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spherical triangles problem

parish_josh

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Joined
Nov 27, 2013
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1
  1. Let T be a spherical triangle with angles α ,β, γ. Let A, B, and C be the great circles of S^2 that contain each of the three edges of T . Show that these great circles subdivide the sphere S^2 into eight spherical triangles whose angles are all of the form α ,β, γ or π –α, π - β, π –γ.
  2. Show that necessarily π < α+β+γ < π +2min{α,β,γ}. Hint: First show that 0< α+β+γ-π <2α
 

stapel

Super Moderator
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Joined
Feb 4, 2004
Messages
15,937
Let T be a spherical triangle with angles α ,β, γ. Let A, B, and C be the great circles of S^2 that contain each of the three edges of T . Show that these great circles subdivide the sphere S^2 into eight spherical triangles whose angles are all of the form α ,β, γ or π –α, π - β, π –γ.
  1. Show that necessarily π < α+β+γ < π +2min{α,β,γ}. Hint: First show that 0< α+β+γ-π <2α
What have you tried? How far did you get? Where are you stuck?

Please be complete. Thank you! ;)
 
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