Is a Circle a Polygon?Date: 03/07/99 at 21:25:33 From: Tyler Coffman Subject: Is a circle a polygon? Is a circle a polygon? Please help me. Date: 03/08/99 at 09:00:26 From: Doctor Peterson Subject: Re: Is a circle a polygon? Here are some answers in the Dr. Math archives about this question: Can a Circle be a Polygon? http://mathforum.org/library/drmath/view/54816.html Polygons, Infinite Sides, and Circles http://mathforum.org/library/drmath/view/54912.html Polygons and Circles http://mathforum.org/library/drmath/view/57723.html The first does not really quite deal with the question, but the second is more or less the answer I would give, explaining the concept of a "limit." The third leaves it open, saying mathematicians disagree. You should look through all of these to get different perspectives. Here is the simple answer: no, a circle is not a polygon. A polygon is composed of a finite set of straight line segments, and a circle is not. But you can make a polygon that is as close to a circle as you want; the more sides you give it, the more it will look like a circle. In fact, the other day a student asked if we could show him what a "googolgon" looks like (a polygon with a "googol" of sides, meaning 10 to the 100th power!). I said I can't make one, but if he looks at a circle he will see what a googolgon looks like as accurately as I could draw one! The sides of a googolgon would be smaller than atoms, so if I tried to draw it, it would look no different from a circle. That is what we mean when we say that a circle is in some sense an "infinite polygon" or "the limit of a sequence of polygons": it is not a polygon, but you cannot tell the difference between a circle and a sufficiently big polygon. And where mathematicians might disagree is simply in their willingness to talk about infinity as if it were a real number, and to leave out careful words like "limit." - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/ |
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