Jon
In one of your documents you say: "Since by definition the value for Pi
is the ratio between the circumference of the circle to its diameter, it
must be representable in the form a/b ..."*
*
This is your fundamental mistake. The *vast* majority of numbers are
simply not expressible as integer ratios. Pi is just one of those.
There is no pair of integers (p, q) such that p/q = pi. None.
As a matter of interest Jon, how would you answer this challenge if someone
put it to you:
Suppose I have a disc and am able to measure it's diameter and its
circumference with complete accuracy using a unit of measurement as small as
I like. If I choose a small enough unit of measurement I will get a whole
numbers for both the diameter and circumference.
If I divide the measured circumference by the diameter I will get a rational
number. So how come pi is irrational?
Phil Hall
