If you're one of those humans who loves math, a question that has surely nagged you at some
point is why a circle is composed of 360 degrees.
Why not something simpler like 10 degrees or 100 degrees?
All the calculations would have been so simple; wouldn’t that be more convenient?
Believe it or not, 360 is actually the ideal solution.
A number like 10 or 100 would have been more inconvenient, mathematically speaking.
You see, the number 360 is divisible by every number from 1 to 10, aside from 7.
It actually divides into 24 different numbers: 1,2,3,4,5,6,8,9,10,12,15,18,20,24,30,36,40,45,60,72,90,120,180
and 360 itself.
These 24 numbers are called the divisors of the number 360.
This is the highest number of divisors for any positive whole number up to its own value
of 360.
For example, the number you might assume would be most convenient for the full circle—such
as 100—has only 9 divisors.
Numbers are said to be highly composite if they are positive integers with more divisors
than any smaller positive integer has.
The only highly composite numbers below 360 are 2, 6, 12, 60 and 120.
Highly composite numbers are considered good base numbers with which to perform common
calculations.
For example, 360 can be divided into two, three and four parts, and the resulting number
is a whole number.
The resulting numbers are 180, 120 and 90.
However, dividing 100 by three doesn’t end in a whole number.
Instead, it provides a decimal value of 33.3 recurring, which makes performing calculations
much more difficult.
Calculations using 360 are quite simple once you become used to them.
One theory for why a full circle is 360 degrees comes from the Babylonians.
The Sumerians and Babylonians used the Sexagesimal numeral system, a system with a base value
of 60, while the current system we use is known as the decimal system and has a base
value of 10.
So, once we reach the 10th number, we start repeating the symbols (of previous numbers,
from 0 to 9) to form new numbers.
The Babylonians had 60 different symbols with which they formed numbers.
Again, why would they use 60?
Because 60, just like 360, is a highly composite number with up to 12 factors.
Just as we can count 10 on our fingers for the decimal system, we can also count to 60.
Start by counting the knuckles of the 4 fingers (not the thumb) on your right hand.
12, right?
Now, on the other hand, raise any of those fingers to note that you finished one iteration
and got the number 12.
Now, repeat the same procedure as many times as the number of fingers remaining on the
left hand.
The number you will end up with is 12 knuckles x 5 fingers = 60.
Now, to tie this all together, if we were to draw an equilateral triangle with the length
of sides equal to the radii of a circle and place one of its vertices at the center of
the circle, then we could fit a total of 6 such equilateral triangles inside a circle.
Since the Babylonians used the sexagesimal numeral system, they considered each triangle
to have a base value of 60.
Thus, 6 triangles x 60 base value again gives us a value of 360.
In many different geometric applications and historical records, the number 360 has been
a useful and powerful tool, and while we may count on the decimal system for most of our
calculations and measurements, the sexigesimal system is far from forgotten!