Talk:Archimedean spiral

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u stink since u dont say why it is named after him gosh darnnit i need to know for my math class, its due next week! Im screwed!HA HA screwed like his invention he made. . .P.S. tell me if you know

[edit] The obvious

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

[edit] Definition Locus vs. polar coordinates

I really think the locus definition should come first. It is the true origin of the curve (there were no functions back then) and it gives the reader a better sense of what it is. The polar coordinates definition is no more precise and, for most people, totally meaningless.

Rather, than just changing it back to my last edit we should talk about this. I mean it's like saying a circle is "r^2 = x^2 + y^2" that only works in ONE context: the cartesian plane-- the locus definition is useful in any context-- futurebird 04:00, 13 June 2006 (UTC)

Here is an even better one:

If a fly crawls radially outward along a uniformly spinning disk, the curve it traces with respect to a reference frame in which the disk is at rest is an Archimedean spiral (Steinhaus 1999, p. 137).


futurebird

Modern notation should come first, historical notes later. There's no point in writing up a mathematical article in words when there's a perfectly good 6-character equation that describes the same thing. As a historical note, it is interesting; that's why I think the second paragraph is the perfect spot for it. As for what lay readers will get the most out of, it's the picture, not the equation nor textual description. -- Xerxes 16:49, 13 June 2006 (UTC)

There is also a neuropsychiatric application -- the patient's drawing of this spiral is analyzed much as it their handwriting67.133.62.42 23:47, 10 May 2007 (UTC)

[edit] Mirror image of an Archimedean Spiral

"Taking the mirror image of this arm across the y-axis will yield the other arm."

If I flip the Archimedean_spiral.png across any single axis, the two arms will intersect regularly. If I flip it across both axes (or rotate it 180 degrees - same thing), they will nest, only intersecting at the origin. Maybe it's a terminology difference, but that's what comes to mind for me when I envision the other arms of a spiral. 206.124.146.40 (talk) 23:27, 23 December 2007 (UTC)

It depends on what the equations say when you plug in negative degrees, not on what's prettiest... AnonMoos (talk) 15:47, 28 December 2007 (UTC)

[edit] a and b

What are a and b supposed to represent? I know they are real numbers, but what do they actually represent in relation to the image of the spiral? —Preceding unsigned comment added by 77.97.89.135 (talk) 21:17, 22 January 2008 (UTC)

[edit] Rectangular equation

Out of curiosity, is it, in any way, shape or form, possible to express the Archimedean spiral in terms of a single equation with rectangular coordinates? Thanks if anyone can answer this. --70.124.85.24 (talk) 18:56, 1 March 2008 (UTC)

Basic substitution gives the following basic equation (first quadrant only):
sqrt(x²+y²)=arctan(y/x)
Where the arctangent function is not confined to giving values less than 2π. You could make it more complex to account for all four quadrants, and various constant parameters... AnonMoos (talk) 22:54, 1 March 2008 (UTC)