Question for any Mathematics Teachers...

[ZoeC]

At GSCE level, do you demonstrate how to derive the formulae for circumference and area of a circle, or are they presented as things to learn and use?

I simply cannot remember if I was shown how to derive area, I have half a memory of something to do with the ratio between radius and circumference of regular polygons - hexagon was exactly 3 from memory and as the number of sides tended to infinity (i.e. tending towards becoming a circle), the ratio tended to pi...can anyone fill in the gaps, i.e. how hexagon is 3 and WHY it tends to pi as the sides increase. Or do you just use measurements to demonstrate approximately?

And would any of this be taught at GCSE anyway, or at a higher level?

Thanks

Not a maths teacher or even a teacher but easy to see how a hexagon is three ? draw regular hexagon, connect the corners with a line through the middle ? you have six equilateral triangles. Distance across centre ? (from corner to corner) is 2 length of one side of the triangles. Circumference is six length of one side of the triangles. Hence ratio = 3.

Actually, yes that is really obvious now you say that thank you!

This is the ratio of the circumference to the diameter, not the circumference to the radius though. The proof of this is beyond GCSE but at GCSE higher level it could be shown to tend to pi by using different regular polygons with an even number of sides and the cosine rule.