Where did 360 degrees came from? Why is it 360 and not another number?
In: Mathematics
360 is three 2s times two 3s times one 5. So it’s the three smallest numbers people divide by with the smaller ones used more often.
3360 is great for dividing.
360 divides evenly by 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180.
100 divides evenly by 2, 4, 5, 10, 20, 25, 50.
With 100 you can do halves and quarters. You can do fifths and tenths.
With 360 you can do halves and quarters; fifths and tenths; thirds, ninths, and eighteenths, etc.
https://en.wikipedia.org/wiki/Degree_(angle)#History
Summary: We don’t know for sure. It might be because early applications of circles were largely for astronomy, and a year is 365 days long (which with early inaccurate methods of measurement meant some calendars were 360 days long). 360 is also fairly easy to work with, because it has so many divisors. It perhaps just got taught onwards from there because no alternative was obviously better.
It was an estimate of how much the positions of the stars change each night (which is an estimate of the length of the year) the civilization who did it used base 60 mathematics so it was a really good number to use.
360 is a highly composite number, which means it can evenly be divided in many fractions without decimals
1/2 rotation is 180º 1/3 rotation is 120º, 1/12 is 30º 1/4 is 45º
And this can be better than fraction decimals or fractions
You can divide 360 a lot of ways and get nice whole numbers, and that’s nice enough that people stuck with it. The French did some hokey pokey with a 100^o right angle around when they invented the metric system but that part didn’t really stick except for civil engineers who measure the steepness of a hill in percent (they also did some weird stuff making clocks and calendars based on making everything nice multiples of ten that didn’t stick either).
Worth noting that the natural unit for angle is the Radian. This is the angle you get if you trace out one radius of length along the arc of the circle. It’s about 57°
Problem with the radian is that it generally involves using fractions of a radian in our calculations. That’s a hassle we’d rather avoid if we can.
So we do. We create some number that represents a full circle, and divide that up accordingly.
If we think smart, we want a number that is
1. sufficiently large that even small angles are likely to be integers
2. capable of being evenly divided by the most numbers
You can go through and find the number of factors any given number has, but 360 is about as good as it’s going to get.
You’ve got:
1,2,3,4,5,6,8,9,10,12,15,18
And that’s just the first 5% of numbers out of 360.
We don’t really know why but there are a few theories. It’s thought that Greeks made isosceles triangle at 60 so they had to make it 360 or the Babylonian’s choice it because it’s a nice round number with 24 whole number it can divide into
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