[Haskell-cafe] Geometry
Joel Koerwer
joelkoerwer at gmail.com
Sun Aug 26 21:23:09 EDT 2007
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
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