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March 19th, 2018, 05:23 AM   #1
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Math Focus: dynamical systen theory
Concerning the circle

Dear My Math Forum Community:
Can one think of the circle as an enclosed space having only one edge? Thank you.
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March 19th, 2018, 01:16 PM   #2
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What is your point?
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March 19th, 2018, 02:00 PM   #3
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Quote:
Originally Posted by Carl James Mesaros View Post
Dear My Math Forum Community:
Can one think of the circle as an enclosed space having only one edge? Thank you.
In geometry, an edge is "a particular type of line segment joining two vertices in a polygon, polyhedron, or higher-dimensional polytope ..."

By that definition, a circle isn't an edge and doesn't have an edge.

https://en.wikipedia.org/wiki/Edge_(geometry)

What is true is that a circle is one-dimensional, even though it typically lives in two-dimensional space.
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March 19th, 2018, 03:06 PM   #4
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A circle can be construed as a polygon with infinite edges.
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March 19th, 2018, 04:10 PM   #5
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Originally Posted by AngleWyrm2 View Post
A circle can be construed as a polygon with infinite edges.
What does that even mean?? Doesn't a polygon by definition have finitely many edges?

Are you saying that a circle is the limiting form of a polygon if you increase the edges? That's quite a different statement!
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Last edited by skipjack; March 19th, 2018 at 04:22 PM.
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March 19th, 2018, 04:30 PM   #6
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Originally Posted by Carl James Mesaros View Post
Can one think of the circle . . .
Did you mean "disk"?
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March 19th, 2018, 09:05 PM   #7
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Originally Posted by Micrm@ss View Post
What does that even mean?? Doesn't a polygon by definition have finitely many edges?

Are you saying that a circle is the limiting form of a polygon if you increase the edges? That's quite a different statement!
If you can conceive of a line with infinite points on it, or a plane with infinite lines on it, then you should also be able to perceive a polygon with infinite edges. A circle doesn't have one edge it has infinitely many, one for every point on it's circumference.

So you'll just have to define "edge" to be two non-congruent points to continue an argument, an exception that as you've already noticed does not play out.
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Last edited by AngleWyrm2; March 19th, 2018 at 09:26 PM.
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March 20th, 2018, 10:45 AM   #8
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Math Focus: dynamical systen theory
A Reply to AngleWyrm2

Dear AngleWyrm2:
Some further evidence that your position of a circle is a polygon that has an infinite number of edges is that pi, which is heavily used in circular measurement, is a transcendental number.
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March 20th, 2018, 10:47 AM   #9
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Dear MathMan:
The point of my question is to do nothing more than stimulate different thinking about the circle. Thank you.
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March 20th, 2018, 11:07 AM   #10
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Quote:
Originally Posted by Carl James Mesaros View Post
Dear My Math Forum Community:
Can one think of the circle as an enclosed space having only one edge?
You need to specify that there is a point contained by the edge that is of the same distance from the edge in any direction.
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