Q: Why is pi not a definite number?

The original question was: If the diameter of a circle is a fixed number, say 10cm, why does Pi go on for billions of numbers even though it extrapolates from the diameter’s value? Why is it not a definite number?

Mathematician: Basically, a diameter of 10cm leads to a circumference that is an irrational number. There is a very simple relationship between diameter and circumference, given by circumference = \pi\timesdiameter. It just so happens that the proportionality constant is an irrational number, which means that it has no [finite length] patterns in its digits that repeat forever. This occurs because, well, that is a property that circles have. \pi is however a “definite” number, in the sense that it is a single fixed number that is well defined. It’s just that since its digits don’t have a single pattern, there is no way to write them out nicely. Note that when you write 10 this is the same thing as 10.00000000000000…. with an infinite number of zeros. We can write this just as 10 because it’s understood that this implies that all other digits after the decimal point are 0. So, it’s not that 10 doesn’t have an infinite number of digits (like \pi), it’s just that those digits are zero (unlike \pi) which makes it easy to come up with a notation for ten (namely, 10).

The definition of Pi. This image is from http://www.mathsisfun.com/geometry/circle.html

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6 Responses to Q: Why is pi not a definite number?

  1. Brad says:

    Just one minor note: there are plenty of irrational numbers which have digits that form patterns, ie .101001000100001000001…

    More interesting, I think, is that pi does have very predictable and regular representations in continued fractions. Of course, the correspondence between continued fractions and decimals is extremely poor, even for continued fractions in so-called standard form.


  2. Bo Brymer says:

    For purpose. Enginuity, engineering and Innovation.

  3. Dr.DKShukla says:

    The value od pi is an enigma that nature has given to mankind to play with.I may say GOD played a joke with the limits making them unlimited within their own limits.God said, those who speak in terms of absolutes are egostical nothings.GOD smiles in paradoxes.In the Sankhya system of philosophy Indian philosophy when the absolute balance is reached among the trigunas all the motion ceases and then there is no existence.It is Pralaya.Then again ,God restarts Creation by disturbing the balance,ie,by introducing an assymetry or perturbation or chaos.He makes a “butterfly” flutter its wing somewhere. DrDKShukla.

  4. brandon says:

    The idea of a “circle” is a human construct. The universe knows nothing of circles, nor cares. The fact that the ratio of cirfumerence:diameter turns out to be this weird number that mystifies everyone is purely a consequence of the abstraction that humans call “mathematics”. The universe didn’t make it a weird “number”, we just describe it that way because we lack the proper language to describe it any other way than “pi”…

  5. Raj says:

    numbers are just a illusion a way to measure things which are not meant to be measured any unknown misunderstood concept has been given a value far enough from reality, to povr to the rest the supermacy.

  6. vikas says:

    Actually the circumference of a circle is a finite lenth , if we measure it.and what pie says it is extended upto infinite decimals. Thats the contradiction. …?

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