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### The Degree Symbol

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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/
```
Associated Topics:
High School Definitions
High School History/Biography
Middle School Definitions
Middle School History/Biography
Middle School Terms/Units of Measurement

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