Pythagorean numbers (determinants)
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| Parent Pythagorean triples (o, p, q) | ^2 ＋ ^2 ＝ ^2 |
| Sub-Pythagorean triples (r, s, t) | ^2 ＋ ^2 ＝ ^2 |
| (u, v, w) | ^2 ＋ ^2 ＝ ^2 |
| (x, y, z) | ^2 ＋ ^2 ＝ ^2 |
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a² + b² = c²
into the following determinant:
( -1 -2 2 ) ( a -a a -a ) ( o r u x )
( -2 -1 2 ) ( b b -b -b ) = ( p s v y )
( -2 -2 3 ) ( c c c c ) ( q t w z )
o² + p² = q²
r² + s² = t²
u² + v² = r²
x² + y² = z²
hold true, forming a ternary tree structure.
(o,p,q)─(a,b,c)┬(r,s,t)
├(u,v,w)
└(x,y,z)