Subject: Re: [HM] Radian Measure
From: Kim Plofker (Kim_Plofker@Brown.edu)
Date: Tue Mar 07 2000 - 01:05:29 EST
Daina Taimina said:
> According to V.Katz "A History of Mathematics" 2nd.ed. p.143-144
> radian measure was used by Hipparchus (190-120.B.C.E.) to produce
> his trigonometric tables.
This is based on the inference that Hipparchus too used a
trigonometric radius R = 3438, a practice that was carried on in the
Indian tradition although it was lost in the Greek (Ptolemy uses R = 60).
Hipparchus' chord table doesn't survive independently; its nature was
reconstructed (although quite plausibly) by G. J. Toomer partly from
the Indian material. (Cf. Toomer's article on Hipparchus in the
Supplement to the _Dictionary of Scientific Biography_, and references
there cited.) Hipparchus, presumably, measured his angles in the
standard Babylonian/Greek degrees and minutes (Katz says only that
"in a circle of this radius, the measure of an angle...equals its
radian measure", not that Hipparchus described it as such). Does
this count as embodying the concept of radians? I'm a little confused
as to how that concept is being defined in this discussion.
With best wishes,
Kim Plofker
Department of the History of Mathematics
Brown University
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