Quote:
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Originally Posted by stingc
The concept of a circle is an abstract idealization. Assuming that physical lengths have meaning to arbitrary precision is also an abstraction. Pi is a well-defined logical construct, but we created it. The "physical definition" of pi is only an approximation to the mathematical one (although a very good one).
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I am not very well schooled in math, but isn't the ratio of a circle's circumference to it's diameter something that just is? And the logical construct comes about when we try to assign a number to it?
In simple terms (for my benefit, LOL) if we take a wagon wheel and place a mark on it's outer rim then roll it in the sand until we come to that mark again we will have a line that equals the wheel's circumference. Then if we lay the wheel down on its side (diameter) over the line, it will take up a certain amount of the line's length. The long line (circumference) and the short line (diameter) will always be the same relation to each other (ratio) no matter what size wheel we use.
Isn't this more like a discovery than a logical construct at least until we try to assign an exact number to it?