Phi and the golden angle

 

The 'golden angle phi' may be found everywhere in the natural world and its mathematics provides the 'golden section' favoured by artists and architects over millenia. 

Key Mathematics of Phi

• Exact Value: \(\phi = \frac{1+\sqrt{5}}{2} \approx 1.6180339887\dots\)
• Quadratic Equation: \(\phi^2 = \phi + 1\) (or \(\phi^2 - \phi - 1 = 0\))
• Reciprocal Property: \(\frac{1}{\phi} = \phi - 1 \approx 0.618\)
• Continued Fraction: \(\phi = 1 + \frac{1}{1 + \frac{1}{1 + \frac{1}{1+\dots}}}\) [1, 2, 3, 4]

Credit: Wikipedia.

The fern in the image above is arranged and unfurling following those precise mathematical rules.👍🪴