English: A depiction of all the primitive Pythagorean triples (a,b,c) with a and b < 1170 and a odd, where a is plotted on the horizontal axis, b on the vertical. The curvilinear grid is composed of curves of constant m − n and of constant m + n in Euclid's formula, ${\displaystyle a=m^{2}-n^{2},b=2mn}$. These curves can be specified parametrically as ${\displaystyle a=(2i-1)(2j+1),b=((2j+1)^{2}-(2i-1)^{2})/2}$, with one of i,j held constant in {1,2,3,...} and the other varied over an interval in R. The oddness of m − n (and of m + n) required for the triple to be primitive is thus built in, with ${\displaystyle m-n=2i-1,m+n=2j+1}$. All primitive Pythagorean triples are represented on this grid. Unlabeled grid intersection points correspond to non-primitive Pythagorean triples.