What shapes should Elly cut out to make a witch's hat? How can she make a taller hat?

How fast would you have to throw a ball upwards so that it would never land?

A spiropath is a sequence of connected line segments end to end taking different directions. The same spiropath is iterated. When does it cycle and when does it go on indefinitely?

Get further into power series using the fascinating Bessel's equation.

By exploring the concept of scale invariance, find the probability that a random piece of real data begins with a 1.

Build up the concept of the Taylor series

Which parts of these framework bridges are in tension and which parts are in compression?

Given the equation for the path followed by the back wheel of a bike, can you solve to find the equation followed by the front wheel?

Dip your toe into the fascinating topic of genetics. From Mendel's theories to some cutting edge experimental techniques, this article gives an insight into some of the processes underlying. . . .

In which Olympic event does a human travel fastest? Decide which events to include in your Alternative Record Book.

Get some practice using big and small numbers in chemistry.

Could nanotechnology be used to see if an artery is blocked? Or is this just science fiction?

Formulate and investigate a simple mathematical model for the design of a table mat.

Where should runners start the 200m race so that they have all run the same distance by the finish?

Work with numbers big and small to estimate and calculate various quantities in physical contexts.

Looking at small values of functions. Motivating the existence of the Taylor expansion.

Work with numbers big and small to estimate and calculate various quantities in biological contexts.

See how enormously large quantities can cancel out to give a good approximation to the factorial function.

Look at the advanced way of viewing sin and cos through their power series.

Explore the properties of this different sort of differential equation.

Two perpendicular lines lie across each other and the end points are joined to form a quadrilateral. Eight ratios are defined, three are given but five need to be found.

This article (the first of two) contains ideas for investigations. Space-time, the curvature of space and topology are introduced with some fascinating problems to explore.

Draw three equal line segments in a unit circle to divide the circle into four parts of equal area.

Where we follow twizzles to places that no number has been before.

Read about the mathematics behind the measuring devices used in quantitative chemistry

Unearth the beautiful mathematics of symmetry whilst investigating the properties of crystal lattices

An introduction to a useful tool to check the validity of an equation.

Fancy learning a bit more about rates of reaction, but don't know where to look? Come inside and find out more...

Use trigonometry to determine whether solar eclipses on earth can be perfect.

On a "move" a stone is removed from two of the circles and placed in the third circle. Here are five of the ways that 27 stones could be distributed.

Investigate constructible images which contain rational areas.

In a snooker game the brown ball was on the lip of the pocket but it could not be hit directly as the black ball was in the way. How could it be potted by playing the white ball off a cushion?

Find all the periodic cycles and fixed points in this number sequence using any whole number as a starting point.

Two polygons fit together so that the exterior angle at each end of their shared side is 81 degrees. If both shapes now have to be regular could the angle still be 81 degrees?

Analyse these repeating patterns. Decide on the conditions for a periodic pattern to occur and when the pattern extends to infinity.

Ever wondered what it would be like to vaporise a diamond? Find out inside...

Take any pair of numbers, say 9 and 14. Take the larger number, fourteen, and count up in 14s. Then divide each of those values by the 9, and look at the remainders.

Take ten sticks in heaps any way you like. Make a new heap using one from each of the heaps. By repeating that process could the arrangement 7 - 1 - 1 - 1 ever turn up, except by starting with it?

We all know that smoking poses a long term health risk and has the potential to cause cancer. But what actually happens when you light up a cigarette, place it to your mouth, take a tidal breath. . . .

What's the chance of a pair of lists of numbers having sample correlation exactly equal to zero?

Can you find some Pythagorean Triples where the two smaller numbers differ by 1?

We think this 3x3 version of the game is often harder than the 5x5 version. Do you agree? If so, why do you think that might be?