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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.
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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
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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
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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
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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
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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
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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
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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
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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
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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,
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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,
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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
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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
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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
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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!
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968:{\displaystyle {\begin{cases}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 \\\end{cases}}}
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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.
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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
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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.)
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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.
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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.
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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
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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.
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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?
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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? —
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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?
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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.--
1416:{\displaystyle {\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}}}
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I removed the following material from the article, as it seems doubtful and lacks citations. Feel free to re-add the content, including appropriate
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I removed the following material from the article, as it seems doubtful and lacks citations. Feel free to re-add the content, including appropriate
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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). --
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true, it is a dismissive and misleading comment that obscures the relationship between spirals and helices, which i am clarifying in place of it.
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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.
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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
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While a "spiral" and a "helix" are distinct as technical terms, a helix is sometimes described as a spiral in non-technical usage.
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Thanks. But is there any other name for that kind of a spiral? What kind of formula would produce that kind of a spiral?
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This image is reminiscent of an
Ouroboros symbol and could be mistaken for a torus with a continuously-increasing diameter:
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Can someone post an mpeg describing the phenomenon above? If I could see it, that would help me understand it better.
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people who can write the parametric equations that specify it, and prove theorems about it, but that's less than what
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Yes, a concurrent polar plot, instantly woven, the polar equation has no control over how long it takes to weave it.
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it "occupies" or "encloses" on a plane surface, so would this spiral/helix "occupy" or "enclose" an ever-increasing
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an unexpectedly simple mathematical specification (of a conical surface being deformable not just into a valveless
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I suggest the article mention the trispiral. Examples are readily found by searching for the term. Thanks!--
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Once the distance between them reaches a minimum, it never again starts decreasing (flyby case).
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I've cleaned up the talk page hiding a lot of images are unrelated to the discussion.--
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Perhaps a section dealing with right verus left handed spirals should be considered? --
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but much neater. As the spiral is developed it passes though every point in space
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As the distance between them monotonically decreases, they meet (collision case).
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I will do some expanding of the symbol and art section over the coming days.--
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requires, and it's hard to imagine a scenario that would provide us with it.
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a wavy spiral, winding tighter together towards the outside, only looks 3d
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coil tighter toward the middle floral spiral shape, like a vanishing point
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Two-dimensional spirals: add more info and pics from German de:Spirale
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an invocation in the apparently now obsolete image-invocation format
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I'll be translating additional material from the German article
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upon, being continuously subjected to acceleration by gravity.
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Image:TORUSA-1 Torus mit variablem Ringdurchmesser.PNG
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998:{\displaystyle \left\lceil \bullet \right\rceil }
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1700:de:Spirale#Dreidimensionale Spiralen
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1683:These prior events provide context:
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361:Spiral becoming ever more circular?
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2565:Chubby cushion spiral, longer hole
1556:We're probably talking here about
758:Sometimes a cigar is just a cigar.
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1778:commons:/File:Ouroboros_Torus.png
1742:Spiral#Three-dimensional spirals
1030:{\displaystyle t\in \mathbb {R} }
1835:Past tense of to weave is woven.
1816:expanding the symbol/art section
1552:started three and half years ago
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782:Equations for a square spiral
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109:and see a list of open tasks.
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2223:field within a Chubby spiral
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1253:... what does this suggest?
730:Some other examples include
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1995:spiral weaved elliptical
1987:spiral weaved ovoid ring
1900:19:02, 12 May 2015 (UTC)
1883:Please do not modify it.
1702:, adding (without refs)
1538:parallel to the axis....
1437:18:41, 21 May 2012 (UTC)
1125:10:07, 21 May 2012 (UTC)
498:19:48, 9 June 2009 (UTC)
461:07:46, 9 June 2009 (UTC)
435:21:51, 8 June 2009 (UTC)
413:21:02, 8 June 2009 (UTC)
395:11:27, 7 June 2009 (UTC)
376:06:29, 7 June 2009 (UTC)
333:06:19, 30 May 2009 (UTC)
266:Right versus left-handed
206:Any progress on that? -
167:This article contains a
141:project's priority scale
2888:spiral caught on a snag
2166:tread around the spiral
1674:tags into the sentence
1640:Re: "Ouroboros" spiral
1090:{\displaystyle t\geq 0}
1060:{\displaystyle t\leq 0}
215:02:50, 8 Jun 2005 (UTC)
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