PlanetMath (more info)
 Math for the people, by the people. Sponsor PlanetMath
Encyclopedia | Requests | Forums | Docs | Wiki | Random | RSS  
Login
create new user
name:
pass:
forget your password?
Main Menu
sections
Encyclopædia
Papers
Books
Expositions

meta
Requests (236)
Orphanage
Unclass'd (1)
Unproven (540)
Corrections (47)
Classification

talkback
Polls
Forums
Feedback
Bug Reports

downloads
Snapshots
PM Book

information
News
Docs
Wiki
ChangeLog
TODO List
Copyright
About
Owner confidence rating: Low Entry average rating: No information on entry rating
spherical trigonometry (Topic)
This entry is broken! Please report this to the author (fernsanz) by filing a correction. In the meantime, you can see if another rendering mode works.
(view preamble | get metadata)

View style:

See Also: area of a spherical triangle

Keywords:  Spherical Trigonometry
Log in to rate this entry.
(view current ratings)

Cross-references: triple vector product, property, cyclic, plane, angle, vectors, unitary, vertex, cosine

This is version 9 of spherical trigonometry, born on 2007-05-22, modified 2007-05-24.
Object id is 9443, canonical name is SphericalTrigonometry.
Accessed 2293 times total.

Classification:
AMS MSC: 51M04 (Geometry :: Real and complex geometry :: Elementary problems in Euclidean geometries)
Pending Errata and Addenda
None.
[ View all 1 ]
Discussion
Style: Expand: Order:
forum policy
Small changes/ differential by jhm on 2007-11-06 08:12:27
Any hints for the solution of the following would be greatly appreciated:

ABC is an equilateral spherical triangle in which small displacements are made in the sides and the angles, of such a nature that the triangle remains equilateral. Prove that:

da/dA = cos(A/2) x cot(a/2).

I assume that 'd' refers to a delta, or small change, rather than a differential, but I've tried taking derivatives and anti-derivatives with no success. Substituting A+dA leads to insanely complicated expressions which might reduce to this result, but I have yet to find a way. This is not a homework or test question (at least not for me), but for my own peace of mind, I would like to get a handle on it. It occurs in "Spherical Astronomy [Smart 1977]"
[ reply | up ]
Sine-formula. by jhm on 2007-10-24 07:51:08
Thanks for this. I'm working my way through "Spherical Astronomy" [Smart, 1977], specifically, the first chapter on spherical trigonometry. I would love to see some treatment of other formulae, especially the sine-formula. My difficulty lies in finding a more rigorous method of choosing between two possible solutions for arcsin(x) = y or 180-y other than drawing a diagram. It is anathema to me that one should rely on a diagram. Are there some properties of spherical triangles analogous to those of planar ones (sum of angles equals 180)?

As a side note, the text defines spherical triangles as having no sides or angles equal or greater than 180 degrees, and I'm wondering why (other than making life much easier) an arc of a great circle could not be the base of a triangle whose area includes a pole as well as a diametric part of the same circle.
[ reply | up ]
Interact
post | correct | update request | add example | add (any)