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Three-dimensional case

المؤلف:  Garnett P. Williams

المصدر:  Chaos Theory Tamed

الجزء والصفحة:  37

9-3-2021

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Three-dimensional case

The Pythagorean theorem also is valid in three dimensions (Fig. 1b). It's written just as it is in the twodimensional case but with the third variable (z) also included:

As in two dimensions, the components (here three) are distances measured along the three axes.

Figure .1: Distance between two points in phase space.

If the coordinates of the two points in Figure 4.1b are (-2,2,3) for A and (4,3,2) for B, then the distance between the two points is