circle constructionsThis year I taught ruler and compass constructions to my year 7 students using the idea of intersecting circles. The image on the right is a construction made by one of the students. You can look at more of these on this blog. What different constructions can you see in this picture (click to enlarge)? How could you develop this idea? 

circles in islamic art
The initial idea for this approach came from the excellent book Islamic Patterns by Keith Critchlow, which describes how many Islamic patterns are based on intersecting circles.
Below are some designs I made inspired by that book. There are a huge amount of islamic pattern ideas on the internet, for example at the NCETM site and on NRICH.
Inspired by these patterns, I went on holiday to the Alhambra Palace in Spain this year. Below are a few pictures I took while I was there. Can you see how these patterns have been constructed?
Following this, you might want to watch this video called how round is your circle? from the excellent website howround.com.