Circular segment: Difference between revisions

Revision as of 01:39, 4 July 2021

Revision as of 16:15, 14 July 2021

Line 33:

In terms of R and h,

:<math>Aa = 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.