Explaining, convincing and proving

problem

Rational Round

Age

16 to 18

Challenge level

Show that there are infinitely many rational points on the unit circle and no rational points on the circle x^2+y^2=3.
problem

Thousand Words

Age

16 to 18

Challenge level

Here the diagram says it all. Can you find the diagram?
problem

Proof of Pick's Theorem

Age

16 to 18

Challenge level

Follow the hints and prove Pick's Theorem.
problem

Road Maker 2

Age

16 to 18

Challenge level

Can you work out where the blue-and-red brick roads end?
problem

Transformations for 10

Age

16 to 18

Challenge level

Explore the properties of matrix transformations with these 10 questions.
problem

Dodgy Proofs

Age

16 to 18

Challenge level

These proofs are wrong. Can you see why?
problem

Interpolating Polynomials

Age

16 to 18

Challenge level

Given a set of points (x,y) with distinct x values, find a polynomial that goes through all of them, then prove some results about the existence and uniqueness of these polynomials.
article
Geometry and Gravity 2

This is the second of two articles and discusses problems relating to the curvature of space, shortest distances on surfaces, triangulations of surfaces and representation by graphs.
article
A Knight's Journey

This article looks at knight's moves on a chess board and introduces you to the idea of vectors and vector addition.
article
Telescoping Functions

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.