Sagitta

$\begin{figure}\begin{center}\BoxedEPSF{Sagitta.epsf scaled 1400}\end{center}\end{figure}$

The Perpendicular distance from an Arc's Midpoint to the Chord across it, equal to the Radius minus the Apothem ,

$\begin{displaymath} s=r-a. \end{displaymath}$

(1)

For a regular Polygon of side length

$\displaystyle s$	$\textstyle \equiv$	$\displaystyle R-r= {\textstyle{1\over 2}}a\left[{\csc\left({\pi\over n}\right)-\cot\left({\pi\over n}\right)}\right]$
	$\textstyle =$	$\displaystyle {\textstyle{1\over 2}}a\tan\left({\pi\over 2n}\right)$	(2)
	$\textstyle =$	$\displaystyle r\tan\left({\pi\over n}\right)\tan\left({\pi\over 2n}\right)$	(3)
	$\textstyle =$	$\displaystyle 2R\sin^2\left({\pi\over 2n}\right),$	(4)

where

is the side length, and

is the number of sides.