4 ms·
I'm kind of in the opposite camp. If Schanuel's conjecture is true, then e^iπ = 0 would be the only non-trivial relation between e, π, and i over the complex nu
by dvt 2y ago
I'm kind of in the opposite camp. If Schanuel's conjecture is true, then e^iπ = 0 would be the only non-trivial relation between e, π, and i over the complex numbers. And the fact that we already found it seems unlikely.
- seanhunter 2y agoyou mean e^(i pi)=-1, which is known as Euler's identity and is a specific case of Euler's formula e^(i theta) = cos theta + i sin theta That formula gives infinitely many trivial relationships like this due to the symmetry of the unit circle e^(i 2 pi) = 1 e^(3i/2pi)/i=1 e^(5i/2pi)/i=-1 e^(i 2n pi) = 1 for all n in Z ... etc
- botanical76 2y agoThanks for ringing some bells. It's been a long time since I used that equation.