Harald Hanche-Olsen 🇳🇴

hagra.no

20 October 2026 21:56

Since I mentioned Euclid's algoritm and the irrationality of the golden ratio, I cooked up a simple figure to illustrate it. Details in alt text.

Daniel McLaury

danielmclaury.bsky.social

17 October 2026 17:49

And then I was imagining some sort of curve that would pass through some of the points and have some nice properties like the golden spiral does for the golden rectangle, something like this? Although maybe also passing through a third vertex of each pentagon, maybe going outside the lines, etc.

Daniel McLaury

danielmclaury.bsky.social

17 October 2026 17:08

Here's what I'm describing in terms of the iterated stacked pentagons.

Daniel McLaury

danielmclaury.bsky.social

17 October 2026 14:45

If we iterate this, it looks like we get two intersecting lines with a infinite number of pentagons stuffed in between them. Is there an analog of the golden spiral here -- that is, a nicely behaved curve that passes through these points?

Colin

colin-fraser.net

16 October 2026 00:23

Awesome