Proof of &#x03C0;<!-- π --> not being a

istremage8o

istremage8o

Answered question

2022-05-19

Proof of π not being a quadratic irrational number.

Answer & Explanation

Buckokasg

Buckokasg

Beginner2022-05-20Added 7 answers

Lambert showed that it's irrational by first demonstrating that the continued fraction expansion holds:
tan ( x ) = x 1 x 2 3 x 2 5 x 2 7 .
He then proved that if x is non-zero and a rational number then the expression must be irrational. Consequently because tan ( π 4 ) = 1, it follows that π 4 is irrational and as a result that π is irrational.

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