What groups of transformations map a regular pentagon to itself?
Proofs that there are only seven frieze patterns involve complicated group theory. The symmetries of a cylinder provide an easier approach.
An introduction to groups using transformations, following on from the October 2006 Stage 3 problems.
An article for students and teachers on symmetry and square dancing. What do the symmetries of the square have to do with a dos-e-dos or a swing? Find out more?
An introduction to the sort of algebra studied at university, focussing on groups.
This article only skims the surface of Galois theory and should
probably be accessible to a 17 or 18 year old school student with a
strong interest in mathematics.
Can you work out what simple structures have been dressed up in these advanced mathematical representations?
An environment for exploring the properties of small groups.
The binary operation * for combining sets is defined as the union
of two sets minus their intersection. Prove the set of all subsets
of a set S together with the binary operation * forms a group.
Explore the properties of some groups such as: The set of all real
numbers excluding -1 together with the operation x*y = xy + x + y.
Find the identity and the inverse of the element x.
Discover a handy way to describe reorderings and solve our anagram
in the process.