Talk:Solid angle

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Suggested Reference

https://books.google.com/books?id=q-75OzZDHrEC&pg=PA4&dq=solid+angle+definition&hl=en&ppis=_c&sa=X&ved=2ahUKEwiliPbEj67lAhUDXawKHbKpD6EQ6AEwA3oECAYQAg#v=onepage&q=nomenclature&f=false Tables of Solid Angles: I. Solid Angle Subtended by a Circular Disk. II ... By William C. Rogers, A. V. H. Maske — Preceding unsigned comment added by 192.188.177.30 (talk) 19:56, 21 October 2019 (UTC)[reply]

Derivation/reference to derivation of the relationship between differential area and differential solid angle

Can a derivation/reference to a derivation for "The solid angle for an arbitrary oriented surface S subtended at a point P is equal to the solid angle of the projection of the surface S to the unit sphere with center P" be added? Nobody seems to derive (formally) the relationship cos(theta)dA/r^2 = domega. It's never derived in any books I have seen either. — Preceding unsigned comment added by 95.91.203.112 (talk) 22:17, 13 January 2019 (UTC) I added a link to derivation in spherical coordinates Chris2crawford (talk) 10:14, 25 May 2019 (UTC)[reply]

Missing definition, and typo.

The last factor α in the last formula is undefined. The α_ij defined in the following line should become a_ij - or the a_xy-s in the formula should become α_xy-s. 22:03, 2 July 2020 (UTC) PS (retreat): But this must be wrong too: wtf were then a_ij! = v_i·v_j! ? 2A01:C22:A86E:1900:6C00:2D52:A42:3BB8 (talk) 23:28, 2 July 2020 (UTC) PS: Clarified see edit 2A01:C23:5C4B:7A00:82F:420:D991:8D9B (talk) 07:41, 3 July 2020 (UTC)[reply]

Extensivity\intensivity of solid angles

It seems to me like the definition is wrong, and solid angles are generally intensive quantities, rather than extensive ones. It can be seen for example by simple dimensional analysis: if all the scales (lengths, energies, entropies) in a system are multiplied by a factor α then the new solid angles of the system will be multiplied by α^2/α^2=1, so they are intensive. Sonicrs (talk) 11:42, 20 January 2021 (UTC)[reply]

I have removed both the parameters from the infobox, as they are not mentioned in the article, nor, as far as I can see, in any hit from Google Scholar or Google Books. - DVdm (talk) 14:20, 20 January 2021 (UTC)[reply]

i don't speak to the terminology of intensive or extensive, but i agree with Sonicrs that the definition is grossly misleading. it is at best an illustration. the solid angle is a RATIO, like kilometers per second. we don't define flux density as, for example, "flux density is the quantity of water that squirts through the area of a nozzle in one second," although that is one of innumerable flawed illustrations of the concept.

the solid angle is a two dimensional area divided by a squared distance, and the steradian is the normalized or "dimensionless" unit of measurement that defines area on the surface of a sphere and the distance as the radius of the sphere. the "surface area" of a solid angle does not represent an obstructing object or surface per se; it can be (and in radiometry is nearly always) a "window" or aperture void, and the apex of the solid angle can be the viewpoint of an observer or it can be the origin of any radiating energy, whether of light through space or sound through air or shock waves through a solid medium or droplets of water spritzed through my lawn sprinkler. the reason we adopt a sphere as the frame of reference is simply because this means whatever is radiating from the source point has an equal energy at an equal distance in any direction; whether the endpoint surface is spherical, flat or the nose on my face then becomes a local problem requiring a local geometrical solution. the first comment on this page links to a google books reference that derives the solid angle subtended by various objects in various orientations to various points of view, but gives a concise and accurate definition of solid angle on the first page. Drollere (talk) 18:58, 28 February 2021 (UTC)[reply]

The natural numbers $\mathbb{N}$ and $0$

The final expression calls itself a Taylor series, and its exponents are given as natural numbers. As there is a diversity of usage of the term ‘natural numbers,’ it is probably worth clarifying that $-$ for present purposes $-$ 0 is a natural number. 2603:7081:700:69EB:A5A3:B0F:F74B:7B50 (talk) 12:49, 7 July 2022 (UTC)[reply]