Originally Posted by
DivideBy0 Doh! Thanks, I tried starting by giving the octagon a side length of 1 and working my way inwards :P
Say, if you tried with my approach, how would you get the length of the longer diagonal?
Hello,
in this case you have to use a little bit trigonometrie:
let s be the length of one side of the octagon.
Then you deal with 8 isosceles triangle with the base s, the two legs r and the angle at the vertex (that is the center of the circle) is 45°.
Now divide one isoscele triangle into 2 right triangles:
The hypotenuse is r and one leg is ½s, the angle opposite of this leg is 22.5°.
Now you can calculate r: Code:
½s ½s
----- = sin(22.5°) ==> r = ----------
r sin(22.5°)
The longest diagonal D = 2r
Let d be the shortest diagonal. Then ½d is the height in one of the isoscele triangles:
Now you can calculate ½d: Code:
½d ½d
----- = sin(45°) ==> r = ----------
r sin(45°)
By the way: This last equation is exactly the same as the one I've posted in my previous post.
EB