March 19th, 2018, 05:23 AM  #1 
Senior Member Joined: May 2014 From: Allentown PA USA Posts: 110 Thanks: 6 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. 
March 19th, 2018, 01:16 PM  #2 
Global Moderator Joined: May 2007 Posts: 6,732 Thanks: 689 
What is your point?

March 19th, 2018, 02:00 PM  #3  
Senior Member Joined: Aug 2012 Posts: 2,265 Thanks: 690  Quote:
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 onedimensional, even though it typically lives in twodimensional space.  
March 19th, 2018, 03:06 PM  #4 
Newbie Joined: Jan 2018 From: Seattle, WA Posts: 20 Thanks: 6 
A circle can be construed as a polygon with infinite edges.

March 19th, 2018, 04:10 PM  #5 
Senior Member Joined: Oct 2009 Posts: 772 Thanks: 279  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! Last edited by skipjack; March 19th, 2018 at 04:22 PM. 
March 19th, 2018, 04:30 PM  #6 
Global Moderator Joined: Dec 2006 Posts: 20,484 Thanks: 2041  
March 19th, 2018, 09:05 PM  #7  
Newbie Joined: Jan 2018 From: Seattle, WA Posts: 20 Thanks: 6  Quote:
So you'll just have to define "edge" to be two noncongruent points to continue an argument, an exception that as you've already noticed does not play out. Last edited by AngleWyrm2; March 19th, 2018 at 09:26 PM.  
March 20th, 2018, 10:45 AM  #8 
Senior Member Joined: May 2014 From: Allentown PA USA Posts: 110 Thanks: 6 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. 
March 20th, 2018, 10:47 AM  #9 
Senior Member Joined: May 2014 From: Allentown PA USA Posts: 110 Thanks: 6 Math Focus: dynamical systen theory 
Dear MathMan: The point of my question is to do nothing more than stimulate different thinking about the circle. Thank you. 
March 20th, 2018, 11:07 AM  #10 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,932 Thanks: 1127 Math Focus: Elementary mathematics and beyond  

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