If a ball is rolled into the corner of a room how far is its centre from the corner?
What 3D shapes occur in nature. How efficiently can you pack these shapes together?
Two circles of equal size intersect and the centre of each circle is on the circumference of the other. What is the area of the intersection? Now imagine that the diagram represents two spheres of equal volume with the centre of each sphere on the surface of the other. What is the volume of intersection?
A look at different crystal lattice structures, and how they relate to structural properties
These formulae are often quoted, but rarely proved. In this article, we derive the formulae for the volumes of a square-based pyramid and a cone, using relatively simple mathematical concepts.
What shape would fit your pens and pencils best? How can you make it?
Proofs that there are only seven frieze patterns involve complicated group theory. The symmetries of a cylinder provide an easier approach.
