Can a Circle be a Polygon?Date: 5/22/96 at 0:42:48 From: Bill Smith Subject: Can a Circle be a Polygon? Could a circle be considered a polygon with an infinite number of sides? Date: 5/22/96 at 9:19:47 From: Doctor Sarah Subject: Re: Can a Circle be a Polygon? Hi Bill - If you've been reading our newsgroup geometry puzzles you'll have seen some of the following discussion, but I'm guessing you haven't, so here it is: From: Mike Slack Newsgroups: geometry.puzzles Subject: Circles Date: 20 May 1996 09:14:52 -0400 How many sides does a circle have? Not as easy as it may seem... It could have 1 curved side! It could have 2 sides - inside and outside! It could have infinite sides? Each side being very small. It could have no sides! If a side is defined as a straight line, no matter how small, then surely a circle has no sides! Why? Because no matter how small a side is it can be halved, and the midpoint of that side is no longer equidistant from the center of the circle compared to each end! Who has the definitive answer? ---------------------------------------------------------------------- From: Curtis - Stephen Dean Newsgroups: geometry.puzzles Subject: Re: Circles Date: 21 May 1996 08:08:34 -0400 By definition a circle is the locus of all points equidistant from a central point. If asked then the number of sides, it is my opinion that the question itself does not apply if "sides" is implied to have the same meaning as in a rectangle or square. However, you could in a non-mathematical sense say that the circle has an inside and an outside, which is mathematically irrelevant. S. Dean Curtis Baltimore County Public Schools Sudbrook Magnet Middle School Baltimore, MD 21208 ---------------------------------------------------------------------- From: Vince Devlin Newsgroups: geometry.puzzles Subject: Re: Circles Date: 21 May 1996 09:22:14 -0400 Mike, You refer to a "curved side." You might want to post your definition of a "side." That might make your puzzle easier to discuss. Vince Devlin ---------------------------------------------------------------------- From: DougKuhlmann-PhillipsAcademy-Math Newsgroups: geometry.puzzles Subject: Re: Circles Date: 21 May 1996 10:49:36 -0400 If you ever studied the Jordan Curve Theorem, you would know that the question of whether a curve determines an inside or an outside is hardly mathematically irrelevant. Doug Kuhlmann Phillips Academy Andover, MA 01810 ---------------------------------------------------------------------- From: Mike Slack Newsgroups: geometry.puzzles Subject: Re: Circles Date: 22 May 1996 07:05:28 -0400 The definition of a "side" is all inclusive in the discussion. But for the sake of completeness here is a definition..... side n. 1. any of the more or less flat outer surfaces of an object, especially as distinct from the top or bottom, front and back. 2. either surface of a flat object. 3. any of the bounding lines of a flat figure such as a triangle or square. (taken from the Oxford Dictionary!) ---------------------------------------------------------------------- From: Walter Whiteley Newsgroups: geometry.puzzles Subject: Re: inside of Circles Date: 21 May 1996 10:30:36 -0400 The fact that a circle, in the plane or on a sphere, has an 'inside' and an 'outside' is mathematically very relevant. In fact, this is a special case of the Jordon Curve Theorem, that any simple closed curve (image of a a continuous 1-1 map from the circle) divides the plane or sphere into two components. This is, of course, not true of some circles on a torus. Walter Whiteley _____________________________________ If you'd like to join this discussion, information on accessing the Forum newsgroups can be found by following the red "info" buttons at http://mathforum.org/discussions/ It's an interesting question! -Doctor Sarah, The Math Forum Check out our web site! http://mathforum.org/dr.math/ |
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