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I have two questions

I am aware of the fact that historically babylonians used sexagecimal systems and it had mathematical advantage that the number $360^\circ$ has all divisors from $1$ to $10$ except $7$.

1)Does using $2520^\circ$ instead of $360^\circ$ give any other mathematical advantage?

2)What mathematical advantage does Radian system of Angles have over degree system?

Dheeraj Gujrathi
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    Do you know calculus? Because it matters for answering #2. – Dan Apr 12 '24 at 18:27
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    You have understood that the advantage of $360°$ : it has many divisors in particuliar angles 30°,45°,60°,90° that are used all the time, and it isn't a too sophisticated number. Taking a larger basis number, even if it has more divisor, is too complicated to manipulat for elementary tasks. – Jean Marie Apr 12 '24 at 18:45
  • @peterwhy,It certainly does answer second part of my question – Dheeraj Gujrathi Apr 12 '24 at 18:57
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    I've always thought that Plato's number was 5040, double your 2520 ; evidently that was the first translator; later translators vary. https://en.wikipedia.org/wiki/Plato%27s_number – Will Jagy Apr 12 '24 at 19:56

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There are reasons why radians are used instead of degrees, such as:

$\boldsymbol{a)}$ Radians are inherently tied with length

$\boldsymbol{b)}$ In calculus radians simplify formulas, Take for example $$ \frac{d}{dx}\left(\sin(x)\right)=\cos(x)\tag{Radians} $$ But for degrees $$ \frac{d}{dx}\left(\sin\left(\frac{\pi}{180^\circ}x\right)\right)=\frac{\pi}{180^\circ}\cos\left({\pi\over180^\circ}x\right) $$

$\boldsymbol{c)}$ Better for approximations $\sin\theta\approx \theta$ for small $\theta$

Also $2520^\circ$, was probably not chosen, being quite a big number

  • I don't understand "Any amount of degrees, are inferior to radians." – Jean Marie Apr 12 '24 at 18:42
  • @JeanMarie yes i agree, i have updated it –  Apr 12 '24 at 18:44
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    I think that a big reason that Babylonians chose 360°, besides it being a highly-composite number, is that it's a convenient approximation of the number of days in a year (365.242), making it useful for astronomy. – Dan Apr 12 '24 at 18:46
  • @Dan That being said I believe that both degrees and radians have use –  Apr 12 '24 at 18:47