Lucas numbers : legs of a right triangle

 

Lucas numbers :   L_{n} \; = \; L_{n-1} \; + \; L_{n-2}
https://en.wikipedia.org/wiki/Lucas_number

 

The legs of a right triangle are:

L_{n-1} \, L_{n+2}
2 \, L_{n} \, L_{n+1}

What feature of the triangle has   L_{n-1} \, L_{n}   as its measure?

 
 
 

Note that:

 
An equation connecting the Fibonacci numbers   F_{n}   to the Lucas numbers   L_{n}   :

L_{n} \; = \; F_{n-1} \; + \; F_{n+1}    for all integers    n

 
 
 
 
 

 
 
 
 
 
 
 
 
 
 
 
 
 
 

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About benvitalis

math grad - Interest: Number theory
This entry was posted in Number Puzzles and tagged . Bookmark the permalink.

2 Responses to Lucas numbers : legs of a right triangle

  1. John McMahon says:

    The length of the Radius of the Incircle.

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