🚀 go-pugleaf

"Jellybean Stonerfish" <stonerfish@tigerlink.net> writes:

>I have a circle...Lets say the diameter is one.
>What are the lengths of the sides of the following inscribed regular
>polygons?


>triangle
sqrt(3)

>square
sqrt(2)

>pentagon
2*sin(36) 

>hexagon
1

>7-gon....(my geometry teacher said that the other names are wrong  call it a
>7-gon )

I've heard it called a septagon or a heptagon.
2*sin(25 5/7)

>octagon
2*sin(22.5)

>Also is there a simple formula f(x) that you put in the number of sides and
>get the lengths of the sides?

Yes, 2*sin(180/x) where the angles are measured in degrees.
By drawing lines from the center of the circle to two consecutive
vertices of the polygon, the side of the polygon is seen to be the third
side of a triangle with two sides of length 1 whose inscribed angle is
360/x.  By dropping down a perpendicular from the center to get a right
triangle; we can use the sine function to get the length of the side.