Eli5: Why are circles specifically 360 degrees and not 100?
In: Mathematics
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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