Draw three equal line segments in a unit circle to divide the circle into four parts of equal area.
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?
What's the chance of a pair of lists of numbers having sample correlation exactly equal to zero?
Some of our more advanced investigations
Investigate constructible images which contain rational areas.
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 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.
Explore the properties of combinations of trig functions in this open investigation.
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?
Look at the advanced way of viewing sin and cos through their power series.
By exploring the concept of scale invariance, find the probability that a random piece of real data begins with a 1.
Explore the power of aeroplanes, spaceships and horses.
Get further into power series using the fascinating Bessel's equation.
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 out the numerical values for these physical quantities.
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?
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?
Get some practice using big and small numbers in chemistry.
Read all about electromagnetism in our interactive article.
Read about the mathematics behind the measuring devices used in quantitative chemistry
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
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. . . .
Can you deduce why common salt isn't NaCl_2?
How fast would you have to throw a ball upwards so that it would never land?
Which parts of these framework bridges are in tension and which parts are in compression?
When is a knot invertible ?
Explore the properties of this different sort of differential equation.
How much peel does an apple have?
Where we follow twizzles to places that no number has been before.
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 be distributed.
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.
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.
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?
Build up the concept of the Taylor series
Use trigonometry to determine whether solar eclipses on earth can be perfect.
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?
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.
Find all the periodic cycles and fixed points in this number sequence using any whole number as a starting point.
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?
Looking at small values of functions. Motivating the existence of the Taylor expansion.
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?
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...
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...
Have you got the Mach knack? Discover the mathematics behind exceeding the sound barrier.