# NavList:

## A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding

**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