perplexus.info :: Numbers : F. to P. generator

F. to P. generator (Posted on 2014-06-25)

Take any 4 consecutive Fibonacci numbers, say d,f,g,h.
Evaluate:
a=2*f*g;
b=d*h;
c=f²+g².

Prove that a triangle with sides a,b,c is a right-angle triangle (for any quadruplet of successive Fibo numbers).

No Solution Yet Submitted by Ady TZIDON

Rating: 5.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)

Even simpler

Comment 4 of 4 |

Since d, f, g, and h are consecutive Fibonacci numbers, d=g-f and h=f+g.

a=2fg

b=(g-f)(g+f)=g^2-f^2

c=f^2+g^2

The formula for a Pythagorean triple is (2fg, g^2-f^2, f^2+g^2). Therefore, (a, b, c) is a Pythagorean triple.

Posted by Math Man on 2014-06-27 16:47:01

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