Isn't PI rational?
PI is equal to the the circumference over the diameter of any given circle. Now, circumference and diameter are both measurements. Aren't measurements rational? Can you have a measurement of infinite precision? Shouldn't any measurement terminate somewhere? Well, if that's the case, it would make PI the ratio of two rational numbers, making itself rational. Therefore PI is rational. Any thoughts?
--Steve
--Steve
posted by Steve at 11:37 PM
3 Comments:
You're confusing length with the measurement of the length. Pi is the ratio of the length of the circumference and the length of the diameter, not the ratio of the measurement of the length of the circumference and the measurement of the length of the diameter. A measurement is actually an interpolation of a something (in this case a distance) onto a scale (in this case a ruler), and that operation is never precise.
Not even considing trying to actually get a measurement of something, if you have a circle, its size is finite. It's not like its size is growing by some extemely small amount and thus you can never determine its true size. But I suppose any real world circle you could prossibly try to make cannot be a perfect circle, and therein lies the problem. Suppose it were possible to make a completely perfect circle in the real world; in that case, PI could be finite because the circle's size is. But alas, a perfect circle is completely impossible to constuct in the real world because, if I can explain well enough, a circle is made up of an infinite number of points and not lines (you can't make a true circle with a bunch of tiny lines, which is what ends up being done in the real world.) In the end, if I would have thought about it I would have proven myself wrong, but I just needed something to blog about.
Here's another way to think about it: What pi's irrationality proves is that, if you were to draw a perfect circle with 1 unit radius, and then swivel an appropriate ruler around the circle, the endpoint would NEVER actually fall on a "tick mark" on the ruler, no matter how closely spaced those tick marks are. So if you're using a meter stick, it would be between 3m14cm and 3m15cm; if you add millimeters, you notice that it's betwween 3m141mm and 3m142 mm, etc.
Post a Comment
<< Home