Visualising - October 2009, Stage 5

This month, our problems involve visualisation, inviting you to reflect on how you "see" mathematics. Everyone imagines a problem in a different way. By sharing our personal visualisations it can deepen our own understanding of the mathematics within a problem, and help us to make sense of someone else's route to a solution.

Problems

problem Icon

Classical Means

Stage: 5 Short Challenge Level: Challenge Level:1

Use the diagram to investigate the classical Pythagorean means.

problem Icon

Coordinated Crystals

Stage: 5 Challenge Level: Challenge Level:1

Explore the lattice and vector structure of this crystal.

problem Icon

Farey Neighbours

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

Farey sequences are lists of fractions in ascending order of magnitude. Can you prove that in every Farey sequence there is a special relationship between Farey neighbours?

Elsewhere...