Modeling PiDate: 01/27/2003 at 13:47:01 From: Imran Subject: Drawing Pi on the real line How can pi, which is irrational, be drawn on the real line? Date: 01/27/2003 at 22:05:24 From: Doctor Ian Subject: Re: Drawing Pi on the real line Hi Imran, Well, pi, like any number, is an idealization. So if I do this, ---|-----|-----|-----|*----| * = pi 0 1 2 3 4 then I've drawn pi on the real line. If I were to _measure_ the distance from 0 to the '*', it wouldn't be exactly pi units, but that doesn't matter all that much. For example, suppose I draw a circle, and say that the diameter is 1 unit. Then if I make a mark somewhere on the circle, the distance from the mark around the circle back to the mark is pi units. Now suppose I cut the circle at the mark, and unroll it. Then I can label the ends 0 and pi, and I've got a number line with pi on it. Drawing it is a little tough using a keyboard, but you don't really need to draw it, because you can model it. Find a (more or less) circular rubber band. In _some_ units, the diameter of this rubber band is 1. (Suppose it's 2.4 inches across. If I define a 'blivet' so that 1 blivet = 2.4 inches, then the diameter of the rubber band is 1 blivet. Does that make sense?) Now, simply cut the rubber band somewhere, and straighten it out on a table (without stretching it). This is basically a number line, where one end corresponds to zero (blivets), and the other end corresponds to pi (blivets). Is that clear? - Doctor Ian, The Math Forum http://mathforum.org/dr.math/ |
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