Talk:Archimedean spiral

The obvious

Search for "Archimedes". Alternatively, use common sense - he was the one that invented it. See his scroll "On Spirals".

OK, whoever posted that question is pretty useless. But here, the "obvious" could be misleading. There are certainly many things not named after their inventors, but after someone the inventor wanted to honor. Uporządnicki (talk) 14:59, 15 February 2019 (UTC)

2024

By definition of $r=\theta$; and over the complexes, $z=|z|e^{i\arg(z)}$: we have $z=re^{i\theta }$. Since $r=\theta$, we can rewrite as $ye^{iy}=x$ with real x and real y and solve for y:

$i\left(ye^{iy}=x\right)$

$W_{n}(iye^{iy}=ix)$

$-i\left(iy=W_{n}(ix)\right)$

$y=-iW_{n}(ix)$

Where $W_{n}$ is the Lambert W function over the complexes. In other words, $-iW_{n}(ix)$ is the set of complexes whose radii and angles are one and the same in magnitude, and Archimedes' Spiral is represented algebraically by this function.

Andrew T Porter (talk) 02:21, 18 April 2024 (UTC)

Length

I am wondering about the arc length of the Archimedean spiral, in particular, at $\theta =2\pi$ and $r=1$. Why is there not a section about this? Is it ${\sqrt {1+(2*\pi )^{2}}}$ which is OEIS: A233700? John W. Nicholson (talk) 21:34, 10 March 2015 (UTC)

Missing the point

The point of Wikipedia is actually not to impress one's fellow fanboys. It is to provide knowledge to the world. (Note the appearance of the Wikipedia logo.) Articles such as this one, which could have the ability to educate the public, don't. Nor do they even try. Pity that Wikipedia does not attract editors who understand the gulf between their understanding and that of the masses, and attempt to do something about it. This "show-off for my bros" approach to writing for Wikipedia is not going to stand the test of time.--71.36.123.89 (talk) 06:32, 22 October 2016 (UTC)

exactly. i am not mathematically trained tho i am a mensan, so the gobbledegook in the article is frustrating, to say the least. try to relate it to something concrete, that's usually the best.70.31.164.76 (talk) 18:51, 21 June 2022 (UTC)

Definition of the parameter a

Concerning the function of the parameter a in formula for the Archimedes spiral, $r=a+b\theta$, the beginning of the article has this statement, "Changing the parameter a will turn the spiral, while b controls the distance between successive turnings." The second half is right but I don't think the first half is. Changing the parameter a does not turn the spiral; at least not if turning is understood as turning it around its axis which projects out of the plane. Changing the parameter a enlarges the "hole" in the middle of the spiral; that is, instead of starting at the origin when $\theta =0$ it starts at a distance a to the right of the origin. Perhaps the meaning of "turning the spiral" needs to be made more clear? Skinnerd (talk) 02:40, 21 November 2018 (UTC)

You know, I obsessed for a while over that very point. Yes, in the equation as given, when the angle θ is zero, the point will be at a distance "a" from the origin. But then I realized, one can consider the angles going negative. As θ goes less than 0, the spiral will, so to speak "spiral inwards." When bθ--b times the angle--is equal to -a, the curve will meet the origin. Now--to put things with a complete lack of mathematical precision, but in a way that might conjure a mental picture that makes things clear--just how far the spiral has to "spiral inwards" to meet the origin will determine which way it's going when it meets the origin. Which, in effect, rotates the spiral. Uporządnicki (talk) 14:56, 15 February 2019 (UTC)

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Code for producing an Archimedean spiral

I don't know the "R" language, so I'm having difficulty telling what the code does. If it produces a simulated appearance of a curve by squishing a lot of dots together, or connecting the dots with short straight line segments, then I'm not sure it's worth including on the article. If it produces an actual curve (e.g. beziers of some kind), then maybe that should be stated... AnonMoos (talk) 22:57, 25 November 2020 (UTC)

I'm not really sure what the point of providing plotting code is either as most math software/function plotters can plot parameter curves directly (like they can plot functions as single command). Illustrating a special sollution in R or with Python library seems to have littlr value for general readers (who in doubt are more likely to use a plotter/math software), the only readers for who that seems beneficials are (bew) programmers in python or R, which is imho too specific to warrant an inclusion into a encyclopedic article.--Kmhkmh (talk) 10:07, 9 February 2021 (UTC)

I agree, the code should be removed. It provides no additional information about the spiral. Nearly any graphical system (for example geogebra) is able do display a parametric curve--Ag2gaeh (talk) 16:54, 9 February 2021 (UTC)