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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.
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