Sunday, July 02, 2006

Powers of Phi and Fibonacci Sequence

Yesterday, I noticed a pattern in the Powers of Phi and the Fibonacci Sequence:

Phi1 = Phi
Phi2 = Phi(0+1Phi)
Phi3 = Phi(1+1Phi)
Phi4 = Phi(1+2Phi)
Phi5 = Phi(2+3Phi)
Phi6 = Phi(3+5Phi)
Phi7 = Phi(5+8Phi)
Phi8 = Phi(8+13Phi)
Phi9 = Phi(13+21Phi)
Phi10 = Phi(21+34Phi)
Phi11 = Phi(34+55Phi)
Phi12 = Phi(55+89Phi)

I thought this was an interesting and novel expression of the powers of Phi and the Fibonacci sequence. From what I can tell, so far, nobody else has noticed this pattern previously.

7/3/6 - Today I extended the above relationship into a type of multiplication table for powers of Phi. Check the link above to see the full table.

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