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Topic: 2 sided polygon on a sphere
Replies: 17   Last Post: Mar 14, 2008 4:54 PM

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Ben Saucer

Posts: 68
Registered: 12/6/04
Re: 2 sided polygon on a sphere
Posted: Oct 5, 2004 10:03 PM
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At 12:48 AM 10/5/2004, you wrote:
>At 05:51 PM 10/4/04 -0400, you [John] wrote:
>>What is the name of a 2 sided polygon on a sphere?
>>It rhymes with moon

>I can't tell whether this is a puzzle for the list to enjoy puzzling over,
>or whether it's something you want answered. I doubt that I'm spoiling
>anyone's fun by suggesting that the answer is "lune".

Also called a "digon".

>Is a figure on the surface of a sphere properly called a polygon? I don't
>know the answer, but would like to. Anyone?

Drawing figures on a sphere is called "spherical geometry", or "elliptic
geometry". Actually, elliptic geometry is drawn on a "real projective plane".

You can draw triangles in spherical geometry, and solve sides and angles
the eay you do in plane geometry. You use "spherical trigonometry" to do
the calculations. The "sides" of the triangles are measured in degrees or
radians just as the angles are.

There's also such a thing as a "hyperbolic" plane, where one does
"hyperbolic geometry". The hyperbolic plane is said to have "constant
negative curvature". The parallel postulate does not hold in either of
these two non-Euclidean geometries.

Ben Saucer
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ICQ: 20610314

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