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.

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.

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, 200916 yr by dr432

wow, pretty impressive.

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.