Hacker News Board Hacker News, browsed like a classic message board
Live data from Hacker News

Turns are better than radians

computerenhance.com

Post reply on HN
Print view View original

181–190 of 494 posts

Re: Turns are better than radians

#181

Post by fluoridation »

littlestymaar wrote: post #113
jgwil2 wrote: post #85

Earlier quoted context omitted.

Are you claiming the author is incorrect that x/0 = 0 is mathematically sound?

Depends how you define “soundness”, but the idea of prolonging a function out of its definition domain with an arbitrary value that doesn't make it continuous is arguably a curious one. From an algebra perspective (the one given in the blog post) it may be fine, but from a calculus perspective it's really not. The lack of continuity really hurts when you add floating points shenanigans into the mix, just a fun exampl…

But for 1/x you have that issue anyway. If x is on the negative side of the asymptote but a numerical error yields a positive x, you'll still end up with a massive difference.

Re: Turns are better than radians

#182

Post by adrian_b »

i_no_can_eat wrote: post #83
adrian_b wrote: post #63

Earlier quoted context omitted.

The simplicity of the Taylor series of sine and cosine is irrelevant, there are no important applications for those series. There is only one consequence of those series that matters in practice, which is that when the angles are expressed in radians, for very small angles the angle, its sinus and its tangent are approximately equal. While this relationship between small angles, sinuses and tangents looks like an arg…

> there are no important applications for those series. Excuse me? Have you done any computation in Physics? Have a look at the pendulum equation, for a start...

Only in school exercises you can solve a differential equation by expanding a sine function into a Taylor series.

In practical physics computations, the solution of differential equations requires numerical methods that do not use the Taylor series of specific functions, even if the theory used for developing the algorithms may use the Taylor series development of arbitrary functions.

For accurate prediction, the simple pendulum equation also requires in practice such numerical methods, which do not rely on the small-angle approximation that enables the use of the Taylor series of the trigonometric functions, for didactic purposes.

Re: Turns are better than radians

#183

Post by js2 »

kortilla wrote: post #175
WastingMyTime89 wrote: post #67

Earlier quoted context omitted.

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.

I'm a 50 yo programmer. I have a CS degree. I don't even remember my college calculus much less my high school trig. I just haven't had cause to use it in my career, not as a sysadmin, not as a programmer. My son is taking calc 3 and I knew I happened to have my calc 3 notes from the mid-90s, so I pulled them out of the filing cabinet and my very carefully taken notes, my proofs, my hand drawn graphs, it was all gibberish to me. That was stuff I knew like the back of my hand when I graduated but it quickly faded away.

Re: Turns are better than radians

#184

Post by ascar »

weinzierl wrote: post #160
ascar wrote: post #64

Earlier quoted context omitted.

I already learnt in school to calculate trigonometry using radians or turns depending on the situation. It was part of the general math curriculum in Bavaria. As far as I am aware both are mathematically sound and there is no reason to religiously use one of them over the other. Let your use-case or input parameters decide. The examples given in the article definitely make no sense in radians.

"I already learnt in school to calculate trigonometry using radians or turns depending on the situation. It was part of the general math curriculum in Bavaria. " Out of interest, when did you go to school in Bavaria and in which grade did you learn about turns? I was in school in Bavaria a long time ago and I don't remember learning about turns there. Could very well be that I forgot or our teacher forgot to teach it…

That should've been about 15 years ago. I don't remember the grade, but based on the subject probably 8th or 9th? I thought it was in the textbook but possibly our teacher just added it himself.

Re: Turns are better than radians

#188

Post by PaulHoule »

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.

C puts the C in Cthulhu.

Re: Turns are better than radians

#189

Post by RunSet »

jgwil2 wrote: post #85
fbanon wrote: post #71

Earlier quoted context omitted.

Or just defining the result of division by zero as zero "for safety": https://www.hillelwayne.com/post/divide-by-zero/ It boggles the mind, truly!

Are you claiming the author is incorrect that x/0 = 0 is mathematically sound?

I don't know about "mathematically sound" but I would rather retain the convention that any number divided by itself equals 1.

Re: Turns are better than radians

#190

Post by RunSet »

chucksmash wrote: post #162
RunSet wrote: post #145

Earlier quoted context omitted.

> Worst I've seen so far was one arguing that equations should be written with long variable names (like in programming) instead of single letters and Greek letters. That could never work. If anything the words comprising mathematical texts should be defined once and thereafter truncated to their first letter to reduce cognitive burden and facilitate greater comprehension. c = "could"; d = "don't"; f = "for"; g1 = "g…

Reference Error: s is not defined.

Thanks for the correction. I will be sure to credit you in the acknowledgements.
Post reply on HN