@johncarlosbaez@mathstodon.xyz
Post #3913861
2026-07-18 15:22 UTC
But be careful:
By "distance", I mean the length of the shortest path moving inside the Sierpiński triangle, not the usual distance between points in the plane.
Also: we compute the "average" distance using the natural measure on the Sierpiński triangle, not Lebesgue measure.
(2/n)
https://arxiv.org/abs/math/0310109
Replies (1)
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@johncarlosbaez@mathstodon.xyz 2026-07-18 15:23
But suppose we measure distance between points in the plane in the usual way. What's the average distance between two points in the Sierpiński triangle with side length 1? I'm getting 0.4226884 ± 0.00004 This is close to 41/(56√3). But is that the answer, or just a coincidence? 🤷♂️ Maybe someone here can compute more decimal places and settle this question! (3/n)