Circular segment: Difference between revisions

Revision as of 01:51, 14 February 2023

Revision as of 20:08, 16 February 2023

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In terms of {{math|''c''}} and {{math|''h''}},

:<math>a = \left(\frac{c^2+4h^2}{8h}\right)^2\arcsinarccos\left(\frac{4chc^2-4h^2}{c^2+4h^2}\right) - \frac{c}{16h}(c^2-4h^2)</math>

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 \ll 1</math>, <math>a = \tfrac{2}{3}c\cdot h</math> is a substantially good approximation.