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Spherical geometry

  1. May 19, 2010 #1
    1. The problem statement, all variables and given/known data

    The area of an equilateral triable is Pi/2.

    1) Find the magnitude of its angles
    2) Find the length of its sides
    3) Find the area of its strict dual

    2. Relevant equations

    Area + Pi = sum of 3 angles
    cosa=cosbcosc + sinbsinccosu
    cosu=cosvcosw + sinvsinwcosa for sides length a,b,c and opposite angles of magnitude u,v,w

    3. The attempt at a solution

    1) I used the formula involving area, so Pi/2 + Pi = 3(magnitude of angle) so the answer is Pi/2. Assuming equilateral means the same in spherical geometry?

    2) I used the cos formula with a=b=c, and the angle is Pi/2, getting to cosa= 0, a=Pi/2, or cosa=1, a=0, so a=Pi/2.

    3) Considering the dual triangle to the triangle with sides a, b, c. This dual triangle has sides
    Pi − u, Pi − v, Pi − w. So we would get that the triangle has sides length Pi/2 again. So area Pi/2 again? I'm not very convinced about this.
     
  2. jcsd
  3. May 19, 2010 #2
    Hi,
    You mean area of a equilateral triangle is Pi/2, which means Pi/2=1.571 ?
    Anyway for your 1st question you no need to know its area..Please see the properties of a equilateral triangle (all 3 sides are equal therefore all the 3 angles in a equilateral triangle are same) If you know it you can derive the value for the sides..(all sides are equal).
    3rd question: i really don't understand sorry.
     
  4. May 19, 2010 #3
    pretty sure those answers are right
     
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