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I'll be translating additional material from the German article de:Spirale. So as to add some nice illustrations to it, I've asked German Wikipedian de:Benutzer:Karl Bednarik if he would mind regenerating his contributed images, saved in PNG format (more appropriate for line-art). I'll use the GFDL'd JPGs otherwise. Hooloovoo 13:22, 13 Apr 2005 (UTC)

Any progress on that? - RoyBoy 800 02:50, 8 Jun 2005 (UTC)
Apparently not. Hooloovoo hasn't been back to Wikipedia since May 1, 2005. Angr/talk 10:11, 2 February 2006 (UTC)

Pop culture[edit]

Does there really have to be a pop culture section with two entries? One of them a manga? I took it out for now ~ sorry, no account —Preceding unsigned comment added by (talk) 23:25, 1 April 2007

spooky spiral

Cuberoottheo (talk) 13:01, 11 May 2015 (UTC)

Right versus left-handed[edit]

Perhaps a section dealing with right verus left handed spirals should be considered? --Seans Potato Business 19:39, 28 April 2007 (UTC)

Spirals are not symmetric, but I'm not sure what we could say about chirality that would add to the article. It would be an excellent point in the Art section, at least - and I'm certain there's much more to be said about spiral motifs in art than I'm qualified to say. Wyvern (talk) 06:51, 5 August 2011 (UTC)

3d spiral[edit]

Is there a name and equation for a spherical 3d spiral, one that would result if a spiral were drawn on a plane surface that was at the same time rotating? The result would look like a neatly made ball of string of ever increasing diameter. Just as a spiral as it develops increases the area it "occupies" or "encloses" on a plane surface, so would this spiral/helix "occupy" or "enclose" an ever-increasing volume in space. I should imagine that if the rate of rotation of the plane surface on which the spiral is drawn was the same as the rate at which the spiral is drawn, then the result would approximate to a sphere, otherwise to a lozenge or 3d eliptical solid (or whatever it may be call ed).--Philogo 13:00, 23 May 2008 (UTC)

Can someone post an mpeg describing the phenomenon above? If I could see it, that would help me understand it better. (talk) 06:19, 30 May 2009 (UTC)
Think of a ball of string, like Ball of string

but much neater. As the spiral is developed it passes though every point in space Philogo (talk) 02:01, 14 December 2010 (UTC)

coil tighter toward the middle floral spiral shape, like a vanishing point

Cuberoottheo (talk) 19:11, 26 April 2015 (UTC)

a wavy spiral, winding tighter together towards the outside, only looks 3d

Cuberoottheo (talk) 19:43, 26 April 2015 (UTC)

Spiral becoming ever more circular?[edit]

What is the name for a spiral whose points depart from the center, go around it N times, but the more revolutions made, the closer to a circle its points begin to approach, but never actually reach it? Is this kind of a curve a parabolic spiral? Or looking at it in reverse, the path of an object just inside of a circle, but spiraling down to the center, as might be the case of an object succumbing to gravitational acceleration, and falling out of orbit? (talk) 06:29, 7 June 2009 (UTC)

Maybe a Limit-cycle? --Salix (talk): 11:27, 7 June 2009 (UTC)
Thanks. But is there any other name for that kind of a spiral? What kind of formula would produce that kind of a spiral? (talk) 21:02, 8 June 2009 (UTC)
Take any function f(x) whos limit as x tends to infinity is 1. Construct the curve with polar coordinates r=f(theta). For example r=atan(theta). --Salix (talk): 21:51, 8 June 2009 (UTC)
Thanks. Are there any real world applications for this kind of a spiral? Does it accurately represent a satellite descending from a nearly perfect orbit? (talk) 07:46, 9 June 2009 (UTC)
Thats why I mentioned Limit-cycle the spiral can be thought of as a special case of a limit cycle, and limit cycles are quite a common phemonema. I would suspect that a completely circular limit cycle would be too regular to exist in a real world situation.
--Salix (talk): 19:48, 9 June 2009 (UTC)
   Salix's spec that lim F(x)x→∞ =1 of course means r =2 atan(θ)/π is the example in question.
   But "succumbing to gravitational acceleration, and falling out of orbit" exposes a fundamental misunderstanding of the physics that makes the attempt to find the formula describing the twilight of a satellite fatally premature.
   Orbiting is not, and does not involve, overcoming nor resisting nor avoiding acceleration by gravity. (I refactored from "gravitational acceleration" not bcz it is wrong, but in the hope that doing so may in this instance be slightly clearer.) Orbiting not only involves, but fundamentally relies upon, being continuously subjected to acceleration by gravity.
   Orbiting is a relationship between two bodies that are sufficiently independent of any other bodies (i.e., a two-body problem), provided two other cases are avoided:
  1. As the distance between them monotonically decreases, they meet (collision case).
  2. Once the distance between them reaches a minimum, it never again starts decreasing (flyby case).
      What the press probably occasionally calls "falling out of orbit" is closer to completing a process that closely resembles the orbital case of the two-body problem: a many-body problem where there are scads of almost insignificantly massive particles swarming around the two major bodies (namely the molecules of the atmosphere of the large body), so that the lighter of the two keeps having collisions with them. This many-body problem is handled by approximation: ignore everything but the exchange of momentum between the smaller body (the satellite) and the atmospheric molecules that splat on its windshield. The satellite kicks them the hell out of the way, but gives up a teeny part of its energy and momentum each time. Years pass, and the satellite is eventually orbiting lower and lower (and faster, i think), and the splat rate gets higher and higher until atmosphere at its level is thick enuf that it's melting and burning and vaporizing fast enuf that it may not reach the ground, even as small, dense remnants.
       So bottom line, don't bother going looking for the function that'll produce a spiral that'll reflect that whole trajectory: you've got the dependence of gravity, and of atmospheric density and composition on altitude, and probably dependencies having to do with ablation of the satellite's antennas and body, and non-linear erosion due to the layers the satellite is designed with and to aerodynamic effects on the pitted surface. (Picture the bizarre contours produced by wind erosion in sandstone deserts.)
    --Jerzyt 01:49, 27 July 2013 (UTC)

Cuberoottheo (talk) 10:58, 1 April 2015 (UTC)

spiral weaved around an elliptical void

Cuberoottheo (talk) 20:23, 25 April 2015 (UTC)

The involute[edit]

Is the involute curve considered to be a spiral? If so, it is a noteworthy one with practical applications, and it's inclusion would add a pertinate example to the article. I am not qualified to do this. —Preceding unsigned comment added by Tonygumbrell (talkcontribs) 17:53, 12 August 2009 (UTC)

Most ancient symbol?[edit]

I removed the following material from the article, as it seems doubtful and lacks citations. Feel free to re-add the content, including appropriate citations of reliable sources. Thanks, Vectro (talk) 16:07, 24 September 2009 (UTC)

The spiral is the most ancient symbol found on every civilized continent. Due to its appearance at burial sites across the globe, the spiral most likely represented the "life-death-rebirth" cycle. Similarly, the spiral symbolized the sun, as ancient people thought the sun was born each morning, died each night, and was reborn the next morning.

Refactored by me:
I removed the following material from the article, as it seems doubtful and lacks citations. Feel free to re-add the content, including appropriate citations of reliable sources.

The spiral is the most ancient symbol found on every civilized continent. Due to its appearance at burial sites across the globe, the spiral most likely represented the "life-death-rebirth" cycle. Similarly, the spiral symbolized the sun, as ancient people thought the sun was born each morning, died each night, and was reborn the next morning.

Thanks, Vectro (talk) 16:07, 24 September 2009 (UTC)
--Jerzyt 21:32, 16 July 2013 (UTC)

Adds to confusion[edit]

I think the second section adds to the spiral helix confusion. The only senses in which I know where spiral is used to mean helix are a stair case and some authors alternative name helical computed tomography scanners. The first is more poetic rather than scientific, and the other is by non-native speakers of English (and to some extent is also because it sounds less technical). Billlion (talk) 11:07, 17 January 2011 (UTC)

I agree that there's confusion, but I've always thought of the term "spiral" as being inclusive (a super-set of, if you like) of the term "helix". So a helix is a (particular class of) spiral but a spiral isn't necessarily a helix. Unfortunately I can't find a reference to either confirm or refute this, but I'm pretty sure that a spiral isn't necessarily planar. How, for example, would you describe the conical springs used in electrical devices to make contact with the batteries? They are not helices because I believe a helix has to be cylindrical, so are they spirals? I would say, yes. I think the terms "helix" and "helicoid" are very tightly defined, whereas a "spiral" is a much more general term. Incidentally, the shape in the illustration coloured green is not a helix but a helicoid as it is a surface, not a line. The red object is also a surface, not a line, but it isn't a helicoid. So what is it? A spiral, a "spiroid", or something else? —MegaPedant 06:08, 25 January 2011 (UTC)
Some other examples include Ekman spiral and "spiral binding" (which in some cases can even refer to comb binding).
This article goes to substantial length to discuss spirals vs helices, but then also describes in great detail spirals drawn on a sphere. Which begs the question to be asked, what shape is a spiral drawn on a cigar? Is a helix just a spiral drawn on a cylinder? (And for that matter, what shape is a helix viewed projected into 2D?)
-- Cesiumfrog (talk) 08:26, 28 December 2012 (UTC)
Sometimes a cigar is just a cigar. Even if a spiral is drawn on it.
--Jerzyt 21:22, 16 July 2013 (UTC)
spiral weaved ovoid ring
spiral weaved elliptical

Cuberoottheo (talk) 20:52, 25 April 2015 (UTC)

Equations for a square spiral[edit]

x = (-1)^{^{\left\lceil\frac{t}{2}\right\rceil}} \cdot \left\lceil\frac{t}{4}\right\rceil\\
y = (-1)^{^{\left\lceil\frac{t - 1}{2}\right\rceil}} \cdot \left\lceil\frac{t - 1}{4}\right\rceil\\

where \left\lceil \bullet \right\rceil is the ceiling function, t \in \mathbb R. The spiral is clockwise if t \leq 0 and anticlockwise if t \geq 0.

--Not A Pipe ¬| 01:40, 2 April 2012 (UTC)

spiral caught on a snag

Cuberoottheo (talk) 15:23, 16 May 2015 (UTC)


Theodorus's spiral is described as approx. Archimedean but its radius does not increase constantly. Guess this could be a General Archimedean, or is it more like Logarithmic? Needs clarification, I think. Chiswick Chap (talk) 10:07, 21 May 2012 (UTC)

Well let's see:  \theta_n - \theta_{n-1} = \arcsin(\frac{1}{r_n}) \approx r_n^{-1} = n^{-1/2} ... what does this suggest?  \frac{d\theta}{dn} \approx n^{-1/2} = 1/r \, ; \frac{dr}{dn} = \frac{1}{2} n^{-1/2} \therefore \frac{dr}{d\theta} \approx \frac{1}{2}, so it does approach the Archimedean, if I haven't blundered. —Tamfang (talk) 18:41, 21 May 2012 (UTC)

Classification of planar spirals[edit]

At present, this section contains only a diagram of some kind. There ought to be some text also, explaining it. There isn't quite enough information in the diagram to guess what it means so as to produce the missing text. We need a mathematician here, and we need 'em bad! Friendly Person (talk) 15:03, 24 July 2012 (UTC)

More than that there is no sourcing as to where this classification came from, it might just be something some has invented. I've now removed the section.--Salix (talk): 15:52, 24 July 2012 (UTC)


I suggest the article mention the trispiral. Examples are readily found by searching for the term. Thanks!--Lbeaumont (talk) 20:21, 4 April 2013 (UTC)

I found a good trispiral image at: — Preceding unsigned comment added by Lbeaumont (talkcontribs) 20:26, 4 April 2013 (UTC)
three lobe spiral (talk) 19:49, 4 April 2015 (UTC)

Dict quote[edit]

   At the risk of putting a band-aid on a severed artery (i.e. focusing too narrowly within an article with much greater problems), an accurately quoted excerpt from the AmHerDict must end with either

parallel to the axis....


parallel to the axis; a helix.

instead of the (presumably gradually decaying) travesty that started three and half years ago.
   We're probably talking here about recklessness rather than vandalism, since i suppose we may assume that the distinction between "constant or continuously varying" and "varying" is not discernible to every editor with a passing interest in the subject.
--Jerzyt 05:20, 16 July 2013 (UTC)

snagged elliptical spiral

Cuberoottheo (talk) 15:41, 16 May 2015 (UTC)

Spirals and helices[edit]

   I keep looking at the unsourced statement

While a "spiral" and a "helix" are distinct as technical terms, a helix is sometimes described as a spiral in non-technical usage.

Even if it is true, it is a dismissive and misleading comment that obscures the relationship between spirals and helices, which i am clarifying in place of it.
--Jerzyt 08:06, 16 July 2013 (UTC)


Re: "Ouroboros" spiral
   At 08:19, 28 December 2012,‎ User:Cesiumfrog summarized

/* Three-dimensional spirals */ tagging dubious synthesis

and placed the {{Dubious}} and {{OR}} tags into the sentence

This image is reminiscent of an Ouroboros symbol[original research?] and could be mistaken for a torus with a continuously-increasing diameter: [dubiousdiscuss]

   These prior events provide context:

  1. At 14:42, 21 August 2004 de:User:Karl Bednarik made a contrib at de:Spirale#Dreidimensionale Spiralen, adding (without refs)
    1. German text and
    2. an invocation in the apparently now obsolete image-invocation format de:Bild:TORUSA-1 Torus mit variablem Ringdurchmesser.jpg, to what is, in the en: article's section in question, aka File:TORUSA-1 Torus mit variablem Ringdurchmesser.PNG.
  2. (Tho i haven't confirmed the timing, i assume the next relevant event was the de: article adding miniatur|Konische Spirale entlang eines Kreises (which is a de: invocation of File:TORUSA-4 Konische Spirale entlang eines Kreises.PNG.)
  3. At 03:29, 20 September 2006 User:Grubber made a contrib at Spiral#Three-dimensional spirals , adding
    1. corresponding English text,
    2. the invocation of Image:TORUSA-1 Torus mit variablem Ringdurchmesser.PNG, and
    3. the invocation of File:TORUSA-4 Konische Spirale entlang eines Kreises.PNG (the first image in the subsection)
    and summarizing
    Two-dimensional spirals: add more info and pics from German de:Spirale
  4.    (Tho i haven't confirmed the timing, i assume the next relevant event was the de: article replacing that (shared) image invocation (TORUSA-1) with an invocation of commons:/File:Ouroboros_Torus.png.)

   So neither the contributor here nor the contributor at de: whose work they translated has offered a ref, in the going-on 7 years or going-on 9 years since their respective contribs. IMO the Ouroboros connection is of no mathematical value, and just an afterthot to a nice demonstration of that there's an unexpectedly simple mathematical specification (of a conical surface being deformable not just into a valveless sousaphone, but into one that's had its mouthpiece not just stuffed into its bell, but stuffed so deeply in that there's tubing inside tubing inside tubing ... well, to as many levels of self-nesting as you care to ask for). I'm glad to have seen it, and i believe there are people who can write the parametric equations that specify it, and prove theorems about it, but that's less than what WP:V requires, and it's hard to imagine a scenario that would provide us with it.
--Jerzyt 05:25, 17 July 2013 (UTC)

Cuberoottheo (talk) 13:46, 3 July 2015 (UTC)== expanding the symbol/art section == I will do some expanding of the symbol and art section over the coming days.--Peabodybore (talk) 22:19, 4 January 2014 (UTC)

spiral around four lobes

Cuberoottheo (talk) 20:10, 4 April 2015 (UTC)

spiral weaved around an egg shaped void

Cuberoottheo (talk) 12:59, 26 April 2015 (UTC)

Past tense of to weave is woven.Billlion (talk) 18:06, 28 April 2015 (UTC)
Yes, a concurrent polar plot, instantly woven, the polar equation has no control over how long it takes to weave it. Cuberoottheo (talk) 19:02, 12 May 2015 (UTC).
a five petal spiral

Cuberoottheo (talk) 11:17, 14 June 2015 (UTC)

star turn

Cuberoottheo (talk) 13:15, 14 June 2015 (UTC)

a four lobe spiral

Cuberoottheo (talk) 13:33, 14 June 2015 (UTC)

a nine petal spiral

Cuberoottheo (talk) 13:33, 14 June 2015 (UTC)

tread around the spiral

Cuberoottheo (talk) 13:46, 3 July 2015 (UTC)

spiral with z,z,z

Cuberoottheo (talk) 13:46, 3 July 2015 (UTC)

twelve petal spiral

Cuberoottheo (talk) 15:57, 15 July 2015 (UTC)

field within a Chubby spiral

Cuberoottheo (talk) 15:57, 15 July 2015 (UTC)

almost a basket

Cuberoottheo (talk) 12:12, 18 July 2015 (UTC)


Cuberoottheo (talk) 12:12, 18 July 2015 (UTC)

more cross sectional

Cuberoottheo (talk) 14:02, 23 July 2015 (UTC)

less cross sectional

Cuberoottheo (talk) 14:02, 23 July 2015 (UTC)

Chubby spiral jenny

Cuberoottheo (talk) 11:39, 30 July 2015 (UTC)

Chubby spiral basket from above

Cuberoottheo (talk) 11:39, 30 July 2015 (UTC)


Cuberoottheo (talk) 12:02, 4 August 2015 (UTC)


Cuberoottheo (talk) 12:02, 4 August 2015 (UTC)

Chubby spiral mixer taps

Cuberoottheo (talk) 09:44, 22 August 2015 (UTC)

Chubby spiral spokes

Cuberoottheo (talk) 09:44, 22 August 2015 (UTC)

Chubby spiral, blank star

Cuberoottheo (talk) 10:09, 24 August 2015 (UTC)

Chubby spiral, another blank star

Cuberoottheo (talk) 10:09, 24 August 2015 (UTC)

Chubby spiny spiral

Cuberoottheo (talk) 11:15, 26 August 2015 (UTC)

Chubby super spirals

Cuberoottheo (talk) 11:15, 26 August 2015 (UTC)