Shows that Pythagoras for Spherical Triangles reduces to Pythagoras's Theorem in the plane when the triangles are small relative to the radius of the sphere.
How efficiently can you pack together disks?
If a is the radius of the axle, b the radius of each ball-bearing, and c the radius of the hub, why does the number of ball bearings n determine the ratio c/a? Find a formula for c/a in terms of n.
An observer is on top of a lighthouse. How far from the foot of the lighthouse is the horizon that the observer can see?
Use simple trigonometry to calculate the distance along the flight path from London to Sydney.
Work with numbers big and small to estimate and calculate various quantities in physical contexts.
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
Get further into power series using the fascinating Bessel's equation.
Can you draw the height-time chart as this complicated vessel fills with water?
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.
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?
Each week a company produces X units and sells p per cent of its stock. How should the company plan its warehouse space?
Build up the concept of the Taylor series
How would you design the tiering of seats in a stadium so that all spectators have a good view?
Looking at small values of functions. Motivating the existence of the Taylor expansion.
Where should runners start the 200m race so that they have all run the same distance by the finish?
Explore the shape of a square after it is transformed by the action of a matrix.
Explore the meaning behind the algebra and geometry of matrices with these 10 individual problems.
Starting with two basic vector steps, which destinations can you reach on a vector walk?
Can you make matrices which will fix one lucky vector and crush another to zero?
Explore the meaning of the scalar and vector cross products and see how the two are related.
Can you sketch these difficult curves, which have uses in mathematical modelling?
Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.
Go on a vector walk and determine which points on the walk are closest to the origin.
Use trigonometry to determine whether solar eclipses on earth can be perfect.
Explore the properties of matrix transformations with these 10 stimulating questions.
Is it really greener to go on the bus, or to buy local?
Have you ever wondered what it would be like to race against Usain Bolt?
Explore how matrices can fix vectors and vector directions.
In which Olympic event does a human travel fastest? Decide which events to include in your Alternative Record Book.
Explore the properties of perspective drawing.
Which dilutions can you make using only 10ml pipettes?
What shapes should Elly cut out to make a witch's hat? How can she make a taller hat?
In Fill Me Up we invited you to sketch graphs as vessels are filled with water. Can you work out the equations of the graphs?
Formulate and investigate a simple mathematical model for the design of a table mat.
Can you work out which processes are represented by the graphs?
Can you work out what this procedure is doing?
Could nanotechnology be used to see if an artery is blocked? Or is this just science fiction?
Get some practice using big and small numbers in chemistry.
Make an accurate diagram of the solar system and explore the concept of a grand conjunction.
To investigate the relationship between the distance the ruler drops and the time taken, we need to do some mathematical modelling...
10 graphs of experimental data are given. Can you use a spreadsheet to find algebraic graphs which match them closely, and thus discover the formulae most likely to govern the underlying processes?
A problem about genetics and the transmission of disease.
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
Invent scenarios which would give rise to these probability density functions.
Use vectors and matrices to explore the symmetries of crystals.
Which pdfs match the curves?
Estimate these curious quantities sufficiently accurately that you can rank them in order of size