Look at the advanced way of viewing sin and cos through their power series.
Get further into power series using the fascinating Bessel's equation.
Build up the concept of the Taylor series
Explore the properties of this different sort of differential equation.
Looking at small values of functions. Motivating the existence of the Taylor expansion.
Explore the properties of combinations of trig functions in this open investigation.
Some of our more advanced investigations
Investigate x to the power n plus 1 over x to the power n when x plus 1 over x equals 1.
What's the chance of a pair of lists of numbers having sample correlation exactly equal to zero?
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. . . .
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?
Explore the power of aeroplanes, spaceships and horses.
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?
Read all about electromagnetism in our interactive article.
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.
By exploring the concept of scale invariance, find the probability that a random piece of real data begins with a 1.
An article demonstrating mathematically how various physical modelling assumptions affect the solution to the seemingly simple problem of the projectile.
Ever wondered what it would be like to vaporise a diamond? Find out inside...
An introduction to a useful tool to check the validity of an equation.
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. . . .
How fast would you have to throw a ball upwards so that it would never land?
When is a knot invertible ?
Which parts of these framework bridges are in tension and which parts are in compression?
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. . . .
Investigate constructible images which contain rational areas.
Formulate and investigate a simple mathematical model for the design of a table mat.
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.
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?
Use trigonometry to determine whether solar eclipses on earth can be perfect.
Analyse these repeating patterns. Decide on the conditions for a periodic pattern to occur and when the pattern extends to infinity.
Read about the mathematics behind the measuring devices used in quantitative chemistry
Unearth the beautiful mathematics of symmetry whilst investigating the properties of crystal lattices
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 deduce why common salt isn't NaCl_2?
How much peel does an apple have?
Have you got the Mach knack? Discover the mathematics behind exceeding the sound barrier.
Work out the numerical values for these physical quantities.
Can you find some Pythagorean Triples where the two smaller numbers differ by 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?
A simplified account of special relativity and the twins paradox.
Get some practice using big and small numbers in chemistry.
Draw three equal line segments in a unit circle to divide the circle into four parts of equal area.
Is the age of this very old man statistically believable?
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...
Is it really greener to go on the bus, or to buy local?
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.
What functions can you make using the function machines RECIPROCAL and PRODUCT and the operator machines DIFF and INT?