If pi is unlimited, how can we get exact values for areas/circumferences of circles?

Question

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

Answer 1

It all depends on what precision you need. Of course, theorically, you’ll never be able to get an totally exact value for an area from the radius or diameter.

But you can get values exact enough for your use.

For a circle with a radius of 5cm, you have an area of

78.5cm2 if Pi = 3.14 or

78.5398163397 cm2 with Pi = 3.141592

Thats 7853.98163397 mm2. And probably 0.0000000097 mm2 could be negligible.

Not precise enough ? Take pi = 3.141592653589793238462643383279502884197169399375105820974944592307816406286. The imprecision here should be around an helium atom diameter…