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Sagitta (geometry) : ウィキペディア英語版
Sagitta (geometry)

In geometry, the sagitta (sometimes abbreviated as sag) of a circular arc is the distance from the center of the arc to the center of its base.〔 It is used extensively in architecture when calculating the arc necessary to span a certain height and distance and also in optics where it is used to find the depth of a spherical mirror or lens. The name comes directly from Latin ''sagitta'', meaning an arrow.
==Formulae==
In the following equations, s denotes the sagitta (the depth of the arc), r equals the radius of the circle, and \ell half the length of the chord spanning the base of the arc. The sagitta may be calculated from these quantities as
: s = r - \sqrt.
The sagitta may also be calculated from the versine function, for an arc that spans an angle of \theta, and coincides with the versine for unit circles:
: s = r \operatorname\frac = r\left(1-\cos\frac\right).
Alternatively, the Pythagorean theorem
: r^2 = \ell^2 + (r-s)^2
may be rearranged to give a formula for the radius as a function of the sagitta and half-chord length:
: r = \frac = \frac+\frac.
Also, this can also be rearranged to find the length of the half-chord.
: \ell = \sqrt.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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