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Brad Klee
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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...