arclength

noun

arc·​length (ˌ)ärk-ˈleŋ(k)th 

-ˈlen(t)th

plural arclengths

geometry

: the length of a segment of an arc

Thus, in a unit circle (radius = 1), any angle of 1 radian cuts off an arc of unit length. All other arclengths are proportional to this; for instance, doubling the radius (to 2) and tripling the angle (to 3 radians) yields an arclength of 6.

—Rheta N. Rubenstein et al., Math Horizons, November 2003

Word History

Etymology

arc entry 1 + length

First Known Use

1849, in the meaning defined above

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