The Degree Symbol

Date: 11/02/98 at 21:41:55
From: Austin M.
Subject: Degrees

Dear Dr. Math,

Today in my 8th grade math class, our teacher asked what the degree 
symbol stood for and what it meant. You know, the little circle after 
a measurement. If you have any infomation on this, or an answer, please 
e-mail me when you get a chance. 

Thanks,
Austin

Date: 11/03/98 at 12:57:25
From: Doctor Peterson
Subject: Re: Degrees

Hi, Austin. I just learned something I never knew before! On this page 
maintained by Jeff Miller, on the Earliest Uses of Symbols from 
Geometry:

   http://jeff560.tripod.com/geometry.html   

it says, quoting A History of Mathematical Notations, by Florian 
Cajori:
                                                            o
   This is the first modern appearance that I have found of  [degree symbol]
   for integra or "degrees." It is explained that the denomination of the 
   product of two such denominate numbers is obtained by combining the 
   denominations of the factors; minutes times seconds give thirds, 
   because 1+2=3. The denomination [degree symbol] for integers or degrees 
   is necessary to impart generality to this mode or procedure. "Integers 
   when multiplied by seconds make seconds, when multiplied by thirds 
   make thirds" (fol. 62, 76). It is possible that Peletier is the 
   originator of the [degree symbol] for degrees. But nowhere in this book 
   have I been able to find the modern angular notation [degree symbol] ' " 
   used in writing angles. The [degree symbol] is used only in multiplication.

What this says, in modern mathematical terms, is that the symbols 
[degree symbol] ' " worked like exponents of 1/60:

    o
   a  b' c" = a * (1/60)^0  +  b * (1/60)^1  +  c * (1/60)^2

and the circle for degrees was essentially a zero exponent. 
Fascinating!

- Doctor Peterson, The Math Forum
  http://mathforum.org/dr.math/