Talk:Legendre's theorem on spherical triangles

Introduction

This page is to complement the comments on spherical excess in the article on Spherical trigonometry. I have not attempted to give a proof since such is available on the web (as per references). The article needs a short example to illustrate how the theorem was used in practice in classical geodesy. I started an example in my draft of this page at User:Peter Mercator/Draft for Legendre but I felt that this was inadequate. Further input from a qualified surveyor is needed. Please check for typos etc.  Peter Mercator (talk) 20:36, 4 September 2013 (UTC)

Error bound in introduction

This edit summary doesn't make sense: What is there without the errors bounds is _not_ a statement of a theorem. Michael Hardy (talk) 22:21, 8 September 2013 (UTC)

Sorry, I was trying to cram too much information into an edit summary. The problems with the statement on error bounds that I removed are:

• The notation is inconsistent with the rest of the article: ε instead of E, R is introduced even though the statement of the theorem specifies a unit sphere.
• Why is M cubed? Isn't this just obfuscation?
• The statement is at odds with the equations at the end of the article where the next term is given in terms of the squares of the sides.
• Given that these last expressions are also more useful (e.g., it's clear that the error depends on how different the sides are from each other) and given that the article is so short, I recommend not cluttering the nice clean statement of the theorem with the baggage of the error estimate.

cffk (talk) 12:10, 9 September 2013 (UTC)

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