Talk:Steradian

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[edit] Definition

So do you take a radian and revolve it around (projecting a circle), or is it a horizontal radian by a vertical radian (projecting a square)?

Neither. The easiest way to think about it, is to imagine projecting whatever range of angles you're interested in onto a sphere of unit radius, centered about the origin of the angles. The surface area of the total sphere is 4π units. If the projected angles "illuminate" the entire sphere, you have 4π sr. If they illuminate half the sphere (any half), you have 2π sr, and so on. It doesn't matter what the shape of the "illuminated" area is. I don't think there is a direct connection to radians, of the type you're trying to make. They are related in the sense that the perimeter of a unit circle is 2π units, and there are 2π radians in a full circle. Similarly, the surface area of a unit sphere is 4π units, and there are 4π steradians in "all directions".--Srleffler 03:32, 23 January 2006 (UTC)
Currently, the article would seem to contradict you (especially the figures)...? 65.183.135.231 (talk) 14:02, 29 May 2008 (UTC)

[edit] Dimensions

Even though we are thinking of a sphere, which has a curved surface, we are only thinking about the surface, and not the volume enclosed by it. Therefore solid angle is a 2-dimensional construct. Lasunncty 17:22, 3 April 2006 (UTC)

Solid angle is used in three-dimensional space in a manner analogous to the way that normal angle is used in two dimensional space. It defines an (infinite) volume within the larger (also infinite) space, in the same way that regular angle defines an (infinite) area within the (also infinite) plane in which the angle is defined. The steradian itself is, of course, neither 2-dimensional nor 3-dimensional. It is a dimensionless number, as noted in the article.--Srleffler 17:31, 3 April 2006 (UTC)
I would disagree. In the case of the circle, I think the area enclosed by an angle is not the same as the angle itself. To me the angle is one dimension of that area, and the (infinite) radius is the other. (I would also say that radians and steradians are unitless measurements, but not dimensionless.) --Lasunncty 20:37, 3 April 2006 (UTC)
I changed the wording in the intro. See if you like the new version better.
Formally, the steradian is definitely dimensionless. I understand your point, though. It's actually sort of irrelevant to think about whether solid angle represents the surface area of some surface or the volume of space enclosed. Either way, it represents the ratio of either the area or the volume to the total area or volume possible, times a constant of 4π. It is dimensionless like any other ratio of like-dimensioned quantities is. I think what the comment in the intro was trying to say was that you use steradians for problems in three-dimensional space, in the same way that you use radians for angles that are confined to a plane. The wording was not very good, though, and was probably not correct as written. I hope the new wording is better.--Srleffler 22:14, 3 April 2006 (UTC)

[edit] yarrr legibility

can someone fix the font for r^2? it took me 4 or 5 firefox ctrl-= zooms just to be able to read it (the arm of the r dives into the left crook of the 2). as it is it's illegible garbage.

here's one context/occurrence quoted from the page:

sphere having an area r²."

The problem is at your end. Try increasing the default font size of you rvrowser, or substituting a better one. At this end, it's plain HTML.
Urhixidur 02:30, 9 November 2006 (UTC)

[edit] SI multiples

I've nominated Template:SI multiples, which appears to be subst'ed into this article, for deletion. Join the discussion on WP:TFD. Han-Kwang (t) 19:52, 23 August 2007 (UTC)