can anybody do this?

[dr432]

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.

[the tree]

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.

[dr432]

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 August 8, 2009 by dr432

[awuser896]

wow, pretty impressive.

[the tree]

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.