Triangles and Petals
Why do this problem?
This problem offers the opportunity to practise calculating arc lengths, working in terms of $\pi$, and calculating interior angles of regular polygons. It also provides an opportunity to generalise from simple examples, and to explain patterns in terms of the underlying structure of the problem.
Possible approach
This printable worksheet may be useful: Triangles and Petals
Start by showing the animation of the triangle rotating around another triangle. Then hide the animation and ask learners to sketch what they saw. Show the animation once more so they can confirm what they saw.
Key questions
What angles do you know? What angles can you work out?
Possible support
An Unusual Shape offers opportunities to visualise sectors of circles and to consider simple loci.
Possible extension
Construct a proof for the formula for finding the perimeter of a flower with a regular $n$-sided polygon at its centre.
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