From Nardelli’s Master Equation to the Golden Ratio: Some Relations
PDF contains high-resolution typeset equations. Below, the first two equations in Wolfram-compatible versions:
D[SC,t]=k*(Integrate[Exp[p] GA, X]+(1/(4Pi))*Integrate[Tr[F^2]-Tr[R^2],S/Z2])+(3k d^2)/((2Pi)^2 lp^2 (r^2+a^2)^2)
(13/(k*(Integrate[Exp[p] GA, X]+(1/(4Pi))*Integrate[Tr[F^2]-Tr[R^2],S/Z2])+(3k d^2)/((2Pi)^2 lp^2 (r^2+a^2)^2))-21)^(1/16)+CMRB/8
\begin{equation}
\left(
\frac{\frac{5}{12}(3+\sqrt{5})d^3}{\frac{4}{3}\pi\left(\frac{d}{2}\right)^3}
\times
\frac{1}{\dfrac{\frac{1}{3}\sqrt{2},a^3}{\frac{4}{3}\pi\left(\frac{a}{2}\right)^3}}
\times
\frac{1}{\frac{\sqrt{2},d^3}{12} \times \frac{1}{\frac{4}{3}\pi\left(\frac{d}{2}\right)^3}}
\right)^{1/(2\pi)}
= 1.6180085459
\end{equation}
\begin{equation}
\sqrt[5]{
\frac{(\sqrt{5}-1)^5}{32}
- 5e^{-(\sqrt{5}\pi)^5}
- 1.638289879709566 \times 10^{-7429}
}
= 1.618033988749894848204586834365638117720309179805762862135…
\end{equation}
\begin{align*}
\text{Where: } & \
\phi &= \frac{1+\sqrt{5}}{2} \quad \text{(Golden Ratio)} \
\kappa_{\mathrm{DN}} &: \text{(2sqrt2)/Pi DN Constant} \
C_{\mathrm{MRB}} &\approx 0.187859 \quad \text{(Costante MRB)} \
\star &: \text{Hodge Operator} \
\mathbb{Z}_2 &: \text{Cyclic Group of Order 2}
\end{align*}
\end{document}
Cubica Aurea e Master Equation.pdf (2.4 MB)