Can you find some Pythagorean Triples where the two smaller numbers differ by 1?
Investigate x to the power n plus 1 over x to the power n when x
plus 1 over x equals 1.
Explore the properties of combinations of trig functions in this open investigation.
Looking at small values of functions. Motivating the existence of
the Taylor expansion.
Use trigonometry to determine whether solar eclipses on earth can be perfect.
Get further into power series using the fascinating Bessel's equation.
Where we follow twizzles to places that no number has been before.
Look at the advanced way of viewing sin and cos through their power series.
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?
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. . . .
Can you deduce why common salt isn't NaCl_2?
Unearth the beautiful mathematics of symmetry whilst investigating
the properties of crystal lattices
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...
Fancy learning a bit more about rates of reaction, but don't know
where to look? Come inside and find out more...
See how enormously large quantities can cancel out to give a good
approximation to the factorial function.
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?
What functions can you make using the function machines RECIPROCAL and PRODUCT and the operator machines DIFF and INT?
Work out the numerical values for these physical quantities.
Is it really greener to go on the bus, or to buy local?
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 all about electromagnetism in our interactive article.
Could nanotechnology be used to see if an artery is blocked? Or is this just science fiction?
Investigate constructible images which contain rational areas.
Formulate and investigate a simple mathematical model for the design of a table mat.
What shapes should Elly cut out to make a witch's hat? How can she make a taller hat?
Get some practice using big and small numbers in chemistry.
In which Olympic event does a human travel fastest? Decide which events to include in your Alternative Record Book.
Find all the periodic cycles and fixed points in this number
sequence using any whole number as a starting point.
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
Work with numbers big and small to estimate and calculate various quantities in physical contexts.
Where should runners start the 200m race so that they have all run the same distance by the finish?
Read about the mathematics behind the measuring devices used in
How much energy has gone into warming the planet?
Explore the properties of this different sort of differential
When is a knot invertible ?
What's the chance of a pair of lists of numbers having sample
correlation exactly equal to zero?
Some of our more advanced investigations
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?
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. . . .
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.
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 much peel does an apple have?
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.
Explore the power of aeroplanes, spaceships and horses.
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?
By exploring the concept of scale invariance, find the probability
that a random piece of real data begins with a 1.
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
Which parts of these framework bridges are in tension and which parts are in compression?
Build up the concept of the Taylor series