Subject: Re: [HM] Radian Measure
From: James A. Landau (JJJRLandau@aol.com)
Date: Mon Mar 06 2000 - 14:46:14 EST
In a message dated 03/05/2000 7:22:22 PM Eastern Standard Time,
jgc@adinet.com.uy writes:
> your question seems to be "who introduced the _circular or radian
> measure_ (concept)?" rather than "who coined the _radian_ (term)?"
It can be argued (but I would consider such an argument to be half-facetious)
that Archimedes used radian measure when he made his famous approximation to
pi by inscribing and circumscribing a circle with a 96-sided polygon. By
computing the length of one side of the two polygons, Archimedes was
approximating the length of an arc of radian measure 2 pi / 96.
More seriously, there is the formula
arctan x = x - x^3/3 + x^5/5 - X^7/7 + ...
Most texts say this formula was discovered by Gregory in 1671 and Leibniz in
1674, but the original discoverer was Madhava in India circa 1400. Since
this formula gives x in radians, can we not argue seriously that Madhava,
Gregory, and Leibniz all worked with radian measure?
James A. Landau
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