Sponsored links: Algebra eBooks
 

Help Index

A

B

C

D

E

F

G

H

I

J

K

L

M

N

O

P

Q

R

S

T

U

V

W

X

Y

Z

The Maxima on-line user's manual

Algebra Calculator

Search:

Fibtophi Calculator

Fibtophi

Function: fibtophi (<expr>) Expresses Fibonacci numbers in <expr> in terms of the constant %phi, which is (1 + sqrt(5))/2, approximately 1.61803399.

Examples:

          (%i1) fibtophi (fib (n));
                                     n             n
                                 %phi  - (1 - %phi)
          (%o1)                  -------------------
                                     2 %phi - 1
          (%i2) fib (n-1) + fib (n) - fib (n+1);
          (%o2)          - fib(n + 1) + fib(n) + fib(n - 1)
          (%i3) fibtophi (%);
                      n + 1             n + 1       n             n
                  %phi      - (1 - %phi)        %phi  - (1 - %phi)
          (%o3) - --------------------------- + -------------------
                          2 %phi - 1                2 %phi - 1
                                                    n - 1             n - 1
                                                %phi      - (1 - %phi)
                                              + ---------------------------
                                                        2 %phi - 1
          (%i4) ratsimp (%);
          (%o4)                           0

(%o1)                                true
(%i2) 

Fibtophi Example

Related Examples

fibtophi-numer-ratsimp

f(x,y,z):=5*fibtophi(...

ratsimp(f(x,y,z)),numer;

f(12,34,36);

Calculate

fibtophi-ratsimp

f(x,y,z):=5*fibtophi(...

ratsimp(f(x,y,z));

Calculate

fibtophi-ratsimp

fibtophi (fib (n));

fib (n-1) + fib (n) ...

fibtophi (%);

Calculate

fibtophi-numer-ratsimp

f(x,y,z):=5*fibtophi(...

ratsimp(f(x,y,z)),numer;

f(12,34,36);

Calculate

fibtophi-ratsimp

f(x,y,z):=5*fibtophi(...

ratsimp(f(x,y,z));

Calculate

fibtophi-ratsimp

fibtophi (fib (n));

fib (n-1) + fib (n) ...

fibtophi (%);

Calculate