[elihu]

My main frivolous gripe with math notation is how everyone uses radians by default, to the point where your first visual clue that something is an angle is not any kind of unit, but rather the fact that it's being multiplied or divided by some multiple or fraction of pi. I think that the most sensible universal angle unit is "rotations". So, 360 degrees is 1, 45 degrees is 1/8, and so forth. Radians are only useful for a few special cases, like determining how far a car rolls if it's 10 inch radius tire rotated by 300 radians. (I wonder if somewhere, there's a mathematician who has modded their car's tachometer to output radians per second rather than revolutions per minute, just to make the math work out easier...)

Anyways, programming languages generally follow math notation, and use radians for trig functions and so on. Usually that's not too much of a problem, but when applied to file formats like VRML which were meant to be human readable, the results are ugly.

For the most part though, I think math notation is pretty good. At least when compared to something like standard music notation, which is full of weird rules and historical accidents.

[mannerheim]

Algorithms for calculating trig functions would probably not look good using degrees. Maybe it might look OK with what I assume is what's usually used (lookup tables + interpolation?), but for the Taylor series expansion you have to multiply by powers of pi/180 everywhere.

Calculus is generally worse with degrees. The derivative of sin(pi/180 x) is pi/180 cos(pi/180 x). That's pretty inconvenient, especially if you're writing any sort of models that need to solve differential equations. Same reason base e is preferred for exponents.

[hervature]

Radians vs. degrees isn't notation, it's a convention. You even say the reason why it is the convention. That multiplying the radius by the radians gives you the circumference. It is the only representation of angles with this special property. I mean, why should 360 represent 1 rotation? Why not use rotations itself? That way 1/4 is 1/4, 1/8 is 1/8, and so forth.

[redsaz]

Using rotations is exactly what the poster proposed:

> I think that the most sensible universal angle unit is "rotations". So, 360 degrees is 1, 45 degrees is 1/8, and so forth.

It was a bit confusing because most of the post was about radians, then switched to degrees. It could have instead read:

> 2pi radians becomes 1 rotation. pi radians becomes 1/2 rotations. pi/2 becomes 1/4 rotations.

[neolog]

https://tauday.com/tau-manifesto/