Circular segment: Difference between revisions

Revision as of 22:02, 25 May 2021

Revision as of 22:16, 25 May 2021

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In terms of R and h,

:<math>A = 2RR^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.