"Repeating itself" doesn't mean anything. It could repeat X sequence of digits once, twice, a billion, or infinite times, and that does not make the equation rational, which is the fundamental issue with pi, i.e. not being able to "Square The Circle".
Any repeating decimal can be expressed as a fraction though so that does make it rational.
I once had a book with the first 1 million digits. That was quite an achievement at the time. I wonder where that book could have gone...
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