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Inversion

Carom Maths provides this resource for teachers and students of A Level mathematics.

This presentation begins with a reminder of some transformations of the plane before introducing the less well known transformation of Inversion. Students are able to experiment with an Autograph file to explore this concept...

Quadratic Reciprocity

Carom Maths provides this resource for teachers and students of A Level mathematics to explore aspects of the subject which may not normally be encountered, to encourage new ways to approach a problem mathematically and to broaden the range of tools that an A Level mathematician can call upon.

This...

Hikorski Triples

Carom Maths provides this resource for teachers and students of A Level mathematics.

This presentation demonstrates how the interesting idea of Hikorski triples was developed from writing a GCSE Equations worksheet in 2002. The triples are identified as (p, q, pq+1/p+q).

The activity is designed to...

Triangle Centres

Carom Maths provides this resource for teachers and students of A Level mathematics.

A triangle can have more than one centre and this presentation demonstrates the application of vectors, in three different situations, to show that the circumcentre, the centroid and the orthocentre of a triangle are indeed...

The ABC Conjecture

Carom Maths provides this resource for teachers and students of A Level mathematics.

This presentation begins by introducing students to the technique used to find the radical of an integer before progressing to the ABC conjecture, which is recognised by mathematicians as being an important unsolved problem...

Elliptic Curves

Carom Maths provides this resource for teachers and students of A Level mathematics.

This presentation uses the fact that 1729 is the smallest number that can be expressed as two cubes in two different ways to introduce the topic of Elliptic curves, which are used more and more in the field of number theory...

Triominoes

Carom Maths provides this resource for teachers and students of A Level mathematics.

This presentation shows how, when placing triominoes onto a chessboard, there is always one empty square. An algebraic proof is developed to show that the empty square will always appear in the same location, or in one of...

Zeroes of a Recurrence Relation

Carom Maths provides this resource for teachers and students of A Level mathematics.

The Fibonacci sequence is an example of a linear recurrence relation (LRS). A matrix is used to calculate future terms, as well as running the sequence backwards to see how many zeroes appear. Algebra is used to prove the...

Cyclotomic Polynomials

Carom Maths provides this resource for teachers and students of A Level mathematics.

Cyclotomic polynomials are explained in this presentation, which uses a regular polygon to illustrate the complex roots of unity and establish which of those are primitive, before demonstrating some intriguing algebra.

...

Could Pi Be 3?

Carom Maths provides this resource for teachers and students of A Level mathematics.

This presentation investigates the value of π in different types of geometry and provides a link for students to experiment with Hyperbolic geometry. The classic definition of a distance function, or metric, is given and a...

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