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*}
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