Build up the concept of the Taylor series
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.
Looking at small values of functions. Motivating the existence of
the Taylor expansion.
Explore the properties of combinations of trig functions in this open investigation.
Get further into power series using the fascinating Bessel's equation.
How much energy has gone into warming the planet?
Work with numbers big and small to estimate and calculate various quantities in physical contexts.
Get some practice using big and small numbers in chemistry.
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
Read all about electromagnetism in our interactive article.
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.
How fast would you have to throw a ball upwards so that it would
Which parts of these framework bridges are in tension and which parts are in compression?
How much peel does an apple have?
Explore the power of aeroplanes, spaceships and horses.
Investigate constructible images which contain rational areas.
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?
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. . . .
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?
Work out the numerical values for these physical quantities.
What's the chance of a pair of lists of numbers having sample
correlation exactly equal to zero?
When is a knot invertible ?
Some of our more advanced investigations
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. . . .
An article demonstrating mathematically how various physical
modelling assumptions affect the solution to the seemingly simple
problem of the projectile.
Can you deduce why common salt isn't NaCl_2?
Ever wondered what it would be like to vaporise a diamond? Find out
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. . . .
An introduction to a useful tool to check the validity of an equation.
Unearth the beautiful mathematics of symmetry whilst investigating
the properties of crystal lattices
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.
Read about the mathematics behind the measuring devices used in
A simplified account of special relativity and the twins paradox.
Fancy learning a bit more about rates of reaction, but don't know
where to look? Come inside and find out more...
Have you got the Mach knack? Discover the mathematics behind
exceeding the sound barrier.
Investigate x to the power n plus 1 over x to the power n when x
plus 1 over x equals 1.
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
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.
There has been a murder on the Stevenson estate. Use your
analytical chemistry skills to assess the crime scene and identify
the cause of death...
Where we follow twizzles to places that no number has been before.
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?
Formulate and investigate a simple mathematical model for the design of a table mat.
Could nanotechnology be used to see if an artery is blocked? Or is this just science fiction?
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?
Is the age of this very old man statistically believable?
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.
Can you find some Pythagorean Triples where the two smaller numbers differ by 1?