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Bigmantonyd (talk | contribs) m →Arc length and area: Fixes typo in asymptotically |
Bigmantonyd (talk | contribs) m →Arc length and area: Wikilinks transcendental function |
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:<math>A = R^2\arccos\left(1-\frac{h}{R}\right) - \left(R-h\right)\sqrt{R^2-\left(R-h\right)^2}</math>
Unfortunately, <math>a</math> is a [[transcendental function]] of <math>c</math> and <math>h</math> so no algebraic formula in terms of these can be stated. But what can be stated is that as the central angle gets smaller (or alternately the radius gets larger) , the area ''a'' rapidly and asymptotically approaches <math>\tfrac{2}{3}c\cdot h</math>. If <math>\theta<<1, a=\tfrac{2}{3}c\cdot h</math> is a substantially good approximation.
As the central angle approaches π, the area of the segment is converging to the area of a semicircle, <math>\tfrac{\pi R^2}{2}</math>, so a good approximation is a delta offset from the latter area:
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