Spheres, cylinders and cones

problem

Tin Tight

Age

14 to 16

Challenge level

What's the most efficient proportion for a 1 litre tin of paint?
problem

Ball Packing

Age

14 to 16

Challenge level

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

Packing 3D Shapes

Age

14 to 16

Challenge level

What 3D shapes occur in nature. How efficiently can you pack these shapes together?
problem

2D-3D

Age

16 to 18

Challenge level

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?
article
The Dodecahedron Explained

What is the shortest distance through the middle of a dodecahedron between the centres of two opposite faces?
article
Volume of a Pyramid and a Cone

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.
article
Mouhefanggai

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.
article
Conic Sections

The interplay between the two and three dimensional Euclidean geometry of conic sections is explored in this article. Suitable for students from 16+, teachers and parents.
article
Curvature of Surfaces

How do we measure curvature? Find out about curvature on soccer and rugby balls and on surfaces of negative curvature like banana skins.
article
Paint Rollers for Frieze Patterns

Proofs that there are only seven frieze patterns involve complicated group theory. The symmetries of a cylinder provide an easier approach.