Thursday, January 5, 2023

Finding Congruent Numbers

 This is why the elliptic,


and congruent numbers together.  Does any elliptic has a set of congruent numbers, \({a,\,b}\) that is the sides of a right angle triangle whose area is a whole number.  \(\cfrac{204}{3}*\cfrac{6}{4}*\cfrac{1}{2}=51\) is the integer, indicated by the area of the triangle.

More likely every curve has more than one, such set.