[kccqzy]

That's actually exactly the question I asked my math teacher when I first learned about radians. I mean, I learnt degrees when I was very little, at an age when one tended not to question why, but I learned radians at an age old enough to question why. The answer I received was about making trigonometric identities cleaner: the derivative of sine becomes "just" cosine rather than a hypothetical turn-based sine (called usin by the article) having a derivative of a turn-based cosine multiplied by 2pi.

But this article seems to do a good job explaining that a lot of those 2pi factors appear when you deal with differentiation. So it seems useful to have both turn-based trigonometric functions and this new differentiation operator.

[paulddraper]

That's a really good answer.

And justification in general for "why radians" vs degrees, gradians, turns, whenever

[linuxdude314]

Due to the fact differential operators are linear and the nature of the accumulation of constants of integration it’s pretty easy to prove that the differential operator proposed is in fact equivalent to the standard derivative operator.

Source: used to tutor calculus and differential equations in college.

Generally speaking this is not a useful trick.

There are _plenty_ of amazing ways to leverage Euler’s identity but I fail to see how this is one of them.

[gerdesj]

I too fail to see a problem. There is a certain degree of trickiness in all walks of life. Sometimes there is a decent hack that simplifies things and sometimes there is a notion that is just as complex to deploy as the current state of the art and hence isn't worth pursuing.

Pi has a definition for a good reason. Sometimes a discipline has to put up with perceived oddities until the real, deep problem is surfaced, grappled with and kicked in the nuts until it gives up and allows a paper or two to emerge without ridicule. With luck it might really show some ankle and a Nobel heaves into view 8)

This isn't it for (n)Pi n Phy Sci.