How efficiently can various flat shapes be fitted together?

A task which depends on members of the group working collaboratively to reach a single goal.

Making a scale model of the solar system

This task depends on groups working collaboratively, discussing and reasoning to agree a final product.

We're excited about this new program for drawing beautiful mathematical designs. Can you work out how we made our first few pictures and, even better, share your most elegant solutions with us?

For teachers. About the teaching of geometry with some examples from school geometry of long ago.

Introducing a geometrical instrument with 3 basic capabilities.

A kite shaped lawn consists of an equilateral triangle ABC of side 130 feet and an isosceles triangle BCD in which BD and CD are of length 169 feet. A gardener has a motor mower which cuts strips of. . . .

M is any point on the line AB. Squares of side length AM and MB are constructed and their circumcircles intersect at P (and M). Prove that the lines AD and BE produced pass through P.

This article gives an wonderful insight into students working on the Arclets problem that first appeared in the Sept 2002 edition of the NRICH website.

This is the first article in a series which aim to provide some insight into the way spatial thinking develops in children, and draw on a range of reported research. The focus of this article is the. . . .

The largest square which fits into a circle is ABCD and EFGH is a square with G and H on the line CD and E and F on the circumference of the circle. Show that AB = 5EF. Similarly the largest. . . .

Keep constructing triangles in the incircle of the previous triangle. What happens?

What can you say about the lengths of the sides of a quadrilateral whose vertices are on a unit circle?