Eli5: Why are circles specifically 360 degrees and not 100?
In: Mathematics
Because we made it up. Back when they were figuring out geometry, they divided circles into 360 because it can be broken down evenly into a lot of different numbers.
360 is a multiple of, and can evenly be divided into: 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 pieces.
100 only has 1, 2, 4, 5, 10, 20, 25, 50, and 100.
Being able to break it down in more ways without dealing with fractions or decimals turned out to be useful.
They could be. You could make up your own unit for 100th of a circle. And call it a Centagree.
We use a unit that is a 360th of a circle, because it’s more convenient. There are more numbers that can easily be broken out without using decimals.
The ancient people who first figured out a lot of circle math did not use a base-10 number system like ours. They used a base-12 number system and counted the knuckles on their not-thumb fingers. 12 is a pretty nice number like 10. It divides evenly by 2 and 3. It was convenient for their math so that’s what they picked. (You can make a lot of arguments it’s more convenient than base-10, but base-10 is still pretty good and we’re real used to it.)
So they divided a circle into 360 degrees. They divided each degree into 60 “minutes”. They divided each “minute” into 60 “seconds”. They picked these numbers because 5 * 12 felt convenient to them I guess. Now you also sort of see how we ended up with our time-telling system: they divided that circle into 12 then reckoned why not keep the minutes/seconds divisions since it was convenient to have more divisions at smaller scales.
I think this was the Babylonians, I’m not sure. Either way, whichever people did it were the biggest empire at the time so they got to teach everybody how to do things. Eventually they fell, but people were used to using these systems and didn’t feel like changing them. How’d people end up with base-10 for other things? The *next* empire showed up with base-10, but didn’t have all of the geometry and other math the Babylonians did, so they just lifted it and kept it as-is because it’s stupid to rewrite an entire branch of math just to change the base, it’s smarter to just keep building on what’s there.
The ancient Babylonian calendar said that there are 12 months of 30 days, and thus 360 days in a year (which got periodically adjusted by big-ass leap years to make up for the 5.25 missing days). This was based on their understanding of astronomy and charted by the movement of constellations.
in ~200 BC the Greek astronomer Hipparchos of Rhodes was studying ancient Babylonian astronomy and needed to do some angular calculations, as astronomers very often do. Since the Babylonian constellations where assumed to move through 360 days, Hipparchos divided a circle into 360 parts, and the concept of the 360-degree circle was born.
We kept this system because it’s actually pretty good, since 360 can be evenly divided very many ways, though these days radians are in more common use because they’re even better.
But it all comes from ancient Greeks studying a fucked-up calendar that was considered ancient by the ancient Greeks.
360 actually comes from the number of days in a year. When early civilizations tried to measure a year they often came up with numbers a little over 360. Thinking the world was made by gods and made sense they decided 360 made sense.
As in a year the stars circle the earth if looked at at the same time, the idea of a year and a circle were very tightly related to each other.
So every degree represents a day.
The Babylonians made it up. They thought it was cool that there are so many ways to divide it up. It’s also why we have 60 minutes in an hour, 60 seconds in a minute. There are also 60 arcminutes in a degree and 60 arcseconds in an arcminute. It’s factors of 60 all the way down.
Having 100 degrees doesn’t make things any easier, really. We mostly talk about angles in triangles, or other acute angle situations, so then you’d mostly have numbers like 25, which still aren’t round and which are harder to subdivide into the angles we normally consider significant like halves and thirds of a right angle.
The only subdivision of a circle that naturally falls out of circle math is radians, where one radian is the angle whose arc length is equal to the radius, and a full circle is 2π. But that’s a pain in casual conversation or for specifying any angle that isn’t a simple fraction of π, so we might as well go with whatever we’re used to using, which happens to be 360 degrees.
A degree is just a word we made up to describe 1/360th of a full rotation.
It should, therefore, not be surprising that 360 degrees gives you a full rotation.
You can make up a new word to describe 1/100th of a full rotation. For sake of argument let’s call that a cenrotal.
It should not be surprising that 100 centrotals makes a full rotation
In addition to what other people are saying, during the creation of the metric system, there was an attempt to create a base ten version of angle. The Gradian.
There are 100 Gradians in a right angle. This sounds nice and reasonable, until you realize what angles come up the most often in practical situations. 30, 45, 60 and 90
45 degrees turns into 50 grad, and 90 degree turn into 100 grad. Those ones work perfectly fine.
However, 30 and 60 degrees turn into 33.33 and 66.66 grad. If you are changing into a base ten decimal system, have two of the most common values be repeating decimals is awkward and unwieldly. While scientists were perfectly happy to switch to to kilograms and meters, nobody wanted to switch to Gradians.
To add to the other responses, when the French were developing their “metric” system following the French Revolution, they did come up with [a 10-based system for angles](https://en.wikipedia.org/wiki/Gradian).
Rather than splitting a circle into 100, they split a right-angle into 100. One gradian, or gon, if 1/400 of a full turn (or 9/10ths of a standard degree). While it didn’t take off as much as other decimal measurements, it is still used – particularly in some areas of surveying and mining, especially by the French. Many scientific calculators will have an option to give angles in gradians (along with degrees and the mathematically-more-satisfying radians).
They also developed a decimal system for time; from 1794 to 1800 the French Republican calendar divided the day into 10 hours, with each hour having 100 minutes, and each minute having 100 seconds (giving a slightly shorter second, one decimal second lasting only 0.86 conventional seconds).
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