Talk:Koide formula
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[edit] Another Interesting Coincidence?
Consider an xyz Cartesian coordinate system and the vectors (1, 1, 0), (1, 0, 1) and (0, 1, 1), the projections of the vector (1, 1, 1) onto the xy, xz, and yz planes respectively. Modify the projection vectors so that they have the lengths, respectively, that correspond to the masses of the electron, muon, and tau particle in units of eV/c2. Applying the pythagorean theorem to each of the projection vectors, we have the system of equations
x2 + y2 = (0.000511)2, x2 + z2 = (0.1057)2, y2 + z2 = (1.777)2.
The solution to this system is given by x2 = -1.5732, y2 = 1.57327, z2 = 1.58445.
The input data only has three place accuracy, so the solutions can not be relied upon beyond three significant figures. But it is interesting (and perhaps only coincidental) that these values cluster about the value of pi/2 = 1.57079... . Samdhatte (talk) 00:14, 19 February 2008 (UTC)
Yep, the one you have found is, it seems to me, other way to arrive to the observation by R. Foot about how to reinterpret Koide formula in terms of a vector 45 degrees away from 1,1,1. 83.138.204.146 (talk) 02:24, 23 February 2008 (UTC)
