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    Re: Spherical Trig
    From: Dan Allen
    Date: 2005 Apr 5, 16:46 -0600

    On Apr 5, 2005, at 4:08 PM, n s gurnell wrote:
    
    > Re Bill's question about the angles in a spherical triangle.
    > Sixty years ago the exams called "Principles for Second Mates" used to
    > have a
    > question:- "What is Spherical Excess?" I've forgotten the exact answer
    > but
    > someone might know. Old Timer
    
    The sum of the angles of a spherical triangle is between pi and 3 pi
    radians (180 deg and 540 deg). The amount by which it exceeds 180 deg
    is called the spherical excess and is denoted E. The difference between
    2 pi radians (360 deg) and the sum of the side arc lengths a, b, and c
    is called the spherical defect and is denoted D.
    
    Girard's formula:
    
       Spherical Excess = E = A + B + C - pi
         where A,B, and C are angles measured in radians
       Surface Area = E * R^2
         where R is the radius of the sphere
    
    Dan
    
    
    

       
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