Spheres, cylinders and cones

Bilbo goes on an adventure, before arriving back home. Using the information given about his journey, can you work out where Bilbo lives?

A look at different crystal lattice structures, and how they relate to structural properties

Find the distance of the shortest air route at an altitude of 6000 metres between London and Cape Town given the latitudes and longitudes. A simple application of scalar products of vectors.

Use simple trigonometry to calculate the distance along the flight path from London to Sydney.

If a ball is rolled into the corner of a room how far is its centre from the corner?

What is the volume of the solid formed by rotating this right angled triangle about the hypotenuse?

How much peel does an apple have?

Prove Pythagoras' Theorem for right-angled spherical triangles.

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.