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
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?
Analyse these repeating patterns. Decide on the conditions for a
periodic pattern to occur and when the pattern extends to infinity.
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?
Explore the properties of combinations of trig functions in this open investigation.
Some of our more advanced investigations
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...
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
Read all about electromagnetism in our interactive article.
Can you find some Pythagorean Triples where the two smaller numbers differ by 1?
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.
How much energy has gone into warming the planet?
What's the chance of a pair of lists of numbers having sample
correlation exactly equal to zero?
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. . . .
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.
An introduction to a useful tool to check the validity of an equation.
Ever wondered what it would be like to vaporise a diamond? Find out
Can you deduce why common salt isn't NaCl_2?
What shapes should Elly cut out to make a witch's hat? How can she make a taller hat?
Have you got the Mach knack? Discover the mathematics behind
exceeding the sound barrier.
An article demonstrating mathematically how various physical
modelling assumptions affect the solution to the seemingly simple
problem of the projectile.
Fancy learning a bit more about rates of reaction, but don't know
where to look? Come inside and find out more...
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. . . .
Unearth the beautiful mathematics of symmetry whilst investigating
the properties of crystal lattices
Get some practice using big and small numbers in chemistry.
An introduction to bond angle geometry.
In which Olympic event does a human travel fastest? Decide which events to include in your Alternative Record Book.
Work with numbers big and small to estimate and calculate various quantities in physical contexts.
Could nanotechnology be used to see if an artery is blocked? Or is this just science fiction?
Use trigonometry to determine whether solar eclipses on earth can be perfect.
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
Investigate constructible images which contain rational areas.
Where should runners start the 200m race so that they have all run the same distance by the finish?
How fast would you have to throw a ball upwards so that it would
Draw three equal line segments in a unit circle to divide the
circle into four parts of equal area.
When is a knot invertible ?
Explore the properties of this different sort of differential
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?
Investigate x to the power n plus 1 over x to the power n when x
plus 1 over x equals 1.
How much peel does an apple 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.
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.
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.
A simplified account of special relativity and the twins paradox.