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lvlastermind
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Im looking for some proofs on the rationality of pi. I also want to know what some people think about it.
fourier jr said:I think the Chinese approximated Pi long before any western people. They said it was 355/113. (see the 1, 1, 3, 3, 5, 5? nice pattern) I don't think it can be dated though since the Chinese typically destroy everything from their past.
Rationality in mathematics refers to a number that can be expressed as a ratio of two integers. For example, 3/4 is a rational number because it can be written as a fraction, while pi (π) is an irrational number because it cannot be expressed as a ratio.
Pi is calculated by dividing the circumference of a circle by its diameter. This calculation has been done using various methods and technologies, resulting in over 31 trillion digits being calculated so far. However, for most practical purposes, only a few digits after the decimal are needed.
Proving the rationality of pi would mean that it can be expressed as a finite number or fraction, which would simplify many mathematical calculations and make them more accurate. It would also provide a deeper understanding of the concept of pi and its relationship to other mathematical principles.
There have been many attempts to prove the rationality of pi throughout history, including geometric methods, infinite series, and continued fractions. However, all of these attempts have failed to prove that pi is rational, leading to the conclusion that it is an irrational number.
As of now, there is no known method or proof that can definitively prove the rationality of pi. It is considered one of the greatest unsolved problems in mathematics, and many mathematicians believe that it may never be proven due to the infinitely complex nature of the number.