Fibonacci Formula (TANTON Mathematics)

[ViciousSheep]

I know it has been a long time since you put this video up. But could you please explain to me how you get

b = - tau / sqrt(5)

Because I am trying to work through it myself and I keep getting

b = tau / sqrt(5) [Notice the positive tau]

I must be going wrong somewhere but I don't know where.

Thanks

[heladobon]

where did u get

a= # / sqr( 5) ?

[DrJamesTanton]

@heladobon

Okay: So we have: a + b = 1 and a*phi + b*tau = 1. Multiply the first equation through by tau and leave the second alone.

a*tau + b*tau = tau

a* phi + b*tau = 1

Subtract to get: a(phi - tau) = 1-tau.

But phi-tau = sqrt(5) and 1-tau = phi (check this!) so we have: a*sqrt(5) = phi giving a = phi/sqrt(5).

Does this help? [Writing math in an e-mail format horrible!!]

[heladobon]

@DrJamesTanton

thanks a lot man =D