Reasoning, convincing and proving

This article for pupils and teachers looks at a number that even the great mathematician, Pythagoras, found terrifying.

Take a complicated fraction with the product of five quartics top and bottom and reduce this to a whole number. This is a numerical example involving some clever algebra.

Here is a proof of Euler's formula in the plane and on a sphere together with projects to explore cases of the formula for a polygon with holes, for the torus and other solids with holes and the relationship between Euler's formula and angle deficiency of polyhedra.

An iterative method for finding the value of the Golden Ratio with explanations of how this involves the ratios of Fibonacci numbers and continued fractions.

Professor Korner has generously supported school mathematics for more than 30 years and has been a good friend to NRICH since it started.

A serious but easily readable discussion of proof in mathematics with some amusing stories and some interesting examples.

Proof does have a place in Primary mathematics classrooms, we just need to be clear about what we mean by proof at this level.

This article discusses how every Pythagorean triple (a, b, c) can be illustrated by a square and an L shape within another square. You are invited to find some triples for yourself.

This follows up the 'magic Squares for Special Occasions' article which tells you you to create a 4by4 magicsquare with a special date on the top line using no negative numbers and no repeats.

An introduction to proof by contradiction, a powerful method of mathematical proof.