Eli5: Why are circles specifically 360 degrees and not 100?
In: Mathematics
Some people split it up into 400 (“gradians”), some people split it up into 2*pi (“radians”). 2pi is the nicest for calculus, if it’s just for geometry then it doesn’t matter at all.
360 is just what we wanted to use. These are called “degrees”.
100 can be (and sometimes IS) used. These are called “gradians”.
There is a very deep mathematical reason why we **really** should be using “2 times Pi” as the value of a full rotation. These are called “radians”.
– The simple reason is “do a quarter rotation” is “normal”. And “do a 90 degree rotation” is bonkers if you think about it. Perhaps “do a half-Pi rotation” is also bonkers … but at least it’s natural mathematically.
– the deep math reasons are because of calculus and complex numbers. inverse tangent of 1 is exactly equal to a quarter rotation. And you can calculate it like this:
arctan(x) = x – (x^3 / 2) + (x^5 / 5) – (x^7 / 7) + …
arctan(1) = 1 – (1 / 2) + (1 / 5) – (1 / 7) + … = pi/4
The value that pops out of that is Pi/4. So really radians is the natural way.
Plus 1 rotation of a circle of radius `1` is 2 * pi * 1 = 2*Pi
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