Ball Bearings

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.

Overarch 2

Bricks are 20cm long and 10cm high. How high could an arch be built without mortar on a flat horizontal surface, to overhang by 1 metre? How big an overhang is it possible to make like this?

Cushion Ball

The shortest path between any two points on a snooker table is the straight line between them but what if the ball must bounce off one wall, or 2 walls, or 3 walls?

Epidemic Modelling

Stage: 4 and 5 Challenge Level:

Mathematics is used in medical research, engineering and finance to model the real world because it is much safer and cheaper to try out theoretical models than it is to experiment with living subjects, to build and test expensive prototypes, or to invest real money in untried schemes.

Find out about how schools were involved in real-life research into epidemic modelling.

Using this probability environment you can be a researcher and use mathematical modelling to investigate the spread of different sorts of diseases. You will be able to model some of the characteristics of your chosen disease. (Click on Configuration Data).

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Your experiment takes place in a community modelled by a square grid. You will see individuals scattered in the community, each occupying one square. The sick individuals are red, the individuals with immunity are dark green and the other healthy individuals are a lighter green. You can set the conditions, watch the epidemic run its course several times, and record the data produced by the computer. You can then observe the effects of changing the conditions of the model.

You can model different diseases by choosing different probabilities of catching the disease and of dying from it and also choosing the time between contracting the disease and becoming infectious to others. You can test the effects of the sort of policy decisions that a Public Health Official makes with regard to vaccination and whether the sick people should stay at home or be put in isolation.

Now decide on what you want to investigate, carry out repeated trials, and write up a report of your findings.

This model will work for diseases that are spread by contact (such as flu, the common cold, measles, meningitis, etc.) but not for sexually transmitted diseases and not for vector borne diseases such as those spread by insects like for example malaria.