Heronian triangles with one side Even of length a = 4,6,8,10 –(Part 2)

 
 
Heronian triangles with one side odd of length a = 3,5,7,9,11    (Part 1)
 

There are infinitely many of primitive Heronian triangles with one side of length   a > 2

 
 
If   a   is even:     two cases

(1)

If   a   is even, say   a = 2 \, n,   where n is odd.

we may use

a,      t \, n \; - \; 2,      t \, n \; + \; 2

where   t   is a solution of the Pelian equation

t^2 \; - \; (n^2 - 4) \, y^2 \; = \; 1

(2)

If   a = 2 \,n   where   n   is even

we may use

a,      t \, n \; - \; 1,      t \, n \; + \; 1

where   t   is a solution of the Pelian equation

t^2 \; - \; (n^2 - 1) \, y^2 \; = \; 1

 
Here are the first few solutions:

 
HERON Side Even 1

HERON Side Even 2

 
 

 
 
 
 
 
 
 
 
 
 
 
 
 
 

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About benvitalis

math grad - Interest: Number theory
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