[Haskell-cafe] Geometry

[Joel Koerwer]

Hi Tony,

x is called the sagitta. At least when making a telescope mirror it is[1].

By bisecting your angle with another radius, you'll see that you have
a right triangle with hypotenuse a, and legs of length (b/2) and
(a-x). Then

sagitta a b = a - sqrt (a*a - b*b/4)

Considered as a function of half the angle subtended by the points on
the circumference, this is called the versine.
http://en.wikipedia.org/wiki/Versine

[1] http://www.stellafane.com/atm/atm_grind/atm_measure_sag.htm