(April 14, 2023 at 11:40 pm)Anomalocaris Wrote: isn’t that just saying a line on a polar plot for which every point has the same ratio between distance from center and angle from fixed reference would be a spiral?
Not quite. There are larger patterns happening.
But, if you plotted using degrees instead of radians, you would simply get a 180 lines through the origin.
The larger patterns are due to how well pi can be approximated by fractions, with the 'missing spirals' determined by exceptionally good approximations.
A similar pattern would be found if you plotted in a way that a full circle was the square root of 2 times some unit and plotted in that unit.
Ultimately, it is an expression of the fact that pi is irrational.
