PythagorasTheoremGeneralizer

An attempt to discover new kinds of Fractals by generalizing Pythagoras's Theorem into higher dimensions and negative numbers.

Pythagoras Theorem when a < 0.0 and b >= 0.0 :

c^2 = a^2 + b^2 * (((a*a + b*b)^0.5 - b)^2.0/(b - (a*a + b*b)^0.5)^2.0)
c^2 = a^2 + b^2 * (((a*a + b*b)^0.5 - b)^2.0/(b - (a*a + b*b)^0.5)^2.0) * 1.0
c^2 = a^2 + b^2 * (((a*a + b*b)^0.5 - b)^2.0/(b - (a*a + b*b)^0.5)^2.0) * (-1.0 / -1.0)

c^2 = a^2 + b^2 * (((((a*a + b*b)^0.5)*i - b*i)^2.0)/(b*i - (((a*a + b*b)^0.5)^2.0)*i))


Pythagoras's Theorem with negative numbers :


For a < 0 and b >= 0 :

c^2 = a^2 + b^2 * (((((a*a + b*b)^0.5)*i - b*i)^2.0)/(b*i - (((a*a + b*b)^0.5)^2.0)*i))


for a >= 0 and b < 0 :

c^2 = b^2 + a^2 * (((((a*a + b*b)^0.5)*i - a*i)^2.0)/(a*i - (((a*a + b*b)^0.5)^2.0)*i))


for a < 0 and b < 0 :

c^2 = a^2 + b^2


for a >= 0 and b >= 0 :

c^2 = a^2 + b^2



There is Pythagoras's Theorem on Complex Plane numbers.