> Degrees are completely arbitrary
Degrees are very natural in the context of ancient astronomy/astrology, where you have (1) ~365 days in a year, so that if you look at the path of something that takes a year you get about one degree change per day but with a number that is more easily divisible. (2) approximately 4y, 10y, 8y, 15y, 12y, 30y cycles for the moon and various planets. (3) A calendar with 12 months, 12 zodiac signs. (4) A timekeeping system which breaks days into 24 hours and then uses divisions by sixty for smaller units. (4) A base-sixty number system – from ancient Mesopotamia, which persisted as the standard for astronomical calculations for millennia, only displaced in the very recent past.
Re:Turns are better than radians
by sicariusnoctis on Monday September 26, 2022 @03:53PM
(#32987506)
All those approximations have error and the behaviour you describe depends on where you are on Earth. Moreover, degrees are not natural from a mathematical perspective.
Out of curiosity, given a degree/calendar/time system could one localize the culture that created it?
You can tell that 'gradians' (and 'decimal time') were created by the base-ten-obsessed French revolutionaries who brought us the metric system.
There are infinitely many sinusoidal functions out there. You can just adjust amplitude, frequency and phase to your heart's content.
Trigonometry basically requires that sine and cosine have specific amplitudes and phases, but gives not one shit about how you map angles to frequency. Degrees are completely arbitrary, but both radians and turns have pretty natural definitions, with turns indeed being the easiest to work with. So far so good.
Calculus does have an opinion on frequency, though. There is exactly one non-trivial pair of sinusoids s(x) and c(x) where c'(x) = - s(x) and s'(x) = c(x), among a bunch of other very useful properties.
When you put calculus and geometry together, s and c are have the same amplitude and phase as sine and cosine from geometry, and the two pairs are exactly the same if you match the frequencies such that the argument is the angle measured in radians. It's just so damned useful to use angles in radians and make everything play together nicely.