Talk:Logarithmic spiral

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What type of spirals do subatomic particles track in cloud chambers?

a log spiral -- if the drag force is proportional to speed (which I doubt). (If a uniform magnetic field runs perpendicular to the complex plane, with Im(z) the strength of the field, -Re(z) the drag coefficient, and

x'

the velocity, then

x''=zx'

. Integrating twice is trivial.) 142.177.124.178 21:05, 20 Jul 2004 (UTC)

Is it "spiralis mirabilis" or "spira mirabilis"? I've seen both, which is correct?

According to my dictionary "spiralis" is used as an adjective, to mean "spiralling", whereas "spira" means "spiral". 99.233.27.82 07:30, 13 November 2007 (UTC) Jordan[reply]

I urge caution with the pedal curve comment (I merely preserved it); I suspect it's only so if the pedal point is the center/origin of the spiral. 142.177.124.178 20:27, 20 Jul 2004 (UTC)

D'oh, it's so obvious. If the pedal point is not the spiral's center then the pedal curve passes through the pedal point an infinite number of times. No log spiral passes through any point more than once. 142.177.124.178 06:58, 23 Jul 2004 (UTC)

I fixed my mistake in the differential geometric definition of the logarithmic spiral.MathMartin 21:50, 20 Jul 2004 (UTC)

Presumably some log spirals are exactly their own evolute (no rotation needed) ... anyone know which? They're the only such curves, ya? 142.177.124.178 07:33, 23 Jul 2004 (UTC)

'Cording to my ciphering, the evolute of

t\mapsto e^{zt}

is

t\mapsto {{\bar {z}}+z \over {\bar {z}}-z}e^{zt}

; if that's right, then the spiral is exactly its evolute iff

{\Re z \over \Im z}\left(2n+{\frac {1}{2}}\right)\pi =\ln {\Re z \over \Im z}

for some integer n. 142.177.124.178 18:05, 23 Jul 2004 (UTC)

z^t vs e^wt

I'd prefer it if

The spiral is nicely parametrized in the complex plane:

z^{t}

, given a z with Im(z)≠0 and |z|≠1.

were changed to use the exponential function directly, rather than relying on complex exponentiation .. there are difficulties there that we need not deal with in this article, plus the exponential function arises more directly from solving certain differential equations.

Comments?

RandomP 12:35, 19 May 2006 (UTC)[reply]

Go for it. Melchoir 21:09, 19 May 2006 (UTC)[reply]

Broken explanation of a and b

This bit of text is internally inconsistent:

with positive real numbers a and b. a is a scale factor which determines the size of the spiral, while b controls how tightly and in which direction it is wrapped. For b >0 the spiral expands with increasing θ, and for b <0 it contracts; the only difference between positive and negative b being that one spirals to the left and the other to the right.

If b is a positive real number it can't be < 0. "Positive real number" is a left-over from the original formula $r=ab^{\theta }$ . We could let b be a real number (and note that for b = 0 you get a circle; b = 1 in the original formula), or we could go back to the original formula.

Negative b won't cause it to spiral to the left. I think the confusion here stems from the word "direction" which I think was meant to indicate inward/outward. I therefore suggest to change it to "direction (inward/outward)". By the way, negative a would make the spiral turn to the left (in essence it mirrors the spiral over the X axis), but we've posited that a is a positive real number. We could drop the "positive".

24.6.122.223 13:40, 24 May 2006 (UTC)[reply]

And that's not all that's broken: "scale factor which determines the size of the spiral"? That's just nonsense. Anyway, a negative a in r=a exp(rt) wouldn't mirror over the X axis; remember we're in polar coordinates. I'll have a go at fixing it... Melchoir 14:21, 24 May 2006 (UTC)[reply]

Merge spira mirabilis

someone suggested we merge Spira mirabilis into here, but didn't start the discussion.

Support. That article is just a stub on the same topic as this one, and includes misinfo e.g. about divine proportion. Dicklyon 00:10, 12 October 2006 (UTC)[reply]

Support. We don't need multiple articles on the same thing just because there are multiple names for it. —David Eppstein 19:03, 15 October 2006 (UTC)[reply]

I merged in a few bits already. All we need to do now is remove the merge tag and convert spira mirabilis to a redirect. And maybe integrate better that what I've done. Any objections? Dicklyon 19:50, 15 October 2006 (UTC)[reply]

Cut-the-knot

Dicklyon has removed the link to cut-the-knot, twice, the first time claiming that it's an adsite, and after I reverted pointing out that it's a legit math site he did it again saying that it has no useful content. I feel this is untrue — the link has an applet demonstrating the self-similarity described in the second paragraph of the article's notes section, and can be used as a source for the (currently unsourced) content in that paragraph, but I don't think getting into a revert war is an appropriate way of handling this. Anyone else want to weigh in? —David Eppstein 18:39, 18 December 2006 (UTC)[reply]

I had a hard time finding any useful content there. But the ads were sure prominent. If anyone else thinks it's worth keeping, I'll leave it alone next time. I didn't see an applet doing anything (I'm on Firefox, Mac OSX), and the explanation link didn't go to a useful place. Here's the link in question:

Alexander Bogomolny, Spira Mirabilis - Wonderful Spiral, at cut-the-knot

Dicklyon 19:21, 18 December 2006 (UTC)[reply]

The applet has two control points shown as pink circles — you can drag them to scale the spiral and see that it doesn't change shape. It also has an option to superimpose two spirals, one with the control points and the other fixed. I have no trouble seeing the applet on Camino and Safari under MacOS X. —David Eppstein 19:44, 18 December 2006 (UTC)[reply]

OK, I guess I should learn to read. Good enough. Dicklyon 21:44, 18 December 2006 (UTC)[reply]

nature / spider web

I believe most spider webs are NOT logarithmic spirals. There tends to be a slight increase in distance between successive rings, but not in proportion to r. See e.g.:

http://gallery.pasty.com/d/141182-2/Spiderweb.jpg

 Xiutwel ♫☺♥♪ (talk) 21:57, 22 December 2007 (UTC)[reply]

Logarithmic Spirals in Nature

The section on Logarithmic Spirals in Nature is interesting, but requires sources. 205.118.82.151 (talk) 02:22, 6 May 2010 (UTC)[reply]

Have any subparticle paths (resulting from particle collisions) been determined to be logarithmic (or golden or Fibonacci) spirals? Thanks! -- TimeDog (talk) 03:55, 14 September 2008 (UTC)[reply]

Broken SVG figure?

In the first picture (http://en.wiki.x.io/wiki/File:Logarithmic_spiral.svg) the spiral doesn't display in IE or Safari, but the polar grid does display. If I click through to the file itself in Safari the spiral appears. Davidgladstein (talk) 06:52, 2 January 2009 (UTC)[reply]

It doesn't work in my Camino browser, either, nor FireFox on Mac. Probably a WP/SVG incompatibility of some sort provoked by the matlab-created SVG. Dicklyon (talk) 07:03, 2 January 2009 (UTC)[reply]

Hi, the observation is corect, as the someone also observed at the picture site. I will recover an older one until someone more capable solves this.Alecsescu (talk) 01:17, 20 January 2009 (UTC)[reply]

Still not working in my browser 91.109.212.229 (talk) 11:37, 22 March 2009 (UTC)[reply]

I hope it's all fixed now. I've uploaded a new version of the figure and it seems to show up alright. Morn (talk) 21:51, 3 September 2009 (UTC)[reply]

Self-congruence

I want to ask about this before editing. There is a sentence "Logarithmic spirals are self-similar in that they are self-congruent under all similarity transformations (scaling them gives the same result as rotating them)." I think "congruent" is not a valid term here, since congruences are supposed to preserve size. Also, surely the word "all" can't be correct: you can't apply any old similarity transformation to a logarithmic spiral and find that it's unchanged. Only selected similarities are symmetries of the spiral. Ishboyfay (talk) 00:28, 4 February 2013 (UTC)[reply]

I rewrote it in an attempt to be more careful; I hope you agree it's an improvement. —David Eppstein (talk) 01:12, 4 February 2013 (UTC)[reply]

Wrong spiral on grave stone

Maybe a image would be nice? Is on his wiki page — Preceding unsigned comment added by 178.83.37.67 (talk) 11:25, 13 July 2018 (UTC)[reply]

Table of symbols needed

This article needs to list (possibly in a table?) what the letters and symbols mean/stand for. That will make this article readable/useful to those of us who don't know what $\in$ or $\mathbb {R}$ are, etc. (And if you're going to explain what e is, makes sense to also explain what i is.) — Preceding unsigned comment added by Niccast (talk • contribs) 21:30, 23 February 2020 (UTC)[reply]

Distance 'a' from the origin of the starting point.

It is true that I have not mentioned reliable sources, the source is me. I am grateful to Wikipedia for using it, with the necessary critical spirit, also comparing the English version with the Italian one. My contribution that was canceled, I had put it in the queue to an entry in which, in my opinion, it must be specified that in the equation 'a' it only determines the distance from the origin of the starting point. Rotation or orientation is only a consequence. 52Dante21 (talk) 12:23, 1 August 2020 (UTC)[reply]

Sunflower heads

Sunflower heads are mentioned (somewhat lost) in the "Spira Mirabilis" section. The spirals used in modelling sunflower heads are parabolic, not logarithmic. The appearance of logarithmic spirals should be better documented. Ci47 (talk) 05:41, 1 March 2021 (UTC)[reply]

Even the emergent spirals are not logarithmic! —Tamfang (talk) 23:25, 29 March 2024 (UTC)[reply]

Yes, lots of popular-mathematics sources are very sloppy about distinguishing logarithmic spirals from other spirals and that sloppiness spills over into our articles. That was a lot of my motivation for recent cleanups of hyperbolic spiral (after seeing someone exclaim about how a photo of a spiral staircase showed a logarithmic spiral when actually it was hyperbolic). —David Eppstein (talk) 23:52, 29 March 2024 (UTC)[reply]

Also, not every log.spiral is the golden spiral. Sigh. —Tamfang (talk) 04:10, 31 March 2024 (UTC)[reply]