# can anybody do this?

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it's not really homework or anything, just something that came into my head.

for a regular shape with n sides of length m inscribed in a circle of radius r, write a formula of m in terms of r and n.

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Sure, the length of a chord is [imath]2 \cdot r \cdot \sin{\frac{\theta}{2} }[/imath] where [imath]r[/imath] is the length radius and [imath]\theta[/imath] is the angle made when radii are drawn between the ends of the chord and the circle's centre. (chord length).

So set [imath]\theta[/imath] to [imath]\frac{2\pi}{n}[/imath] or [imath]\frac{360}{n}[/imath], depending on your preferred units.

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wow nice i'm surprised i thought it would calculations i didn't know it was already kind of defined

so [imath]m =

2 \cdot r \cdot \sin{\frac{180}{n} }

[/imath]

nice work

Edited by dr432
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• 3 weeks later...

wow, pretty impressive.

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It's really not, chord lengths can be derived easily from very basic trig. The chord and the centre define an isosceles triangle which can be divided into two right-angled triangles and it's all trivial from there.

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