# NavList:

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

**Re: Mathematical Question**

**From:**Bill Murdoch

**Date:**2002 Sep 20, 20:46 EDT

In a message dated 9/19/02 8:33:09 PM Eastern Daylight Time, enoid{at}NUNANET.COM writes:

The length of an arc of a circle is measured in radians. An arc with the length of its radius has an angle of one radian. The area of a sphere is measured in steradians. A spherical surface with an area of its radius squared has a solid angle of one steradian.

While the arc has only one shape because it is part of a one dimensional closed figure (all arcs differ only in length), the spherical surface could have an infinate number of shapes because it is part of a two dimensional closed figure. It could be a triangle, square, pentagon, hexagon.... (figures on a spherical surface differ not only in area or solid angle but also in shape).

Bill Murdoch

What is the term used to describe a small 2 dimensional section of a sphere? Or to put it another way, if a small section of a circle is called an "arc", what is the equivalent in a sphere?

The length of an arc of a circle is measured in radians. An arc with the length of its radius has an angle of one radian. The area of a sphere is measured in steradians. A spherical surface with an area of its radius squared has a solid angle of one steradian.

While the arc has only one shape because it is part of a one dimensional closed figure (all arcs differ only in length), the spherical surface could have an infinate number of shapes because it is part of a two dimensional closed figure. It could be a triangle, square, pentagon, hexagon.... (figures on a spherical surface differ not only in area or solid angle but also in shape).

Bill Murdoch