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&[Wolfram Notebook][1] [1]: https://www.wolframcloud.com/obj/2ac57d66-461d-4ac5-ab3d-e33c11aac290 |
&[ finalization ][1] [1]: https://www.wolframcloud.com/obj/f4340d89-8e1a-4b09-b285-adc9e6dd3abf |
Hi Michael, Just scanning the list, and then, almost randomly, but perhaps subconsciously, clicking the first item to not even really jump out at me, I found my way [to intersecting circles][1]. Intersecting circles is a bit more difficult... |
&[another method][1] [1]: https://www.wolframcloud.com/obj/81211ed2-3985-402d-911a-183355efbe2e |
&[Wolfram Notebook][1] [1]: https://www.wolframcloud.com/obj/40d6cbee-724c-4fe4-b7bd-da4612844e64 |
Compared to [Liu Hui's 3.1416][1], the answer 3.14159 doesn't seem too bad. But you are right, now that we have computer technology there's really no excuse for 率 deniers, or anyone else who thinks it's cute to complain about irrationality. ... |
This reminds me that the (non-existant?) theory of linkage pendulums is still calling my curiosity. Assume the linkage has one angular coordinate $\theta$, which is aligned along the gravitational vertical to give every valid configuration a... |
Hi Paul and Ed, When I say "Eisenstein Integers" I just mean hexagonal lattice + group action. Divisibility properties are not necessary in any of my calculations so far. It's possible that Eisenstein integers have some interesting relative... |
Hi Silvia! Nice topic... Also worth mentioning, people have actually done this experiment, [for example here][1], and at MoMath in NYC. [1]: https://www.youtube.com/watch?v=peMrrstOmDA |
[Over on stack exchange][1], someone asked something along the lines: is it possible to prove that Rule 110 outputs black cells with an average asymptotic density $4/7$? This question is now over $10$ years old, but a similar question [came up again... |