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January 14th, 2021

packbat: A selfie shot of a light-skinned black plural system from above, with grass behind zir. (from above)
Thursday, January 14th, 2021 04:34 pm

Here are the conditions of the experiment:

  1. Starting with F0 = 0 and F1 = 1, calculate all Fibonacci numbers up to F[ten] via addition.
  2. Using long division, calcuate the ratio of F[ten] and F[nine] to estimate ϕ (the golden ratio).
  3. Repeat for every positional system base that has a Wikipedia page: 2, 3, 4, 5, 6, 8, 10, 12, 16, 20, and 60.
And here are some thoughts. (425 words) )

I think as far as practical utility of bases of arithmetic, there is a lot we didn't test by doing this operation, but the stuff we did test was very informative.

Edit 2021-02-12: Here is a Twitch highlight of the stream where we did the experiment, for people who want to watch nearly two and a half hours of arithmetic by hand.