I am trying to find an explicit expression for the length of each side $L$ of a regular $N$-sided polygon if I want the total height of the polygon to equal some unknown height $H$. I want $L$ to be in terms of the unknown height $H$ and the number of sides $N$
Asked
Active
Viewed 148 times
0
-
One possible strategy: Both $L$ and $H$ are closely related to the radius $R$ of the circumscribing circle of the regular polygon. Can you represent a formula for $L$ and $H$ in terms of $R$ and trigonometric functions of $N$? – cjackal Oct 04 '17 at 00:40
-
I am trying to find $L$ in terms of only $H$ and $N$. I believe that by introducing a new unknown $R$ it is only further complicating the problem – Brothersquid Oct 04 '17 at 00:44
-
Well, actually it is not that bad as you might think of. Both $L$ and $H$ are linear in $R$, so you can immediately eliminate $R$ to get a formula for $L$ in terms of $H$ . – cjackal Oct 04 '17 at 00:46
-
What is it height of a regular polygon? – Michael Rozenberg Oct 04 '17 at 03:18
-
The height is unknown variable – Brothersquid Oct 04 '17 at 17:08