Talk:Angle excess
How does this generalize to more than three dimensions? For instance, with four points on a 3-dimensional hypersphere (the surface of a 4-dimensional hyperball
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Higher dimensions?
How does this generalize to more than three dimensions? For instance, with four points on a 3-dimensional hypersphere (the surface of a 4-dimensional hyperball) what can we say about the 3-volume (as measured in hypersteridians?) within the hypersphere that is contained between them? I am hoping for a formula or algorithm that allows the number of hypersteridians to be computed as a function of the angles between the radial vectors to the four points. —Quantling (talk | contribs) 17:37, 10 March 2011 (UTC)
- It seems that there is no easy counterpart for higher dimensions. See for example work about Schläfli formulas. —Quantling (talk | contribs) 17:28, 7 July 2025 (UTC)
Proof that area equals radius squared times angle excess?
Can anyone add a short proof of the statement that "The area of any polygon on a sphere is proportional to the polygon's angle excess, with the proportionality constant being the square of the sphere's radius when the angle excess is given in radians"? —Quantling (talk | contribs) 17:41, 10 March 2011 (UTC)
- I made a bold edit to spherical trigonometry. —Quantling (talk | contribs) 17:26, 7 July 2025 (UTC)
Redirects
Would someone please create redirects for Excess angle and Defect angle, as appropriate? — Preceding unsigned comment added by 75.139.254.117 (talk) 17:17, 14 February 2017 (UTC)
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