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Re: Mathematical Question
From: Bill Murdoch
Date: 2002 Sep 20, 20:46 EDT
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@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
