4 ms·

I'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 tu

I'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.

CogitoCogito 4y ago
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.
pestatije 4y ago
So now the diameter is 1/pi turns?
- ncmncm 4y ago
  No, 2/tau turns, philistine. ;-)
jjgreen 4y ago
... and the derivative of sin(x) is ... ?
- jan_Inkepa 4y ago
  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.
  - ncmncm 4y ago
    When you store a value that will be reused, like in an array of points, if every time you walk the array multiplying by a constant, you should seek to store values in such a way that it does not need that treatment. If you are taking sin and cos each time through (presumably, added to some angle), it should be pre-multiplied for the fastest implementation of sin and cos available.
- trashtester 4y ago
  Re(exp(ix)). Using degrees, turns, etc instead of radians, is like using 10^y instead of e^x (where y=x/ln(10)). Useful for many practical things, but useless for a lot of math applications, especially involving differential equations, complex numbers etc.
- Dan42 4y ago
  > and the derivative of sin(x) is ... ? I believe it's cos(x). And I fail to see how that would change regardless of what unit x is expressed in. Sorry, my trig is veeery rusty.
  - jjgreen 4y ago
    Only when the angle is in radians ...

CogitoCogito 4y ago

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.

pestatije 4y ago

So now the diameter is 1/pi turns?

ncmncm 4y ago
No, 2/tau turns, philistine. ;-)

jjgreen 4y ago

... and the derivative of sin(x) is ... ?

jan_Inkepa 4y ago
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.
- ncmncm 4y ago
  When you store a value that will be reused, like in an array of points, if every time you walk the array multiplying by a constant, you should seek to store values in such a way that it does not need that treatment. If you are taking sin and cos each time through (presumably, added to some angle), it should be pre-multiplied for the fastest implementation of sin and cos available.
trashtester 4y ago
Re(exp(ix)). Using degrees, turns, etc instead of radians, is like using 10^y instead of e^x (where y=x/ln(10)). Useful for many practical things, but useless for a lot of math applications, especially involving differential equations, complex numbers etc.
Dan42 4y ago
> and the derivative of sin(x) is ... ? I believe it's cos(x). And I fail to see how that would change regardless of what unit x is expressed in. Sorry, my trig is veeery rusty.
- jjgreen 4y ago
  Only when the angle is in radians ...