π \pi

Number Theory Level 2

( 2 π ) 2 = \huge(2 \pi)^2 =

Clarifications: When I mean "all of them" and "none of them" I am referring to the solutions that include τ \tau and π \pi

None of them τ 2 \tau^2 All of them 4 π 2 4 \pi^2

Mohammad Farhat by Mohammad Farhat , 16, Singapore

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1 solution

Mohammad Farhat
Sep 1, 2018

If you did not know but τ \tau means 2 π 2 \pi . So one of the solutions is clearly τ 2 \tau^2 . But ( 2 π ) 2 (2 \pi)^2 also = 4 π 2 4 \pi ^2 because ( 2 π ) 2 (2 \pi)^2 = ( 2 π ) ⋅ ( 2 π ) = 2 2 ⋅ π 2 = 4 π 2 (2 \pi) \cdot (2 \pi)= 2^2 \cdot \pi ^2 = 4 \pi ^2 So the answer has to be All of them. \text{So the answer has to be All of them.}

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