Talk:Ellipsoid

From Wikipedia, the free encyclopedia

Why isn't there some explanation of the relationship between an ellipse and an ellipsoid? Lir 20:01 Nov 9, 2002 (UTC)

Contents 1 Missing info 2 Volume 3 Incorrect formulas? 4 Diagram 5 Incorret parametric form 6 As applied to angular momentum

[edit] Missing info

hello There must be a formula for the integrated mean curvature out there. This would complete the set of invariant measures of ellipsoids. Bela Mulder 09:27, 25 Nov 2004 (UTC)

I think the oblate/prolate explanation is backwards. a>b=c seems like a cigar, while a<b=c seems like a disk.

No it's not:

← Oblate;   Prolate →

Remember a is the equatorial radius/axis:

For Earth, an oblate spheroid, a = 6378.135 and b = 6356.75. So if the north and south poles were different (say, b_n = 6357.0 and b_s = 6356.5), then it would be triaxial, where (it would seem) a = 6378.135, b = 6357.0 and c = 6356.5, wouldn't it? ~Kaimbridge~15:43, 31 July 2006 (UTC)

[edit] Volume

The volume of an ellipsoid is 4/3 times pi times A times B times C. But what's A, what's B, and what's C? It doesn't say? Jared 19:40, 28 October 2005 (UTC)

They're the ellipsoid's axes, as used throughout the article.

Urhixidur 02:57, 29 October 2005 (UTC)

a is the length from the center of the ellipsoid to its surface at Sphereical Coordinate, in radians, (π/2, 0), which is generally the maximum y coordinate on the surface of the ellipse.

b is the length from the center of the ellipsoid to its surface at Sphereical Coordinate, in radians, (0,0), which is generally the maximum x coordinate on the surface of the ellipse.

c is the length from the center of the ellipsoid to its surface at Sphereical Coordinate, in radians, (0, π/2), which is generally the maximum z coordinate on the surface of the ellipse.

Edward Solomon 5/18/06 69.117.220.101 21:28, 18 May 2006 (UTC)

You are right about what an oblate spheroid and a prolate spheroid looks like, but the equations were reversed. If 2 of the semi axis are the same, and the third is smaller this will be an oblate spheroid, and as such when b = c, a < b will be an oblate spheroid. If however, the third is larger this will be an prolate spheroid, and as such when b = c, a > b will be an oblate spheroid.

No, No, NO, that's backwards!!!

This is an oblate spheroid, like Earth: a > b! Why is this fact always being overlooked?!? P=/ ~Kaimbridge~10:39, 24 August 2006 (UTC)

[edit] Incorrect formulas?

I think I've found two errors on this page. First, the formula for calculating the eccentricity (e), seems to be backwards. It divides the larger number with the smaller and subtracts one from the result, which leads us almost always into a negative square root. I don't think this is intended. The correct form can be found from the Spheroid page, which divides the smaller with the larger, resulting in a positive number. Also it's stated on Eccentricity(mathematics) page, that the eccentricity of an ellipse is greater than zero, less than one.

Also, the formula for a prolate spheroid seems to be incorrect. This might be a result from the false eccentricity formula. After using the correct form for the eccentricity, I'm getting rather wild results:

a 0.2m b 0.2m c 0.5m

Area: 2.37m²

Surface area of a cylinder with the same dimensions: 1.51m²

There is an alternate formula on the Spheroid page, which yields an area of 1.05m²

I changed the formula explaining a scalene elipsoid a ≠ b ≠ c to a ≠ b ≠ c ≠ a because the original formula could still be satisfied if a = c

[edit] Diagram

I am sure this is a real ellipsoid, but it does look a lot like a prolate spheroid. Perhaps the difference in the shorter axes could be made more marked so its clearer at a glance what the deal is? Deuar 19:35, 15 June 2006 (UTC)
Now we also have what looks for all intents like an oblate spheroid (although a close look at the axes reveals different scales if you're real keen)... Deuar 12:51, 26 June 2006 (UTC)

I was just about to mention this when I saw you said the same thing. All spheroids are ellipsoids, but to avoid confusion I think it would be a good idea to add images af ellipsoids that aren't spheroids, as well as images of spheroids.

[edit] Incorret parametric form

i dont no how to change the range for the Phi and theta, can someone please change the theta value to : 0 <= theta <= 2pi, and the Phi to: 0 <= Phi <= pi. Pprrff 01:29, 2 December 2006

There are different ways to express Cartesian coordinates——the way you were reverting to is the more common (as so, I believe, more to do with its likely application, rather than correctness) "spherical coordinates", which is itself contradictory and confusing——the more recognizable (coordinate-wise) is the geographical(h=0), but the most formatically elementary is using the parametric latitude, as that is what is used in the equation of the ellipse. I'm finishing up a major rewrite of the first parts of this article (including the relationships of the parametric, planetographic and planetocentric latitudes), which should make the different Cartesian forms clear.  ~Kaimbridge~15:43, 2 December 2006 (UTC)

[edit] As applied to angular momentum

Imparting angular momentum on a sphere transforms it into an oblate spheroid. The ratio of volume to surface area of a sphere is constant (r/3), but does not generalize to other spheroids. So when one imparts angular momentum to such a sphere, does the volume change, does the surface area change, or do both change?

Put another way, will two black holes of equal mass, one spinning, one not, necessarily have either equal volume (within their horizons) or equal surface area (of the horizon itself) ?

--76.209.50.222 23:44, 19 February 2007 (UTC)