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This Concept Map, created with IHMC CmapTools, has information related to: Why_are_there_pythagorean_triples, Z C ,, <math xmlns="http://www.w3.org/1998/Math/MathML"> <msqrt> <mtext> I²+J² </mtext> </msqrt> <mtext> = K </mtext> </math> and interpreted differently, C C, Z C ., <math xmlns="http://www.w3.org/1998/Math/MathML"> <mtext> I² + J² </mtext> <mtext> = K² </mtext> </math> and interpreted differently, Y b, Y b, 0 f(X, Y) =C² = X²+Y², 0 x, So what is the chemistry behind those facts? By accident the equation to calculate the Euclidean norm of a vector in R² is equal to the equation that defines a circle as by definition the circle is the set of points in R² that have the same distance to a fixed point., <math xmlns="http://www.w3.org/1998/Math/MathML"> <mrow> <mtext> to the origin is just the square of that distance and so 
the contour line is a circle too. </mtext> </mrow> </math> The point is: the shape defined by this function is a paraboloid of rotation and this shape can be created by the function, as an rotation of a parabola around the z-axis or as a rotation of the coordinate system., This equation can be seen as the length of a vector (I, J) in R² of Euclidean norm So what is the chemistry behind those facts?, 1 1, , 1, 0 i,j, 0 A/C ,, But this equation can be morphed <math xmlns="http://www.w3.org/1998/Math/MathML"> <msqrt> <mtext> I²+J² </mtext> </msqrt> <mtext> = K </mtext> </math>, . ., Z C ,, k k