It is utterly impossible to construct a triangle whose sides' sizes are expressed by 3 different Fibonacci numbers.
Prove it.
let the 3 sides be a,b,c with a<b<c.
In order for it to be a non degenerate triangle we need a+b>c.
However, the largest possible values for a,b are the two fibonnaci numbers immediately before c, in which case a+b=c from the definition of the fibonacci sequence. Thus a+b<=c and thus it is impossible to make a triangle using 3 different fibonnaci numbers.
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Posted by Daniel
on 2018-08-28 08:48:47 |
Proof
