E.g. how can we say that a circle has an area of 25.00cm^2 if pi is irrational?? How can a circle, a closed shape, have a limited area if pi is unlimited??
In: Mathematics
> how can we say that a circle has an area of 25.00cm2 if pi is irrational??
3 < pi < 4. Therefore, 3 r^(2) < pi r^2 < 4 r^(2). The size of the circle is bounded and therefore finite. The sharper you bound pi, the better the estimate of the area will be. With a sharp enough bound, the difference between the estimated area and the actual area will be too small for you to measure. At that point, does it really matter?
> How can a circle, a closed shape, have a limited area if pi is unlimited??
pi is not infinite. It has an infinite decimal expansion. These are two completely different concepts.
An infinite decimal expansion just means that you cannot write the number exactly as digits. The number has an exact, finite value, it just takes infinitely many digits to write it down on paper. No matter how many digits you write down, the number on the paper will always be just a bit higher/lower than the actual value. Adding more digits gets you closer to the exact value, but you’ll always be just a little bit off.
Pi isn’t special here. All irrational numbers have this property. If you only use base-10, even some rational numbers have it. 1/7 has an infinite decimal expansion in base-10, for instance.
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