One of the foremost properties of $\mathrm{\varphi }$ is that it is approximated worse, by the method of fractions of integers, than any other number, so it is known as the most irrational number. This becomes obvious when looking at the continued fraction for $\mathrm{\varphi }$,  $\mathrm{\ϕ} \=1\+\frac{1}{1\+\frac{1}{1\+\frac{1}{1\+\frac{1}{1..\.}}}}$. When approximating a number with a continued fraction, the continued fraction is truncated, and a fraction is used in the last step of the approximation. If this is a small number, such as $\frac{1}{200}$, then the approximation is considered precise. In ϕ's continued fraction, the final fraction is always "$\frac{1}{1}$", which is not small, and that's why ϕ is coined "the most irrational number". This fact makes the golden angle interesting. For instance, if a point were placed around a circle every $0.2$ rotations. After $5$ rotations, the point would have returned to its initial position since $0.2$ is a rational number that can be expressed as $\frac{1}{5}$. After $10$ rotations, the same is still true. Since a rational number of rotations around a circle produces a pattern that will repeat forever, a natural question would be to ask what happens when you rotate around a circle in the same way but place the points after an irractional number of rotations. Additionally, what would differentiate the graph of the most irrational number from that of other irrational numbers?