Why are there 360 degrees in a circle?

Question

Angle can be measured in two units. Radians and degrees.

In radians, $\pi$ means half circle as $2*\pi*r$ represents the circumference of whole circle. Thus this unit can be easily justified.

But I am curious about degrees. Why a circle has only 360 degrees? Why not 1000 degrees. A quarter circle can have 250 degrees. Is it just a convention like Kg or metre, or there is some reason for choosing 360 degrees.

I hope I am clear with my question. If you want more details about what I am asking, let me know.

This question may already have an answer on HMSSE and, if not, may be a good question for that platform. The root of the answer lies in the fact that the the Babylonians used a sexagesimal number system. — Xander Henderson, Jun 29 '19 at 12:36
https://hsm.stackexchange.com/questions/1884/origin-of-360-degrees — Xander Henderson, Jun 29 '19 at 12:37
For the same reason as an hour is $60$min and a minute is $60$ s: the Babylonians made their calculations in basis $60$. — Bernard, Jun 29 '19 at 12:38
I suppose so. If it had been inherited from Gaul, the basis would have been $20$. — Bernard, Jun 29 '19 at 12:43
If your question is essentially “Why are there 360 degrees in a complete circle”, you should use that as the title of the question. It would be more likely to get clicked by people who might want to answer it, and that’s good for you. — David K, Jun 29 '19 at 12:45
Radians are not something we choose. Radians exist in nature. Degrees don't. — Bman72, Jun 29 '19 at 12:50
There are other ways besides radians and degrees. See Wikipedia — Steven Alexis Gregory, Jun 29 '19 at 12:58

score 2 · Accepted Answer · answered Jun 29 '19 at 12:40

2

There is an angle measure called a "gradian," which divides a right angle into 100 equal pieces. See

https://en.wikipedia.org/wiki/Gradian

There are advantages to using a base-60 system. First, 60 (and 360) have lots of small divisors. Second, in the case of measuring angles, the special angles of 30-degrees and 60-degrees come out even. In the gradient system, the 30-degree angle is $33 $ $1/3$ (ick.)

answered Jun 29 '19 at 12:40

B. Goddard

1

@Xanderhenderson He never said that a gradian is 1/100 th of a circle. He said that for a right angle. – Aditya Jain Jun 29 '19 at 13:03
@AdityaJain Oi... I misread it. Nevermind. – Xander Henderson Jun 29 '19 at 13:08

Why are there 360 degrees in a circle?

1 Answers1