Harmonious Pythagorean Tetrahedra Apex Singularity D1 for tetrahedron ABCD1 (The Z negative solution D2 is not explicitly shown here but may be inferred.) For base right triangle ABC: b = n b/4 < a > 4b c = √(a2+b2) Point A = (0,b,0) Point B = (a,0,0) Point C = (0,0,0) Line g is y = x Curve f(x)=√(4a2+(√(4c2+(c-√(4b2+(b±√(x2-4b2))2-4c2))2-4a2)-a)2) ** x (or y) component of f,g intersection is hx (this is length of CD1) -or- Solve 0=(√(4a2+(√(4c2+(c-√(4b2+(b±√(x2-4b2))2-4c2))2-4a2)-a)2))-x Point D1X = if a < 8.0622575 then -√(hx2-(2a)2) else √(hx2-(2a)2) Point D1Y = if a < 1.98455575342734 then √(-(4b2-4a2)+X2) else...
Continue reading...