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Thread: spherical triangles problem

  1. #1

    spherical triangles problem

    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

  2. #2
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    I'm just an imagination of your figment !

  3. #3
    Elite Member stapel's Avatar
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    Cool

    Quote Originally Posted by parish_josh View Post
    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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