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How is the exact value of pi determined?

My answer to: How is the value of pi determined if all formulas we have are just approximations? (To vote and comment on Quora, visit the link here.)

Pi is an exact value, and its exact value is known, in fact accurately. The exact value is represented by the Greek letter π. What our problem is, we don’t know how to express pi accurately in the format we are familiar with: numerals.

We don’t need to find the decimal representation of pi; it is just a number like 1, 2, 3,… Just as 3 represents the value of three, pi represents the ratio between a circle’s circumference and diameter. There is no need to know its exact value!! If we want to know its digits, it’s purely an obsession with representing numbers with numerals, even when you understand what those numbers actually mean. The truth is, numbers can be represented in any way we want, if we have a conceptual understanding of the number. The digits of pi never help.

Example: Even though their values are same, I believe 4 and 2² are different; when we write 4, we are representing the number “four”, whereas saying 2² puts the focus on the fact that we are talking about a square. Representing numbers by values is unnecessary, when you know what the number means. 2² gives more information than 4 in certain cases. Similarly, in context of permutations and combinations, saying 4C2 gives more information than saying 6, even though they have the same value.

Drawing the analogy to pi, representing it as “π” and leaving it at that is more helpful than finding out its digits. WE DON’T NEED ITS DIGITS!!

The association of geometry with trigonometry, calculus, and complex numbers has given us various beautiful infinite series that total to pi (exactly). But of course, since they are infinite, they can’t be evaluated.

Since numerals are the format of numbers we are used to working with, we have approximated pi to some easy fractions such as 22/7, 333/106, etc. That does not make them equal to the actual value of pi.

To differentiate between the number represented adequately as π, and the number expressed by numerals such as 3.14, we need to just simply understand that pi is an irrational number with non-repeating, non-terminating decimal representation.

Useful links:

Pi (Wikipedia article, for infinite series)

Joshua Engel‘s answer to If pi is not equal to 22/7, how do we know its value?
(for a theoretical way to reach pi)

Also read  Intuition behind converting a number of base n to decimal

My answer to  If pi is not equal to 22/7, how do we know its value? (for more insight into this)

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