occasional meanderings in physics' brave new world
- Name: Kea
- Location: New Zealand
Marni D. Sheppeard
Tuesday, February 10, 2009
In the approximation of a cubed root cosine by a square root, if one starts with the exact number $26/27$ (for the CKM row sum), then equality implies a numerator not of 723, but of 722.9792412. On the other hand, assuming an exact numerator of 723 results in the number $26.003436/27$. Anyway, $723 = 697 + 26$ and these integers appear in the decomposition of the symmetric magic matrix $U$ into 1-circulant and 2-circulant integer matrices: Observe that the small value of 3 (off the $U(2) \times U(1)$ block) limits the number of positive integer decompositions to four. The 2-circulant piece always takes the form $(26,0,0) + kD$, where $D$ is the democratic matrix and $k \in 0,1,2,3$.