My Math Forum  

Go Back   My Math Forum > College Math Forum > Calculus

Calculus Calculus Math Forum


Reply
 
LinkBack Thread Tools Display Modes
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?
Jmlee19 is offline  
 
December 6th, 2012, 09:05 AM   #2
Math Team
 
zaidalyafey's Avatar
 
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 .
zaidalyafey is offline  
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"!
HallsofIvy is offline  
December 6th, 2012, 12:14 PM   #4
Newbie
 
Joined: Dec 2012

Posts: 4
Thanks: 0

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.
Jmlee19 is offline  
December 6th, 2012, 01:14 PM   #5
Global Moderator
 
Joined: May 2007

Posts: 6,807
Thanks: 716

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 ?.
mathman is offline  
December 6th, 2012, 02:23 PM   #6
Global Moderator
 
greg1313's Avatar
 
Joined: Oct 2008
From: London, Ontario, Canada - The Forest City

Posts: 7,958
Thanks: 1146

Math Focus: Elementary mathematics and beyond
Re: Making a Circle out of line segments

See this topic.
greg1313 is offline  
Reply

  My Math Forum > College Math Forum > Calculus

Tags
circle, line, making, segments



Search tags for this page
Click on a term to search for related topics.
Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
Geometry piecewise line segments master555 Applied Math 0 December 2nd, 2011 05:56 PM
Find the center of overlap between two line segments 1101 Algebra 4 February 22nd, 2011 11:43 AM
Line segments-distance andoxx Algebra 7 February 8th, 2011 08:09 PM
divide ellipse or circle by same length of segments losbellos Algebra 5 April 21st, 2010 02:52 PM
Overlap of line segments Cheesy74 Algebra 4 November 17th, 2009 05:23 AM





Copyright © 2019 My Math Forum. All rights reserved.