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Google El blog de Pedro Hugo García Peláez: One sequence of powers of Phi, Phi and two Fibonacci sequences

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viernes, 9 de septiembre de 2016

One sequence of powers of Phi, Phi and two Fibonacci sequences

One sequence of powers of Phi, Phi and two Fibonacci sequences



1.618^2 = 2.618
1.618 * 1 + 1 = 2.618
1.618^3 = 4.2358
1.618 *2 + 1 = 4.236
1.618^4 = 6.853
1.618 *3 + 2 = 6.854
1.618^5 = 11.089
1.618 *5 + 3 = 11.09
1.618^6 = 17.942
1.618 *8 + 5 = 17.944
1.618^7 = 29.03
1.618 *13 + 8 = 29.03
1.618^8 = 46.97
1.618 *21 + 13 = 46.978
1.618^9 = 76.012
1.618 *34 + 21 = 76.013
1.618^10 = 122.9911
1.618 *55 + 34 = 122.911


1.618^n = 1.618*(n_1 + n_2) + (m_1 + m_2)


Para n>=2
n_(0) = 1
n_(1) =2
m0 = 1
m1 = 1

n,n_,m_  are natural numbers.

Aso limit of: 1.618*(n_1 + n_2) / (m_1 + m_2) = 2.618 = Phi^2


Copyright   Pedro Hugo García Peláez, 2016

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