Talk:Spherical trigonometry

message: this artical seems over complicated by use of both degrees and radians. I propose to a change to make it entirely radians.
so for example
"E=A+B+C-π radians"  —Preceding unsigned comment added by 138.251.30.10 (talk) 15:52, 3 October 2007 (UTC)
thread_title: Radians or degrees

message: It seems necessary to say something about the radius in the sin law?  —Preceding unsigned comment added by 71.230.115.205 (talk) 20:07, 7 May 2009 (UTC)
thread_title: Explicit Radius?

message: I corrected the image for Neper's circle
Eroica 08:30, 1 November 2005 (UTC)
replies: text: Since the image is a projection into R^2 and none of the angles are labelled with an "L" type symbol indicating an angle of pi/2, i think that the figure can be used as a general spherical triangle on S^2 without much problem... Boud (talk) 16:57, 4 March 2008 (UTC)
thread_title:  Napier's circle 

message: No idea why someone would want to remove large sections of this page as has been done recently. The last edit (which i reverted) was from someone at an IP in Kowloon, P.R.China. Maybe just experimenting to see if wikipedia is available. Or a Chinese censor trying to be disruptive? Who knows, this is just speculation... Let's just revert to the full version. Boud (talk) 16:57, 4 March 2008 (UTC)
thread_title:  Minor vandalism 

message: This entry needs some work before it is explanatory. It uses a lot of terms without defining them. For example, the formula sin A/sin a etc is stated without explaining what a, A, b, B etc refer to. The diagram is pretty but the letters in it do not correspond to those used in the entry.  —Preceding unsigned comment added by Gnomon (talk • contribs) 23:06, 21 November 2008 (UTC)
thread_title:  Some Work Needed 

message: The Hyperbolic Geometry page credits J.H. Lambert with Girard's Theorem; this page Harriot.  (At least you agree it wasn't Girard!  :-)
Perhaps there was a Harriot-->Girard-->Lambert progression?  Anyway, I think the two pages should be consistent.Jamesdowallen (talk) 14:24, 20 January 2010 (UTC)
replies: text: I don’t know the facts of the case, but Hyperbolic Geometry no longer mentions Girard’s Theorem at all AFAICT, and Thomas Harriot#Legacy agrees with this article—with a citation, yet! —Odysseus1479 (talk) 07:49, 21 September 2012 (UTC)
thread_title:  Credit for Girard's Theorem 

message: The figure showing a spherical triangle can be improved to display the projection of the circles as ellipses. Bo Jacoby.  —Preceding unsigned comment added by 89.239.205.120 (talk) 22:05, 27 January 2011 (UTC)
thread_title:  Figure 

message: The spherical sine law as given under Spherical trigonometry#Islamic world uses Greek letters for angles and italics for sides, mathematician-style as at Law of sines#Spherical case, but under Spherical trigonometry#Identities they’re respectively large and small letters, as is more usual among navigators and consistent with the others in the section. Moreover, FWIW, the first is ‘upside down’ WRT the other two. Do we need to provide this formula twice in one article, anyway? —Odysseus1479 (talk) 07:40, 21 September 2012 (UTC)
thread_title:  Inconsistency in notation 

message: The image of the Polar Triangle shows references to A',B',C',A,B,C.  Yet, the text formulas that seem to be associated with it include a,b,c,a',b',c' but these lower-case points are not shown on the image.  It may be confusing for the easily confused such as me.  Tesseract501 (talk) 06:02, 1 April 2014 (UTC)
replies: text: By convention, where vertices are labelled with capital letters, the corresponding small letters refer to the sides opposite, respectively—as shown in the illustration immediately above. Adding all six labels to this drawing could make it look rather cluttered and impede visualization in three dimensions.—Odysseus1479 06:31, 1 April 2014 (UTC)
thread_title:  Polar Triangle Question 

message: I have added a paragraph on alternative derivations of the fundamental formulae and at the same time I have given a reduced description of the proof added by recent editors. I hope the article will not be expanded to include more of the alternative derivations and thereby lose its concision. I would be grateful if experienced editors can comment. Peter Mercator (talk) 20:23, 10 May 2017 (UTC)
replies: text: I like your edit as it provides a sensible approach to the alternative derivation "problem". I say problem because I have seen too many articles where some editors have felt that every alternative should be reported on. This may be alright if the subject of an article is the proof of a result, but outside of that limited scenario I don't see that it has much value. --Bill Cherowitzo  (talk) 21:16, 10 May 2017 (UTC)
replies: text: I agree—avoid multiple derivations and keep the article concise. cffk (talk) 01:11, 11 May 2017 (UTC)
thread_title:  Alternative derivations 

message: I have recently made some changes in this section that I think need some additional explanation. The issue has to do with the comparison of the spherical laws with their planar counterparts. The phrasing "in the limit" that had been used is ambiguous without referring to the changing variable, in this case an increasing radius. An editor objected to my inclusion of this information with the rationale that the page was written from the viewpoint of a fixed radius for the sphere (in fact, unity), so an increasing radius should not be mentioned. I am not sold on this rationale, but fortunately an alternative phrasing was given (that I have now adopted) that made the point moot. Unfortunately, another editor, for the sake of parallel construction, changed this back to a limit statement (without a variable). My recent edit keeps the parallel construction but removes the limit statement. In this setting, one can either talk about limits or about approximations, but if you phrase things in terms of limits you need to specify the variable in an article at this level, otherwise you are falling into the "math jargon" trap. Yes, it is easy for an experienced reader to figure out what "in the limit" is going to mean in this setting, but this is not the intended audience. Also, the terms, "reduces to" and "is a special case" which had been used here are inaccurate and misleading, so had to be removed. There is one more instance of the use of "in the limit" occurring in the last section. I have left this alone for the time being (assuming that only more sophisticated readers would get that far), but the same reasoning could be applied there.--Bill Cherowitzo  (talk) 18:10, 23 July 2017 (UTC)
thread_title:  Limits in sine and cosine rules 

message: The image of the polar triangle (upper right) is wrong. For all corners of the polar triangle to lie on the visible half of the sphere the origin in the image must lie inside ABC. As AB lies SE of the origin, the corner C' lies on the backside. The image with the poles as shown in the figure implies that AB is the other side of the great circle (i.e. ellipse in the figure) that lies to the NW of the origin (also opposing poles should be at the same distance from the rim in the image, which they are not, and the polar axises be perpendicular to the major axises of the ellipses, which looks doubtful). Compare my figure to the lower right (note that the angles between the "equatorial planes" are not the same in both images). Episcophagus (talk) 08:13, 16 July 2019 (UTC)
replies: text: Also: the smaller triangle you start with, the greater polar triangle you will get (when the sides are all 90° the triangles are identical, and when one of the triangles is a dot, the other is a great circle). In the current image both the original and the polar triangles are smaller respectively than in my image, which is a contradiction. The sides of the polar triangle does not look like correct ellipses, which should be symmetrical around the origin (look at B'C'in the current image - in no way can that be part of an ellipse centered around the origin with the major axis equal to the diameter of the sphere, and neither can A'B' nor A'C'). Episcophagus (talk) 09:43, 16 July 2019 (UTC)
thread_title:  The image of the polar triangle 

message: On the Lexell's theorem page, appears the formula
\sin \tfrac12 \varepsilon = \tan \tfrac12 c \, \tan\tfrac12 h_c
where  is the area of the spherical triangle,  is a side length, and  is the angular difference between two parallel small circles -- one is through the points ,  and the antipodal point  and the other is through ,  and .  I'd like to see this area formula described in this Spherical trigonometry article too (or at the very least a summary and then a link to Lexell's theorem.).  I could give it a try but ... anyone know enough about this formula to do it properly?  Thank you —Quantling (talk | contribs) 18:59, 3 June 2024 (UTC)
thread_title:  Add an area formula