Turns are better than radians
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Turns are better than radians
1–10 of 494 posts
Re: Turns are better than radians
#2I'm so glad someone else finally said this. This article takes the approach of simplicity of code, which I do agree with, but additionally I've been thinking turns would have to be more intuitive and easier to teach (particularly to disinterested teenagers) for YEARS, and I finally feel vindicated at least one person agrees with me.
Turns are really the most neutral way to count an angle. We don't use them for everyday physical things because the numbers we'd deal with would be too small to work well for feeble human minds, hence degrees. But for the mathematical world where we currently use radians, turns make so much more sense.
Re: Turns are better than radians
#3I'm so glad someone else finally said this. This article takes the approach of simplicity of code, which I do agree with, but additionally I've been thinking turns would have to be more intuitive and easier to teach (particularly to disinterested teenagers) for YEARS, and I finally feel vindicated at least one person agrees with me. Turns are really the most neutral way to count an angle. We don't use them for everyd…
... and the derivative of sin(x) is ... ?
Re: Turns are better than radians
#4I'm so glad someone else finally said this. This article takes the approach of simplicity of code, which I do agree with, but additionally I've been thinking turns would have to be more intuitive and easier to teach (particularly to disinterested teenagers) for YEARS, and I finally feel vindicated at least one person agrees with me. Turns are really the most neutral way to count an angle. We don't use them for everyd…
The mathematical world doesn't only use radians. Parametrizing with a factor of 2*pi is totally common. Sometimes it’s called the winding number which here is called turns.
But yeah the overall point is good. Use language appropriate to the problem at hand.
Re: Turns are better than radians
#5I'm so glad someone else finally said this. This article takes the approach of simplicity of code, which I do agree with, but additionally I've been thinking turns would have to be more intuitive and easier to teach (particularly to disinterested teenagers) for YEARS, and I finally feel vindicated at least one person agrees with me. Turns are really the most neutral way to count an angle. We don't use them for everyd…
So now the diameter is 1/pi turns?
Re: Turns are better than radians
#6My favourite way of handling angles was always with either unsigned char or 16bit unsigned int that was treated as 1/nth of turn. Usually in these cases cos/sin tables were pre-calculated for speed, although that need went away to an extent. As long as as the calculations wrap around on the underlying system, it makes angles much easier to manage, because angle1 + angle2 = angle3 is always within 0 to 255 or 0 to 65535. Unfortunately I mostly work with higher level languages now that have mostly dropped integer types.
If anybody knows how similar calculations can be easily achieved in JS for example, I'd love to hear about it. I'm sure there must be a better way than boundary checks and manual wrap-around.
Re: Turns are better than radians
#7I'm so glad someone else finally said this. This article takes the approach of simplicity of code, which I do agree with, but additionally I've been thinking turns would have to be more intuitive and easier to teach (particularly to disinterested teenagers) for YEARS, and I finally feel vindicated at least one person agrees with me. Turns are really the most neutral way to count an angle. We don't use them for everyd…
... and the derivative of sin(x) is ... ?
Right - there's a negotiation in terms of complexity. The coefficient baggage has to go somewhere.
For me I don't want to care which units I use (and I'm rarely inspecting the exact angle as a number) - consistency is most important. I'm rarely interested in the precise numerical value of an angle - it's just a thing in the graphics/physics pipeline somewhere.
I don't know if that makes me agnostic about this proposal or conservative.
Re: Turns are better than radians
#8That was quite convincing actually. I guess we all have this realization at some point in early math education.
Why is it 360 degrees? Mainly because that's a nicely divisible number, no other good reason. Sometimes you find a 400 degree system on calculators but it doesn't seem to be taught anywhere (is it a French thing?)
Then at some point you get shown radians, which relates the arc length to the radius. That somehow seems natural, but it does mean there's going to be this constant lying around somewhere in your calculations.
Parameterizing the angle as a proportion of how big it can be (number of full circles) seems pretty sensible. I mean if you can avoid the constant for at least some of your geometry, then why not?
Re: Turns are better than radians
#9Turns sound fine.
But they are turns of a circle of a given radius.
So as long as everything conforms to that coordinate system, we're groovy?
Radians (circle fractions) are generally preferred because we can compare, e.g. two planetary orbits, conveniently, no?
Or did I miss something?
Re: Turns are better than radians
#10This is quite convincing but it would have been more convincing if he'd acknowledged the downsides and explained why it is in radians in the first place. (On balance I think he's probably still right.)
Perhaps we can make new named functions that operate in turns, along the same lines as ln/log. sint, cost, etc. Ok maybe not cost.