Series

Cone transitions — the series

One essay so far on this idea, and more questions about it than one essay answers.
  1. The rise falls as one over the distance from the apex. A straight line of slope −1 on log axes. The dashed horizontals are the transition rises of the cylinder's ladder, computed with no cone anywhere in them; where they cross, the count changes. Consecutive crossings are 2.62, 2.62, 2.62, 2.62 apart — φ² is 2.618.

    Transitions a factor of φ² apart

    The ladder's rungs are a factor of 1/φ² apart in rise. A disc's rise falls as one over radius squared and a cone's as one over distance, so the same rungs land a factor of φ apart on a seed head and a factor of φ² apart on a cone — measured, on both, by a counter that has never heard of either.

    part 3 · cylinder

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