Quote by suprised
Unfortunately the following site is in german so can't be understood by anyone

Be sure that I understand the point in the website, it is very clear, and it is really no different that the decimal system itself. Note that the program allows each number to generate six different ones via powers, plus some allowance for pi and 2 and its powers, so it has a lot of available combinations to cover ten thousand numbers (four digits). That is, assuming that really you have checked the page. Because it seems that you people do not actually read the posts...
Here, it is not about getting multiple quantities with different formulae, it is the puzzle that we are getting multiple quantities with a single formula.
Namely, we have taken Koide equation for a z,x,y triplet:
[tex] {(\sqrt z + \sqrt x + \sqrt y)^2 \over (z+x+y) } = \frac 3 2 [/tex]
and we have solved for z
[tex]z=f(x,y)=\left[ ( \sqrt x +\sqrt y )\left(2 \sqrt{3+6 {\sqrt{xy} \over (\sqrt x+\sqrt y)^2}}\right) \right]^2[/tex]
It was known since 1981 that this formula, for y=1.77668 and x=0.105659 gets f(x,y)=0.000510, ie, that [itex]n_e \equiv f(m_\tau,m_\mu)[/itex] was equal to the physical [itex]m_e[/itex]. Up to now, one can live with this and appeal to GIGO arguments, garbage it garbage out, disregarding the point that the equation was actually found from physical models. There is a lot of physical models, some of them could hit in a random equation.
NOW, the new observation is that taking as input [itex]m_t[/itex] and [itex]m_b[/itex], and iterating down four times to produce six particles, the total spectrum does not fare bad neither.
[tex]n_c \equiv f(m_t,m_b) \approx m_c[/tex] [tex]n_s \equiv f(m_b,n_c) \approx m_s[/tex] [tex]n_u \equiv f(n_c,n_s) \approx 0 [/tex] [tex]n_d \equiv f(n_s,n_u) \approx m_d[/tex]
So we have verified that the Koide equation also does a decent work in the quark ladder. Not a different equation. Nor different parameter. Nor different powers. The SAME equation. Just 30 years later.
Still, it can be argued that charm and strange have a very broad range of values in the experimental sector, some of them even arguable up to definition of the concept. Thus, we have looked for comparison between the quark and lepton spectrum and found that:
1) [itex] (m_b + n_c + n_s) / (m_e + m_\mu + m_\tau)= 3 [/itex]
2) The phase angle to built the triplet [itex] (m_b , n_c , n_s)[/itex] is about 3 times the phase angle of the triplet [itex](m_e , m_\mu , m_\tau)[/itex]
Both 1 and 2 can be described telling that the triplets, in its square root form, are almost orthogonal when ordered in the cone around (1,1,1).
We can either keep 1 and 2 as a verification of the values of charm and strange, and stop here, or use it as extra postulates to produce all the masses from only two values.