You're bumping up against the Fundamental Theorem of Calculus here. Pi
DOES have a precisely defined value, but you cannot express it in decimal
form. You can express it as an infinite expansion, however.
Just as you can never get to the end of pi, though its value is known, you
can never PRECISELY note the area of a circle -- you can only express it
more and more accurately, depending on how accurate the value of PI you use is.
Thus, the limit of the area of a circle as your approximation for pi
approaches an infinite expansion is pi*r^2.
At 12:06 AM 2/9/00 -0600, you wrote:
>Hi, I have been considering the possible role pi might play in the
>progression of mersennes. It is generally accepted that the value of pi is
>a never ending series.
>
>But when I look at the circle, the formula for the area of a circle with a
>radius of 6 inches is: A=pi*r^2 = 3.1416 * (6)^2 = 113.0976.
>
>We did not, however, use the full and correct expansion of pi in the
>calculation.
>
>Pi has been figured out to over a billion (not sure of the exact figure)
>digits with no apparent end or pattern.
>
>But when I look at a circle I see a finite area within the circle with no
>means of growing or escape. Logic seems to indicate that pi would have to
>be a finite exact value since the area in the circle is finite.
>
>So, either the figure for pi is in error (not likely) or pi has a end.
>
>The end.
>What say ye?
>Dan
>
>
>
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