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### a2+b2=c2 & e=mc2

WHOIS DOT & NOT  a2+b2=c2 & e=mc2 .E=M*n

PYTHAGORAS               EINSTEIN                    TYCHON

RECONVERSE!                                  n   liquid city architects

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The Circle With an Off-centered Dot

As shown in Figure 2, the length of OP in the triangle COP is , where r = |CP| is the radius of the circle, and r0 is the length |CO|. (Without loss of generality, in Beghi et al. (1991a), the origin O of the Oxy system is positioned half way between the center of the circle, C, and the off-centered dot E. The same convention is adopted here.) Hence, the speed of point P is (the 4th equation from bottom left, p. 429): (12) Figure 2. A circle and a dot E are rotating around the origin O in plane Oxy. O is halfway between E and the center of the circle C. P is an arbitrary point on the circle.

By adding an additional velocity component in depth, Beghi et al. (1991a) obtain (their Equations 5 & 6): (13)

Then (Equation 8 of Beghi et al. (1991a)): (14)

The remainder of this section assigns the 3-D coordinates of the circle and dot without mathematical reasoning. So there are no derivations to be analyzed. Still, the introduction of vz(P) makes the circle non-planar in 3-D due to the nonlinearity of Equation 14 (as in the case of the rotating bar). This contradicts the prediction of the model, e.g., in Figure1b of Beghi et al. (1991a), and of the empirical perceptual result. Since the alternative method in Beghi et al. (1991a) claims that the circle remains planar in 3-D (p. 430), which contradicts Equation 14, and since the alternative method claims to yield the same result, it is self contradictory.

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