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 December 6th, 2012, 08:54 AM #1 Newbie   Joined: Dec 2012 Posts: 4 Thanks: 0 Making a Circle out of line segments Is it possible to make a Circle using only infinitely small line segments?
 December 6th, 2012, 09:05 AM #2 Math Team     Joined: Aug 2012 From: Sana'a , Yemen Posts: 1,177 Thanks: 44 Math Focus: Theory of analytic functions Re: Making a Circle out of line segments The length of any curve can be found using integration which is the sum of rectangles when the base of each one approaches zero. Moreover , in the past they would estimate the area of circle using polygons and make the number of sides of polygons approaches infinity. So you can use infinitely line segments to make a circle and let the length of each approaches zero .
 December 6th, 2012, 12:03 PM #3 Math Team   Joined: Sep 2007 Posts: 2,409 Thanks: 6 Re: Making a Circle out of line segments You can, of course, find the perimeter of a polygon of n sides for any positive integer n. And then take the limit as n goes to infinity. But phrases like "infinitely line segments" always have to be understood in terms of limits. There is simply no such thing as a "circle made of infinitely short line segments". Indeed, there is no such thing as "infinitely short line segments"!
December 6th, 2012, 12:14 PM   #4
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Re: Making a Circle out of line segments

Quote:
 Originally Posted by HallsofIvy You can, of course, find the perimeter of a polygon of n sides for any positive integer n. And then take the limit as n goes to infinity. But phrases like "infinitely line segments" always have to be understood in terms of limits. There is simply no such thing as a "circle made of infinitely short line segments". Indeed, there is no such thing as "infinitely short line segments"!
Okay, so if you made a polygon with N sides, and took the limit as N approached infinity, would it be a Circle?
Do "infinitely short line segments" not exist because they are infinitely small and therefore shrink down into nothingness? Or something else?

Thanks.

 December 6th, 2012, 01:14 PM #5 Global Moderator   Joined: May 2007 Posts: 6,727 Thanks: 687 Re: Making a Circle out of line segments There are two restrictions. The polygons should be regular and the vertices should always be at the same fixed distance from the center. Note in passing - this is how Archimedes estimated ?.
 December 6th, 2012, 02:23 PM #6 Global Moderator     Joined: Oct 2008 From: London, Ontario, Canada - The Forest City Posts: 7,929 Thanks: 1124 Math Focus: Elementary mathematics and beyond Re: Making a Circle out of line segments See this topic.

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