radian

drawing illustrating radian

Since the late 19th century, a unit used to measure plane angles in SI and elsewhere, equal to the angle between two radii of a circle that cut off a piece of the circumference whose length is equal to the length of the radius. Symbol, rad.

Since the circumference of a circle is pi times the diameter, or two radii, one radian is 360 divided by 2 pi degrees, or approximately 57° 17′ 45″ (about 57.295 779 513°).

According to Florian Cajori,1 the term “radian” was first used in print by James Thomson in 1873.  (Thomson was a brother of Lord Kelvin.) 

Convert between radians and degrees

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A variety of symbols have been used for the radian, including, in a raised position like an exponent, R, r, (r) and c. In 1929 Cajori wrote “Evidently there is, as yet, no approach to uniformity in the designation of radians.”2

1. Florian Cajori. History of Mathematics (2nd ed., 1919), page 484.

2. Florian Cajori. A History of Mathematical Notations. La Salle, Illinois: Open Court, 1929. Volume 2, page 148.

 

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