The trouble with five

Share this page
December 2007

The patch from figure 14 contains decagons and pentacles divided up as follows:

Each of these two substitutions introduces rhombi. These can be swallowed up by the two new shapes introduced here:

This substitution turns the patch on the left (the original figure 14) into the patch on the right (our new figure 20):

Back to the article
  • Want facts and want them fast? Our Maths in a minute series explores key mathematical concepts in just a few words.

  • What do chocolate and mayonnaise have in common? It's maths! Find out how in this podcast featuring engineer Valerie Pinfield.

  • Is it possible to write unique music with the limited quantity of notes and chords available? We ask musician Oli Freke!

  • How can maths help to understand the Southern Ocean, a vital component of the Earth's climate system?

  • Was the mathematical modelling projecting the course of the pandemic too pessimistic, or were the projections justified? Matt Keeling tells our colleagues from SBIDER about the COVID models that fed into public policy.

  • PhD student Daniel Kreuter tells us about his work on the BloodCounts! project, which uses maths to make optimal use of the billions of blood tests performed every year around the globe.