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Turns are better than radians

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Re: Turns are better than radians

#171

Post by eesmith »

SuchAnonMuchWow wrote: post #54
eesmith wrote: post #23

Earlier quoted context omitted.

It's a correct description. (Perhaps further refined as "technically correct".) The following are not exact values of π or τ, only approximate ones: >>> import math >>> math.pi 3.141592653589793 >>> math.tau 6.283185307179586

The effort wanted to replace all uses of Pi (including the ones in math formulas) and not just their use in (floating-point) computer programs where we implement approximations of those formulas.

Sure.

But just because there was {a lot of work to replace all uses of pi with tau} doesn't mean there wasn't {a lot of work to replace all approximate uses of pi with approximate uses of tau in computer programs}.

Re: Turns are better than radians

#172

Post by Olreich »

doliveira wrote: post #148
Olreich wrote: post #130

Earlier quoted context omitted.

If you go watch math lectures, there's a bunch of "x means Puppy Constant" or, "let's substitute in k for the Real component", or "let's signify by collecting these terms into a variable". My argument wouldn't be to replace ALL the variables with meaningful names, just the ones with a lot of meaning that a reader might not understand. It'd also be great if constants, variables, and functions all got naming convention…

Again, try to solve the Schrodinger Equation for even an infinite well using long variable names.

Got a reference for what that looks like with current notation? The internet is basically just showing the starting equation and ending equation and skipping all the intermediaries.

Re: Turns are better than radians

#173

Post by throwawayffffas »

Well I don't think they are. Sure they make computing the function simpler. But I would hazard that most people that use these functions are not doing geometry and they are already working with radians. In short if you give any kind of engineer working on any kind of signal processing domain a sine function where sin(1) = 0 you are only going to confuse them.

PS: that's why mathematicians don't use turns they are mostly not doing geometry and radians in that case typically make for better formulas.

Re: Turns are better than radians

#174

Post by sbaiddn »

Saying "rad" are bad units for sin is like saying e is a bad base for logarithms.

The only "bad" thing about rads is that they're not taught early enough so that culturally 45 degrees are not know as pi/4. Then a turn would be known as simply as 2pi (or "a one eighty" as Americans infuriatingly like to call it when someone rotates 360 about themselves)

Re: Turns are better than radians

#175

Post by kortilla »

WastingMyTime89 wrote: post #67
fbanon wrote: post #32

>But math never decreed that sine and cosine have to take radian arguments! Ummm, actually it did. The Taylor-series of sine and cosine is the simplest when they work with radians. Euler's formula (e^ix = cosx + isinx) is the simplest when working with radians. Of course you can work in other units, but you'll need to insert the appropriate scaling factors all over the place. "Turns" don't generalize to higher dimens…

The writer don’t seem to realise that radian is not an arbitrary unit but a dimensionless one which is defined so that 1rad is actually just 1. Reading the submission and the comments here, I’m under the impression that trigonometry is not extensively taught in middle schools and high schools in the USA. While I’m slightly envious you might not have to suffer developing powers of cosine and sine but that would explai…

> Am I wrong?

Yes. Trigonometry is extensively taught in the US. People forget this stuff if they don’t use it.

Ask some 30 year old chef in whatever country you fantasize teaches properly to compare and contrast turns vs radians and you’ll get similar responses.

Re: Turns are better than radians

#176

Post by fluoridation »

bonzini wrote: post #131
11235813213455 wrote: post #109

Earlier quoted context omitted.

any angle unit is dimensionless, radian is no exception

But they're not equal to 1, for example a degree is 0.01745...

1° is actually 0.0174... radians. 1 radian is 57.295...°. The choice of unit to specify an angle is arbitrary.

Re: Turns are better than radians

#177

Post by aaaaaaaaaaab »

weinzierl wrote: post #147
genewitch wrote: post #110

Earlier quoted context omitted.

I was a bad student through 8th grade, but managed to get selected for a STEM magnet school. I was supposed to enter 9th grade with Geometry, then algebra II, trig, Calc for the 4 years. But they discovered i'd never passed algebra prior, they put me in algebra, which means i would have finished in trig. Due to a crazy 3.5 years, i never got a high school math education. Calculus makes my eyes glaze over, and all i k…

"[..] and then C never made sense to me" I had my fair share of higher math, but C never made really sense to me either. It's not us, it's C that's to blame.

So which programming language makes sense to you? Dare I say… Rust?

Re: Turns are better than radians

#178

Post by johnbcoughlin »

dosshell wrote: post #159
fbanon wrote: post #32

>But math never decreed that sine and cosine have to take radian arguments! Ummm, actually it did. The Taylor-series of sine and cosine is the simplest when they work with radians. Euler's formula (e^ix = cosx + isinx) is the simplest when working with radians. Of course you can work in other units, but you'll need to insert the appropriate scaling factors all over the place. "Turns" don't generalize to higher dimens…

I was taught that Eulers formula defined complex exponents? If we used turns for cos and sin we could redefine what e^ix means so it works without radians. From the other answer I guess this is completely wrong... (I do understand it is nuts to redefine, i'm just interested as a theoretical thought) Now, how is Eulers formula is deduced? How did we figure out what e^ix means?

One way to understand where the formulas come from is the power series of e^x, remembering that that function is (can be) defined as the function whose derivative is itself. Sin and cos are functions whose second derivative is -sin and -cos respectively. If you plug in ix to the power series for e^x, the complex exponential comes right out.

There are a couple other "paths" to this result, and the choice we have is by far the most elegant.

Re: Turns are better than radians

#179

Post by krastanov »

nkurz wrote: post #108
throwaway9870 wrote: post #91

Earlier quoted context omitted.

Just out of curiosity, where did tau come from? I never heard of it used for 2pi, and frankly, it seems like a poor choice because in engineering it is one of the most common symbols used (time constant tau).

It apparently was chosen because it's the starting sound of "turn": Hartl chose tau to represent 2pi because it nicely ties in with the Greek word “tornos,” meaning “turn,” and “looks like a pi with one leg instead of two.” https://blogs.scientificamerican.com/observations/the-tao-of... There was an earlier effort that used a new "two pi" symbol consisting of a "π" with an extra leg in the middle: https://www.math.ut…

Funny coincidence: π with an extra leg is the Cyrillic cursive letter for the sound t.

Re: Turns are better than radians

#180

Post by estomagordo »

sbaiddn wrote: post #174

Saying "rad" are bad units for sin is like saying e is a bad base for logarithms. The only "bad" thing about rads is that they're not taught early enough so that culturally 45 degrees are not know as pi/4. Then a turn would be known as simply as 2pi (or "a one eighty" as Americans infuriatingly like to call it when someone rotates 360 about themselves)

Hmm. I don't think I have ever witnessed someone describe a full rotation as a one eighty.
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