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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...

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...

The Cross-ratio

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

This presentation looks at the theorem of cross-ratio, of four complex numbers, which is of great interest in a field of mathematics known as projective geometry and has an ancient history.

The activity is designed to...

Geodesics

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

A geodesic is the shortest distance between two points and here two problems involving cuboids and cylinders are investigated.

The resource is designed to explore aspects of the subject which may not normally be...

Inequalities

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

This presentation starts with the inequalities associated with triangles and challenges students to develop proofs of the inequalities found in other situations, using the arithmetic, geometric and harmonic means.

The...

Coincidences

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

This thought provoking presentation introduces the mathematics of coincidences, challenges students to produce a spreadsheet which shows the probabilities of sharing a birthday, as well as highlighting the coincidence of...

The Least Road Problem

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

In this presentation students have to find the least amount of road needed to enable each town to be linked to others in a variety of scenarios. There is an explanation of the common theme to be found in the examples and the...

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