Stage 3 problems.
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Paint Rollers for Frieze Patterns

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

Age

16 to 18

Challenge level

In this 'mesh' of sine graphs, one of the graphs is the graph of the sine function. Find the equations of the other graphs to reproduce the pattern.
problem

Screwed-Up

Age

11 to 14

Challenge level

A cylindrical helix is just a spiral on a cylinder, like an ordinary spring or the thread on a bolt. If I turn a left-handed helix over (top to bottom) does it become a right handed helix?
problem

Counting Triangles

Age

11 to 14

Challenge level

Triangles are formed by joining the vertices of a skeletal cube. How many different types of triangle are there? How many triangles altogether?
problem

Transformations Tables

Age

7 to 11

Challenge level

These grids are filled according to some rules - can you complete them?
problem

Rots and Refs

Age

16 to 18

Challenge level

Follow hints using a little coordinate geometry, plane geometry and trig to see how matrices are used to work on transformations of the plane.
problem

Squares, Squares and More Squares

Age

11 to 14

Challenge level

Can you dissect a square into: 4, 7, 10, 13... other squares? 6, 9, 12, 15... other squares? 8, 11, 14... other squares?
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Matching Frieze Patterns

Age

11 to 14

Challenge level

Sort the frieze patterns into seven pairs according to the way in which the motif is repeated.