Visualising and representing

A circle is inscribed in an equilateral triangle. Smaller circles touch it and the sides of the triangle, the process continuing indefinitely. What is the sum of the areas of all the circles?

Do you have enough information to work out the area of the shaded quadrilateral?

Given any three non intersecting circles in the plane find another circle or straight line which cuts all three circles orthogonally.

Stick some cubes together to make a cuboid. Find two of the angles by as many different methods as you can devise.

Draw graphs of the sine and modulus functions and explain the humps.

Match the descriptions of physical processes to these differential equations.

How do you choose your planting levels to minimise the total loss at harvest time?

Investigate the family of graphs given by the equation x^3+y^3=3axy for different values of the constant a.