Why Does 1 Degree Equal 60 Minutes?

Date: 07/28/2004 at 21:59:45
From: Nicholas
Subject: Why does 1 degree equal 60 minutes?

I bought a book over the summer to help me get perpared for geometry.
    The book states that to be more precise, a degree is divided up into 
sixty equal parts called minutes, and that each minute is divided into 
sixty equal parts called seconds.

This makes sense since we already know that there are sixty seconds in
a minute.  However, it just doesn't make sense to me how 60 minutes 
can equal 1 degree.

I guess my confusion comes when I think of a clock.  60 minutes on a
clock is a full rotation by the minute hand, and a full rotation is 
360 degrees.  To think that 1 degree somehow equals 60 minutes really 
leaves me perplexed.

Date: 07/28/2004 at 23:18:01
From: Doctor Peterson
Subject: Re: Why does 1 degree equal 60 minutes?

Hi, Nicholas.

There are two entirely different kinds of "minute" or "second", and 
you have to be careful not to confuse them.  In each case, they are 
1/60 of some larger unit.  When we measure time, we divide each HOUR 
into 60 equal parts called "minutes", and each minute into 60 equal 
"seconds".  We also do the same thing when we measure angles, so that 
each DEGREE is divided into 60 minutes, and each minute OF ANGLE is 
divided into 60 seconds.  The units are different; an hour is not the 
same as a degree in any sense, and their relationship has nothing to 
do with the angle corresponding to a minute on a clock, or in the 
earth's rotation.

Here's what happened.  The ancient Babylonians liked the number 60, 
and in fact based their number system on it almost the way we base 
ours on 10.  So any unit would be divided naturally into 60 equal 
parts.  That worked well for various reasons, so early astronomers 
used that scheme to measure angles, dividing a circle into 360 parts 
(6 times 60), and then dividing each of those parts into 60 minutes, 
and then into 60 seconds.  The word "minute" just meant "little 
part", and "second" meant "second division into little parts"!

At some point people started wanting to divide time into smaller parts 
too; in ancient times it was hard enough to measure hours, but once 
mechanical clocks were invented it became possible to divide hours up.  
How many units should there be in each hour?  They might have used 12, 
as they had long before divided the day and the night each into 12 
parts; but someone felt that 60 parts would be nice (probably an 
astronomer!).  So they needed a name for 1/60 of an hour, and since 
"minute" already meant "1/60 of something", they called it a minute.  
They probably never considered the confusion it would cause when 
someone looked at a clock and asked how far the hand had moved.  If I 
say it moved 30 minutes, do I mean 30/60 of an hour on the dial, or 
30/60 of a degree of angle?  That's unfortunate; but if you remember 
that the size of a degree has nothing to do with the length of an 
hour, and that the two kinds of minutes are just 1/60 of an hour or a 
degree respectively, then you can see that they just aren't related.

If you have any further questions, feel free to write back.

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