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?
Investigate constructible images which contain rational areas.
Draw three equal line segments in a unit circle to divide the circle into four parts of equal area.
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?
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.
Where should runners start the 200m race so that they have all run the same distance by the finish?
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. . . .
Explore the properties of combinations of trig functions in this open investigation.
Some of our more advanced investigations
An introduction to bond angle geometry.
Use trigonometry to determine whether solar eclipses on earth can be perfect.
Have you got the Mach knack? Discover the mathematics behind exceeding the sound barrier.
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?
What shapes should Elly cut out to make a witch's hat? How can she make a taller hat?
What's the chance of a pair of lists of numbers having sample correlation exactly equal to zero?
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 this different sort of differential equation.
How much peel does an apple have?
Can you deduce why common salt isn't NaCl_2?
An introduction to a useful tool to check the validity of an equation.
Fancy learning a bit more about rates of reaction, but don't know where to look? Come inside and find out more...
Unearth the beautiful mathematics of symmetry whilst investigating the properties of crystal lattices
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 quantitative chemistry
Read all about electromagnetism in our interactive article.
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
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. . . .
Work with numbers big and small to estimate and calculate various quantities in physical contexts.
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.
In which Olympic event does a human travel fastest? Decide which events to include in your Alternative Record Book.
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.
Get some practice using big and small numbers in chemistry.
Could nanotechnology be used to see if an artery is blocked? Or is this just science fiction?
Analyse these repeating patterns. Decide on the conditions for a periodic pattern to occur and when the pattern extends to infinity.
Formulate and investigate a simple mathematical model for the design of a table mat.
Ever wondered what it would be like to vaporise a diamond? Find out inside...
An article demonstrating mathematically how various physical modelling assumptions affect the solution to the seemingly simple problem of the projectile.
When is a knot invertible ?
Look at the advanced way of viewing sin and cos through their power series.
A simplified account of special relativity and the twins paradox.
Looking at small values of functions. Motivating the existence of the Taylor expansion.
Build up the concept of the Taylor series
Is the age of this very old man statistically believable?
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 wheel?
By exploring the concept of scale invariance, find the probability that a random piece of real data begins with a 1.
How fast would you have to throw a ball upwards so that it would never land?
Can you find some Pythagorean Triples where the two smaller numbers differ by 1?
Explore the power of aeroplanes, spaceships and horses.
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?