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Saturday, January 28, 2012

[Video] Deriving Binet's formula for the Fibonacci numbers

One of those formulas every mathematician loves ( I think ):

$$F_n = \frac{1}{\sqrt{5}}( \phi^n - (1-\phi)^n )$$

Here's how MathDoctorBob explains it.

Although I like The Doctor's videos ( I wished the real doctor would show up accusing me for abusing his name but taking me for a ride in his phone box anyway ), I wouldn't like to have Doctor Bob as a tutor in class, I simply wouldn't be able to catch up and I am not the audible type anyway. I like to read a bit, play and think a bit, read a bit, and so on. Every person has its own unique style of learning that works for him. Part of studying is discovering your own learning style.

Oh, and I think this formula beats the one of Binet ( although strictly speaking not in closed form ), because it fascinates me that the Fibonacci numbers are actually -in- the triangle of Pascal.

$$F_{n+1} = \sum_{k=0}^{n} {n-k \choose k}$$

1 comment:

1. walking here with a smile. take care.. have a nice day ~ =D

Regards,
http://www.lonelyreload.com (A Growing Teenager Diary) ..

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(Raumpatrouille – Die phantastischen Abenteuer des Raumschiffes Orion, colloquially aka Raumpatrouille Orion was the first German science fiction television series. Its seven episodes were broadcast by ARD beginning September 17, 1966. The series has since acquired cult status in Germany. Broadcast six years before Star Trek first aired in West Germany (in 1972), it became a huge success.)