Quote:
Originally Posted by sjastro
If you use Mathis' geometrical step construction you will in fact find the sum of the lengths of the hypotenuses of the sub triangles is a constant value irrespective of the number of sub triangles used.
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I didn't find any reference to this constancy, which is patently ridiculous as sqr(x1^2+y1^2)+sqr(x2^2+y2^2)<>sqr( (x1+x2)^2+(y1+y2)^2). The fact is that the length of any curve can be obtained by integrating ds where ds^2=dx^2+dy^2.
dx and dy can be considered the horizontal and vertical components of an infinitesimally small right triangle drawn on the section of curve. His assumption that ds=dx+dy is a clear contradiction of Pythagoras' Theorem. As I mentioned before ds<dx+dy for all right-triangles on the curve. His assumptions are unjustifiable.
Regards, Rob