2 out of 3
What's the most efficient proportion for a 1 litre tin of paint?
3 out of 3
If a ball is rolled into the corner of a room how far is its centre from the corner?
3 out of 3
What 3D shapes occur in nature. How efficiently can you pack these shapes together?
1 out of 3
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?
1 out of 3
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.
Imagine two identical cylindrical pipes meeting at right angles and think about the shape of the space which belongs to both pipes. Early Chinese mathematicians call this shape the mouhefanggai.
This article outlines the underlying axioms of spherical geometry giving a simple proof that the sum of the angles of a triangle on the surface of a unit sphere is equal to pi plus the area of the triangle.
