# NavList:

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

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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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