Slides

the golden ratio

\[ \large \frac{a}{b} = \frac{b}{a+b}\]


\[ \large \mathbf{\Phi^2 \, - \, \Phi \, - \, 1= \, 0 }\\\]


\[ \large \mathbf{roots\; of\; \phi \, := \, \left\{ \left(\frac{-\sqrt{5} + 1}{2}, 0 \right), \left(\frac{\sqrt{5} + 1}{2}, 0 \right) \right\} }\]


\[ \large \mathbf{\color{#C90}{\phi} \, = \, \frac{\sqrt{5} + 1}{2} } \approx 1.618033989\\ \large \mathbf{\color{#C90}{\varphi} \, = \, \frac{\sqrt{5} - 1}{2} } \approx .618033989\\\]


\[ \large .5 \times 5^.5 + .5\]