Find all the periodic cycles and fixed points in this number
sequence using any whole number as a starting point.
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
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...
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?
Analyse these repeating patterns. Decide on the conditions for a
periodic pattern to occur and when the pattern extends to infinity.
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?
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?
What functions can you make using the function machines RECIPROCAL and PRODUCT and the operator machines DIFF and INT?
When is a knot invertible ?
Can you find some Pythagorean Triples where the two smaller numbers differ by 1?
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. . . .
How fast would you have to throw a ball upwards so that it would
Work out the numerical values for these physical quantities.
Explore the power of aeroplanes, spaceships and horses.
How much energy has gone into warming the planet?
Get further into power series using the fascinating Bessel's equation.
See how enormously large quantities can cancel out to give a good
approximation to the factorial function.
Unearth the beautiful mathematics of symmetry whilst investigating
the properties of crystal lattices
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?
Get some practice using big and small numbers in chemistry.
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.
Fancy learning a bit more about rates of reaction, but don't know
where to look? Come inside and find out more...
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
Can you deduce why common salt isn't NaCl_2?
Look at the advanced way of viewing sin and cos through their power series.
What's the chance of a pair of lists of numbers having sample
correlation exactly equal to zero?
Some of our more advanced investigations
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.
Explore the properties of this different sort of differential
By exploring the concept of scale invariance, find the probability
that a random piece of real data begins with a 1.
How much peel does an apple have?
Draw three equal line segments in a unit circle to divide the
circle into four parts of equal area.
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 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?
Explore the properties of combinations of trig functions in this open investigation.
Where we follow twizzles to places that no number has been before.
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
Build up the concept of the Taylor series
Looking at small values of functions. Motivating the existence of
the Taylor expansion.
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?
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.
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.
Investigate x to the power n plus 1 over x to the power n when x
plus 1 over x equals 1.
An introduction to bond angle geometry.