Fibonacci Formula (TANTON Mathematics)

The Fibonacci numbers begin 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, .... What's the 100th number in this list? The 587th number?

In this video we derive a general formula the N-th Fibonacci number.

(WARNING: This video assumes complete familiarity with solving a quadratic equation, basic properties of exponents, and solving a tiny system of equations.)

Category:

Education

Tags:

• Fibonacci
• Formula

[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!!]

[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]

@DrJamesTanton

thanks a lot man =D