Mathematicas y plantas

Numeros de Fibonacci

fib[n_]:=fib[n-1]+fib[n-2];
fib[0]=1; fib[1]=1;

fib[26]

Fibonacci[200]

fibplot=ListPlot[Table[Fibonacci[n], {n, 0, 20}]]

Formula para (Subscript[F, n])?

Es exponencial (Subscript[F, n])?

a=1.5;Show[Plot[a^t, {t, 0, 20}], fibplot]

Clear[x];Solve[x^2-x - 1==0,x]

(1/2) (1+(Sqrt[5]))/((1/2) (1-(Sqrt[5])))

Simplify[1-1/((1/2) (1+(Sqrt[5])))]

Clear[c, d];
Solve[{c((1/2) (1-(Sqrt[5])))+ d((1/2) (1+(Sqrt[5])))==1, c+d==0}, {c, d}]

Fibo[n_]:=Simplify[-(1/(Sqrt[5]))((((1/2) (1-(Sqrt[5]))))^n)+ (1/(Sqrt[5]))((((1/2) (1+(Sqrt[5]))))^n)]

Fibo[45]

Fibonacci[45]

Relacion con el numero de oro

mesaracio=Table[N[Fibonacci[n+1]/Fibonacci[n], 10], {n, 20}]

ListLinePlot[mesaracio, PlotRange->All]

Clear[n];Simplify[(-(1/(Sqrt[5]))((((1/2) (1-(Sqrt[5]))))^n)+ (1/(Sqrt[5]))((((1/2) (1+(Sqrt[5]))))^n))/(-(1/(Sqrt[5]))((((1/2) (1-(Sqrt[5]))))^(n-1))+ (1/(Sqrt[5]))((((1/2) (1+(Sqrt[5]))))^(n-1)))]

Tutorial 1

Listas

Table[2+3 n, {n, 1, 8}]

ListPlot[Table[2+3 n, {n, 1, 8}]]

Usa “Table” y “Fibonacci” para formar y trazar la lista 
{0,1,1,2,3,5,8,13,21,34,55,89,144,233,377,610,987,1597,2584,4181,6765}