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Subject: Re: Mathematical Question
WSMurdoch@XXX.XXX
Date: Fri Sep 20 2002 - 20:46:05 EDT
In a message dated 9/19/02 8:33:09 PM Eastern Daylight Time,
enoid@XXX.XXX writes:
> 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
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