What fraction of these regular polygons is shaded red?
What's the same or different about these images?
As a child, I remember working for a couple of weeks on a challenge set by my brother: In a snooker triangle there are 15 balls arranged in 5 rows. How many would there be in 100 rows? 25 years on, this is my response!
I was playing around with images to represent geometric series and was pleasantly surprised by the connections between these two.
While exploring the patterns in the exact values of sine and cosine for 30, 45 and 60 degrees, I discovered other right-angled triangles where the lengths and angles are known.
This image came out of a conversation, with a friend, about what can be seen directly and how this differs from insight gained from doing calculations.
While working with a group of teachers on approaches to proving Pythagoras' Theorem, these diagrams led to rich conversations in many directions.
I first drew this image when doing my PGCE, while thinking about the work of Caleb Gattegno and the power children have, from an early age, to make transformations. I've used this image in my teaching ever since; there are opportunities for considering transformations both within and between the four shapes.
Comparagrams 