Explore the properties of combinations of trig functions in this open investigation.
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
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
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?
Some of our more advanced investigations
Get further into power series using the fascinating Bessel's equation.
What's the chance of a pair of lists of numbers having sample
correlation exactly equal to zero?
How much energy has gone into warming the planet?
Work with numbers big and small to estimate and calculate various quantities in physical contexts.
Investigate constructible images which contain rational areas.
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
Read all about electromagnetism in our interactive article.
What functions can you make using the function machines RECIPROCAL and PRODUCT and the operator machines DIFF and INT?
See how enormously large quantities can cancel out to give a good
approximation to the factorial function.
Explore the properties of this different sort of differential
Look at the advanced way of viewing sin and cos through their power series.
When is a knot invertible ?
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?
How much peel does an apple have?
All types of mathematical problems serve a useful purpose in
mathematics teaching, but different types of problem will achieve
different learning objectives. In generalmore open-ended problems
have. . . .
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.
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. . . .
Ever wondered what it would be like to vaporise a diamond? Find out
An article demonstrating mathematically how various physical
modelling assumptions affect the solution to the seemingly simple
problem of the projectile.
Have you got the Mach knack? Discover the mathematics behind
exceeding the sound barrier.
Can you deduce why common salt isn't NaCl_2?
Get some practice using big and small numbers in chemistry.
An introduction to a useful tool to check the validity of an equation.
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. . . .
Read about the mathematics behind the measuring devices used in
Unearth the beautiful mathematics of symmetry whilst investigating
the properties of crystal lattices
Work out the numerical values for these physical quantities.
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.
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.
Looking at small values of functions. Motivating the existence of
the Taylor expansion.
Which parts of these framework bridges are in tension and which parts are in compression?
A simplified account of special relativity and the twins paradox.
Investigate x to the power n plus 1 over x to the power n when x
plus 1 over x equals 1.
Can you find some Pythagorean Triples where the two smaller numbers differ by 1?
Draw three equal line segments in a unit circle to divide the
circle into four parts of equal area.
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.
Where we follow twizzles to places that no number has been before.
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?
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
How fast would you have to throw a ball upwards so that it would
Explore the power of aeroplanes, spaceships and horses.
Could nanotechnology be used to see if an artery is blocked? Or is this just science fiction?
An introduction to bond angle geometry.