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F. to P. generator (Posted on 2014-06-25) Difficulty: 3 of 5
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)

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Solution 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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