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Could someone please fix the first formula in section "Other properties"? All I can see in my browser is this error message: Failed to parse(unknown function '\begin'): {\begin{aligned}\theta &=\arccos \left({\frac {r-h}{r}}\right)\\&=\arccos \left(1-{\frac {h}{r}}\right)\\&=\arccos \left(1-{\frac {1}{2\pi }}\right)\approx 0.572\,{\text{ rad,}}{\mbox{ or }}32.77^{\circ }.\end{aligned}} Thanx! 188.219.235.35 ( talk) 16:08, 10 February 2014 (UTC)
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)?
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)
I disagree that angle and solid angle are dimensionless. Angle is a dimension in the same sense as length, time, mass, etc. The common argument that angle is dimensionless ("angle is a ratio of lengths") is flawed. It is not correct to say that "angle is the ratio of arclength to radius." Rather, it is "angle in radians is the ratio of arclength to radius." When we say "quantity (in this case, angle) in unit (in this case, radian)" we typically mean (barring offsets and nonlinear transformations, e.g., degC and dB) "quantity divided by unit," since as BIPM states (International Bureau of Weights and Measures, "The International System of Units (SI)," 8th ed., 2006.), "The value of a quantity is generally expressed as the product of a number and a unit." We all agree that the radian is a unit of angle, so "angle in radians" is dimensionless but "angle" has whatever dimension we call it to be. Let's call it what it is -- angle.
Likewise, the correct statement is "solid angle in steradians is the ratio of the area cut out of a sphere to the square of the radius." The steradian is a unit of solid angle, so "solid angle in steradians" is dimensionless. "Solid angle" has whatever dimension we call it to be -- squared angle. -- daviesk24 19:18, 6 March 2014
AFAIK, Physics has proven that the radian is dimensionless (to the extent physics ever proves anything). Sisima70 ( talk) 20:00, 14 March 2017 (UTC)
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."
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)
I think this is incorrect: A steradian is defined as the solid angle subtended at the center of a sphere of radius r by a portion of the surface of the sphere...
I think it should say something more like: A steradian is defined as the solid angle at the center of a sphere of radius r subtended by a portion of the surface of the sphere... Gwideman ( talk) 02:19, 17 March 2010 (UTC)
I'm pretty sure the equation at the bottom of the definition section is incorrect, unless theta is the apex angle. If it's half the apex angle, apex angle values of pi and 2*pi don't work out as expected. —Preceding unsigned comment added by Martin.duke ( talk • contribs) 19:09, 24 September 2010 (UTC)
This is a big problem with articles related to maths, physics and other technical fields. The language is complete gobbledegook and while it is no doubt technically and scientifically exact and correct, it serves readers of encyclopedias poorly. Encyclopedias are not simply and only reference books but the are purveyors of knowledge to the masses. Speaking as one integer member of this mass, I can't read it!
-Morris, UK — Preceding unsigned comment added by 92.20.206.0 ( talk) 00:45, 16 August 2013 (UTC)
Assuming there is a practical purpose for this measurement, it might be useful to add a short list to the bottom of the page indicating where it is used, or even just a list of links to diciplines where it is useful. (I personally don't see any purpose to this measurement, so I'm curious to know why it would be of import.) Rashkavar ( talk) 01:41, 8 November 2012 (UTC)
Sorry, but a steradian is a solid angle, not the ratio of spherical-surface area to the sphere's radius. The "contributors" have really gotten carried away and have implanted a bunch of interesting but bogus notions, such as the "size" of Zimbabwe in sr. Good grief. And dump all the stuff about unit spheres. It's just confusing and irrelevant. It doesn't matter whether the sphere is a unit sphere or a non-unit sphere. A steradian is the same in either case. -- MarkFilipak ( talk) 03:21, 11 September 2014 (UTC)
-- agreed - much of this needs to be removed - and the stuff about surface area on earth is bogus - the earth is not a sphere — Preceding unsigned comment added by 82.8.228.52 ( talk) 20:51, 16 November 2016 (UTC)
It does matter if the sphere is a unit sphere or not, since the ratio between the area and the radius of a sphere is afflicted by the rotation of the sphere (even if this is not measurable under normal circumstances). Sisima70 ( talk) 20:00, 14 March 2017 (UTC)
In my opinion in the legend of the first image should be A/r2 sr instead of A sr/r2, because you can't divide a unit of measure to a geometrical value. Doru001 ( talk) 20:04, 8 December 2015 (UTC)
That is mathematics and apparently it is possible to do so (mathematics is experimental axiom exploration after all) Sisima70 ( talk) 20:03, 14 March 2017 (UTC)
the solid angle substended made with the centre of a sphere by an area aqual to square of radius of same sphere is called steradian — Preceding unsigned comment added by 119.154.179.233 ( talk) 14:24, 3 September 2016 (UTC)
The solid angle for a unit sphere with a variable spherical cap height, is given by , , height h, is taken from the imagined cross-section of the unit sphere. angle theta, is obtained by measuring the arc length over the cap, from the imagined cone wall to the imagined center line of the cone (top of cap) . Cuberoottheo ( talk) 13:46, 16 September 2016 (UTC)
one steradian is seen at parallax of 65.54°, so an observer (standing at the center of the sphere) see a circle (just the same as moon in the night sky, but much larger) with the diameter of 65.54°, so the area of such circle would be: A = ½ ρd2 = 0.5×1.57×(65.54)2 = 3373.67121 square degrees, but in Definition section is said: "A steradian is also equal to the spherical area of a polygon having an angle excess of 1 radian, to 1/(4π) of a complete sphere, or to (180/π)2 ≈ 3282.80635 square degrees ..." how could this be happened?
Tabascofernandez (
talk)
01:44, 21 September 2017 (UTC)
Although, in learning, it's helpful to picture steradians as 3-d solid chunks of a sphere extending from the center, or as areas on the surface of a sphere, steradians in fact have no dependence on spheres at all or any other bounded 3-d shape or 2-d surface. In a 3-d (Euclidian) space, any point has 4-pi steradians of solid angle around it, whether projected to infinity, to a sphere surface, a cube, or the surface of a surrounding potato. This should be clarified, technically and accurately, towards the end of the article, after the "teaching" parts that do mention spheres. A nice thing about a sphere is that surface area happens to correspond directly to solid angle, but they're not the same thing; a purist will not deign to mention spheres. (Similarly, ordinary plane angle doesn't really depend on 2-d circles or any other shapes, even though the circular compass rose is handy for showing plane angle.) — Preceding unsigned comment added by 108.73.1.253 ( talk • contribs) 11 dec 2017 20:21 (UTC)
Separately, System International should not exclude steradian amounts including prefixed-amounts larger than the unit sphere. A large blanket may wrap many times around a basketball. A cabbage leaf could wrap more than once around the head of cabbage, subtending more than 13 steradians of solid angle. (Yottasteradians would imply a big cabbage.) The current sentence in the article: "Any range in excess of the whole area of a sphere would only be needed in conjunction with non-Euclidean, spherical geometry." is wrong and should be corrected or removed. 108.73.1.253 ( talk) 19:19, 11 December 2017 (UTC)
An editor has asked for a discussion to address the redirect Planck solid angle. Please participate in the redirect discussion if you wish to do so. Andy Dingley ( talk) 22:48, 26 February 2020 (UTC)
Is there a way to explain the analogy between the radian and the steradian using coordinate transforms? For example, making a circle in a plane, measuring the angle, and then making another plane at a right angle to that plane and measuring the same angle in the plane that perpendicular/normal/orthogonal to the first plane? ScientistBuilder ( talk) 19:32, 12 October 2021 (UTC)ScientistBuilder ScientistBuilder ( talk) 19:32, 12 October 2021 (UTC)
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Could someone please fix the first formula in section "Other properties"? All I can see in my browser is this error message: Failed to parse(unknown function '\begin'): {\begin{aligned}\theta &=\arccos \left({\frac {r-h}{r}}\right)\\&=\arccos \left(1-{\frac {h}{r}}\right)\\&=\arccos \left(1-{\frac {1}{2\pi }}\right)\approx 0.572\,{\text{ rad,}}{\mbox{ or }}32.77^{\circ }.\end{aligned}} Thanx! 188.219.235.35 ( talk) 16:08, 10 February 2014 (UTC)
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)?
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)
I disagree that angle and solid angle are dimensionless. Angle is a dimension in the same sense as length, time, mass, etc. The common argument that angle is dimensionless ("angle is a ratio of lengths") is flawed. It is not correct to say that "angle is the ratio of arclength to radius." Rather, it is "angle in radians is the ratio of arclength to radius." When we say "quantity (in this case, angle) in unit (in this case, radian)" we typically mean (barring offsets and nonlinear transformations, e.g., degC and dB) "quantity divided by unit," since as BIPM states (International Bureau of Weights and Measures, "The International System of Units (SI)," 8th ed., 2006.), "The value of a quantity is generally expressed as the product of a number and a unit." We all agree that the radian is a unit of angle, so "angle in radians" is dimensionless but "angle" has whatever dimension we call it to be. Let's call it what it is -- angle.
Likewise, the correct statement is "solid angle in steradians is the ratio of the area cut out of a sphere to the square of the radius." The steradian is a unit of solid angle, so "solid angle in steradians" is dimensionless. "Solid angle" has whatever dimension we call it to be -- squared angle. -- daviesk24 19:18, 6 March 2014
AFAIK, Physics has proven that the radian is dimensionless (to the extent physics ever proves anything). Sisima70 ( talk) 20:00, 14 March 2017 (UTC)
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."
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)
I think this is incorrect: A steradian is defined as the solid angle subtended at the center of a sphere of radius r by a portion of the surface of the sphere...
I think it should say something more like: A steradian is defined as the solid angle at the center of a sphere of radius r subtended by a portion of the surface of the sphere... Gwideman ( talk) 02:19, 17 March 2010 (UTC)
I'm pretty sure the equation at the bottom of the definition section is incorrect, unless theta is the apex angle. If it's half the apex angle, apex angle values of pi and 2*pi don't work out as expected. —Preceding unsigned comment added by Martin.duke ( talk • contribs) 19:09, 24 September 2010 (UTC)
This is a big problem with articles related to maths, physics and other technical fields. The language is complete gobbledegook and while it is no doubt technically and scientifically exact and correct, it serves readers of encyclopedias poorly. Encyclopedias are not simply and only reference books but the are purveyors of knowledge to the masses. Speaking as one integer member of this mass, I can't read it!
-Morris, UK — Preceding unsigned comment added by 92.20.206.0 ( talk) 00:45, 16 August 2013 (UTC)
Assuming there is a practical purpose for this measurement, it might be useful to add a short list to the bottom of the page indicating where it is used, or even just a list of links to diciplines where it is useful. (I personally don't see any purpose to this measurement, so I'm curious to know why it would be of import.) Rashkavar ( talk) 01:41, 8 November 2012 (UTC)
Sorry, but a steradian is a solid angle, not the ratio of spherical-surface area to the sphere's radius. The "contributors" have really gotten carried away and have implanted a bunch of interesting but bogus notions, such as the "size" of Zimbabwe in sr. Good grief. And dump all the stuff about unit spheres. It's just confusing and irrelevant. It doesn't matter whether the sphere is a unit sphere or a non-unit sphere. A steradian is the same in either case. -- MarkFilipak ( talk) 03:21, 11 September 2014 (UTC)
-- agreed - much of this needs to be removed - and the stuff about surface area on earth is bogus - the earth is not a sphere — Preceding unsigned comment added by 82.8.228.52 ( talk) 20:51, 16 November 2016 (UTC)
It does matter if the sphere is a unit sphere or not, since the ratio between the area and the radius of a sphere is afflicted by the rotation of the sphere (even if this is not measurable under normal circumstances). Sisima70 ( talk) 20:00, 14 March 2017 (UTC)
In my opinion in the legend of the first image should be A/r2 sr instead of A sr/r2, because you can't divide a unit of measure to a geometrical value. Doru001 ( talk) 20:04, 8 December 2015 (UTC)
That is mathematics and apparently it is possible to do so (mathematics is experimental axiom exploration after all) Sisima70 ( talk) 20:03, 14 March 2017 (UTC)
the solid angle substended made with the centre of a sphere by an area aqual to square of radius of same sphere is called steradian — Preceding unsigned comment added by 119.154.179.233 ( talk) 14:24, 3 September 2016 (UTC)
The solid angle for a unit sphere with a variable spherical cap height, is given by , , height h, is taken from the imagined cross-section of the unit sphere. angle theta, is obtained by measuring the arc length over the cap, from the imagined cone wall to the imagined center line of the cone (top of cap) . Cuberoottheo ( talk) 13:46, 16 September 2016 (UTC)
one steradian is seen at parallax of 65.54°, so an observer (standing at the center of the sphere) see a circle (just the same as moon in the night sky, but much larger) with the diameter of 65.54°, so the area of such circle would be: A = ½ ρd2 = 0.5×1.57×(65.54)2 = 3373.67121 square degrees, but in Definition section is said: "A steradian is also equal to the spherical area of a polygon having an angle excess of 1 radian, to 1/(4π) of a complete sphere, or to (180/π)2 ≈ 3282.80635 square degrees ..." how could this be happened?
Tabascofernandez (
talk)
01:44, 21 September 2017 (UTC)
Although, in learning, it's helpful to picture steradians as 3-d solid chunks of a sphere extending from the center, or as areas on the surface of a sphere, steradians in fact have no dependence on spheres at all or any other bounded 3-d shape or 2-d surface. In a 3-d (Euclidian) space, any point has 4-pi steradians of solid angle around it, whether projected to infinity, to a sphere surface, a cube, or the surface of a surrounding potato. This should be clarified, technically and accurately, towards the end of the article, after the "teaching" parts that do mention spheres. A nice thing about a sphere is that surface area happens to correspond directly to solid angle, but they're not the same thing; a purist will not deign to mention spheres. (Similarly, ordinary plane angle doesn't really depend on 2-d circles or any other shapes, even though the circular compass rose is handy for showing plane angle.) — Preceding unsigned comment added by 108.73.1.253 ( talk • contribs) 11 dec 2017 20:21 (UTC)
Separately, System International should not exclude steradian amounts including prefixed-amounts larger than the unit sphere. A large blanket may wrap many times around a basketball. A cabbage leaf could wrap more than once around the head of cabbage, subtending more than 13 steradians of solid angle. (Yottasteradians would imply a big cabbage.) The current sentence in the article: "Any range in excess of the whole area of a sphere would only be needed in conjunction with non-Euclidean, spherical geometry." is wrong and should be corrected or removed. 108.73.1.253 ( talk) 19:19, 11 December 2017 (UTC)
An editor has asked for a discussion to address the redirect Planck solid angle. Please participate in the redirect discussion if you wish to do so. Andy Dingley ( talk) 22:48, 26 February 2020 (UTC)
Is there a way to explain the analogy between the radian and the steradian using coordinate transforms? For example, making a circle in a plane, measuring the angle, and then making another plane at a right angle to that plane and measuring the same angle in the plane that perpendicular/normal/orthogonal to the first plane? ScientistBuilder ( talk) 19:32, 12 October 2021 (UTC)ScientistBuilder ScientistBuilder ( talk) 19:32, 12 October 2021 (UTC)