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