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Post ApQ1DlKE6AXNoecfXE by [email protected] |
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More posts by [email protected] |
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Post #ApLRsdSmdwPdhT1MbA by [email protected] |
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The number pi has an evil twin! It's a number called ϖ with many propert… |
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Post #ApLS6Q39JKvw9YbSqW by [email protected] |
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@johncarlosbaez John I think the reason it didn't catch on is probably beca… |
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Post #ApLSIukqybn2rF0IQS by [email protected] |
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@dannotdaniel - they made February short especially to avoid this. |
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Post #ApLSS7i6B3rfe36euG by [email protected] |
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@johncarlosbaez it's the only thing that makes sense I for one am done with… |
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Post #ApLTOFPFioDuJG0UtM by [email protected] |
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@johncarlosbaez A culture that may be interested in the mathematics of the sha… |
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Post #ApLUb2oPxQZqy6RZOS by [email protected] |
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Take 2 points. Draw all the curves where the product of the distances from the… |
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Post #ApLUg30AgEAx0KKKki by [email protected] |
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@CptSuperlative - did you read the last line of my post? 😈 |
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Post #ApLUv2vNFYvb6lEdOK by [email protected] |
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@johncarlosbaez this instagram account has posted quite a few things on the le… |
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Post #ApLVGN63ReyrkiOpZw by [email protected] |
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@CptSuperlative - I decided to edit reply to your question and give you a more … |
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Post #ApLVTND0L7S1rfqlJQ by [email protected] |
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@johncarlosbaez Apparently, this is a form of communication. |
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Post #ApLVTNLVpUFyI3pYZc by [email protected] |
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@MartinEscardo - interesting! I wonder if there is a differential equation th… |
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Post #ApLWQlJiLib9ijJ6xc by [email protected] |
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Lots of nice formulas for π have partners that are formulas for the number ϖ!… |
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Post #ApLXNHGzhA7HctwAPg by [email protected] |
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If you're a serious mathematician who has been suffering through all this p… |
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Post #ApLYGiKimuIrTl7Atk by [email protected] |
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@johncarlosbaez @MartinEscardo The search pattern of the desert ant Cataglyphis… |
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Post #ApLYGiR6PBPJnY6GqO by [email protected] |
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@alex - interesting! I'll check out literature on 'search density'… |
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Post #ApLajeXKBOQI0fw7yS by [email protected] |
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@johncarlosbaez can you remind me — did we go over the Wallis-style product f… |
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Post #ApLcitULJ3Bc08J8fA by [email protected] |
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@johncarlosbaez I've been browsing "Squigonometry: The Study of Imperf… |
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Post #ApLiFhciwKe4WvgwWO by [email protected] |
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@duetosymmetry - no, we did not get into that stuff! I think a bit of it is on… |
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Post #ApLk5vibsdM1G0udvM by [email protected] |
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@johncarlosbaez it also shows up in the area of a squircle! https://en.m.wikipe… |
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Post #ApLlsFsML5MRd050ka by [email protected] |
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@johncarlosbaez UInteresting... I wonder if ϖ makes interesting music like pi … |
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Post #ApLpuvOHMI5GmPXRdQ by [email protected] |
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@johncarlosbaez In the universe next door to our own division by zero is always… |
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Post #ApLsp66otWjO9CHjqS by [email protected] |
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@aadmaa @johncarlosbaez @MartinEscardo What are you saying here? Both from memo… |
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Post #ApLsp6HoEfWOhHQVyS by [email protected] |
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@dougmerritt @aadmaa @MartinEscardo - Interesting! It could be a different lem… |
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Post #ApLtiakSgCQd6JHyE4 by [email protected] |
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@aadmaa @dougmerritt @MartinEscardo - the fact that my favorite figure 8 is oft… |
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Post #ApLty2OGBptdAsGlcm by [email protected] |
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@johncarlosbaez they don't teach this in school because it would *absolutel… |
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Post #ApLvOKWLVIv2t89WD2 by [email protected] |
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@womble - practically all of math is dirty if you look at it right. |
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Post #ApLvhnW3vKs2JmIpqC by [email protected] |
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@leon_p_smith - wow, this could be cool if it gets into enough detail. |
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Post #ApM96z0Le66SanoB7Y by [email protected] |
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@johncarlosbaez @MartinEscardo Here's a lemniscate from Euler that arises a… |
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Post #ApMVBfZVWRMklItTAO by [email protected] |
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@johncarlosbaez are sl and cl pronounced sline and cosline? or sline and closin… |
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Post #ApMWMfQoU3gJSzdQyu by [email protected] |
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@WizardOfDocs - heh! Probably "lemniscatic sine" and "lemniscat… |
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Post #ApMby33S7EUvDaLtnE by [email protected] |
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@johncarlosbaez Is there a mutant version of the exponential too? |
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Post #ApMcxoQuZvO5p9mCSO by [email protected] |
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@cyd - great question! I haven't seen it discussed. I'd have to do so… |
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Post #ApMikgPpfv5Kv2OVqi by [email protected] |
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@johncarlosbaezInteresting. This also reminds me of the phase plane diagram of … |
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Post #ApMpV827vParcSpupU by [email protected] |
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@johncarlosbaez Gerudo Flag math |
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Post #ApMt5lTL4LrUDyj356 by [email protected] |
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I love the way you manage to exhibit 3 different spellings in one short paragra… |
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Post #ApMzG3qwBW3Hqs3ZWi by [email protected] |
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@johncarlosbaez Fans of Charles Muses should study whether this can help to con… |
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Post #ApN9cAvjYDt7iLU2ee by [email protected] |
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@johncarlosbaez Your thread is on hackernews: https://news.ycombinator.com/ite… |
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Post #ApNJboEUwEbgrSiz1E by [email protected] |
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@qrios - aha, that''s why I'm getting so many new requests to follo… |
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Post #ApNKEUyUTQFKQWgZdI by [email protected] |
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@johncarlosbaez "the arithmetic-geometric mean of 1 and √2 is the ratio … |
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Post #ApNLXxzstPZptXBVYm by [email protected] |
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@f4grx - Yeah! Gauss was amazing! |
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Post #ApNMIIh6H2dbPFUZea by [email protected] |
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@NickPizzoOceans - that's very interesting. It seems Euler's lemniscat… |
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Post #ApNMYQX4tmnsLkUgro by [email protected] |
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@duetosymmetry - oh, this paper may do what you want:https://arxiv.org/abs/1212… |
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Post #ApNMl6ei6zw6T26st6 by [email protected] |
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@johncarlosbaez hah! That's why it was in my subconscious... You linked it … |
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Post #ApNNPfIgirgnV29JEO by [email protected] |
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@johncarlosbaez gotcha.Is there a lemniscatic SOH CAH TOA equivalent I can use … |
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Post #ApNU1vj4hUQFAi7XlI by [email protected] |
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@johncarlosbaez As someone who's really into math but suffers from poor att… |
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Post #ApNUTnSr0iC7enozNw by [email protected] |
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@november - thanks! Believe me, even supposedly good mathematicians like mysel… |
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Post #ApNb43UTVDRFVlFh68 by [email protected] |
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@johncarlosbaez "the arithmetic-geometric mean of 1 and √2 is the ratio … |
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Post #ApNbXE0ZTdOWWsAr8i by [email protected] |
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@johncarlosbaez The introduction gives three equivalent definitions of sine and… |
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Post #ApNtnLdqf64o0pNpoW by [email protected] |
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@johncarlosbaez @MartinEscardo Bernoulli's seems to be a subset of the Cass… |
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Post #ApNvvG4XS8eOxolco4 by [email protected] |
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@NickPizzoOceans - I want to know whether Bernoulli's lemniscate is the sam… |
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Post #ApOkoOIPZeXY6Xjs12 by [email protected] |
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@johncarlosbaez Isn't there a notable, publicized description of a strange … |
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Post #ApOkoOP9AbvaRQtFVw by [email protected] |
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@rezmason - it sounds vaguely familiar, but I don't think I've ever see… |
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Post #ApOyqbt5PWnyCAqUEa by [email protected] |
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@johncarlosbaez @f4grx I only know that arithmo-geometric mean can be used to c… |
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Post #ApPMVzVKo3LEGDR97o by [email protected] |
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@johncarlosbaez here's a plot of the imaginary part of sl I made recently (… |
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Post #ApPaXUd3BgGb3vbxmi by [email protected] |
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@doctroid - gee, thanks for catching that. You seem to be the first person who… |
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Post #ApPbW9ZY5bBbQBtlz6 by [email protected] |
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@Danpiker - nice! I really have little intuition for these particular elliptic… |
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Post #ApPcHiJYjjdkma68zA by [email protected] |
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@mau @f4grx - I studied that a bit. Here's the trick; then I'll show w… |
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Post #ApPcN0KdAzOC6t7dC4 by [email protected] |
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@mau @f4grx - here's the underlying math, due to Gauss.(2/2) |
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Post #ApPkeSvWue6vLvDbNI by [email protected] |
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@johncarlosbaez I really don't understand this: "Just as the perimeter… |
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Post #ApPySRPc7LRMXPRzEG by [email protected] |
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@gsrdzl - good point. The perimeter of the unit circle is 2π, and the perimet… |
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Post #ApPzJmFhMhTEWJFGOu by [email protected] |
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@johncarlosbaez OK. According to Wikipedia, the equation for a Bernoulli's … |
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Post #ApQ0IVZ21f24QYFMkS by [email protected] |
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@johncarlosbaez I get that this is real inside-blaseball stuff, but the silly n… |
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Post #ApQ0IVgTZyzGndjJLs by [email protected] |
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@WizardOfDocs - I don't know if anyone has bothered to invent lemniscatic v… |
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Post #ApQ113wbYv1LnUWBxA by [email protected] |
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@gsrdzl - yes, a is analogous to the radius. And I now see that a is the dista… |
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Post #ApQ1A0kOok1qUM4mTw by [email protected] |
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@johncarlosbaez Thanks to you. I've learned a lot. |
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Post #ApQ1DlKE6AXNoecfXE by [email protected] |
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@johncarlosbaez @gsrdzl In the case of a non-unit lemniscate I think the perime… |
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Post #ApQ1DlUrSd2oLdbA6y by [email protected] |
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@davidruffner @johncarlosbaez Yes, I'm guessing so, but not sure. |
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Post #ApQ1DlbF4u9GfQaG3c by [email protected] |
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@gsrdzl @davidruffner - I did a bit of work to check, and yes David's remar… |
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Post #ApQRVTKYL4Be1jsfBo by [email protected] |
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@johncarlosbaez @MartinEscardo They are not. There are a few ways to show this … |
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Post #ApR4RZ0rAO6ShjnMRs by [email protected] |
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How about a series of π, ϖ, ... for lemniscates defined for 1, 2, ... points? |
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Post #ApSInRtXu8PhW2fJho by [email protected] |
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@johncarlosbaez I've never seen much about lemniscate functions, but Lemmer… |
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Post #ApSR5aH6HnPsLqqDuy by [email protected] |
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@tmack - wow, that's interesting. Leminiscate functions are really the ell… |
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Post #ApVUQrfFi4YXharBtA by [email protected] |
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@johncarlosbaez A graphic designer friend who was playing with Cassini ovals to… |
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Post #ApVgEj9ciushHd2eMC by [email protected] |
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@mattmcirvin @johncarlosbaez : If I had a kind of shape named after me, then I… |
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Post #ApVgEjKG5NO7oc18vw by [email protected] |
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@TobyBartels @mattmcirvin - yes, this claim is on Wikipedia, and it puzzled me:… |
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Post #ApVi5ZbT41jWxopQGG by [email protected] |
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@johncarlosbaez @TobyBartels and he's saying "you undoubtedly know...&… |
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Post #ApVio9H9nPo6LEaELI by [email protected] |
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@johncarlosbaez @gsrdzl : But notice that \( (x^2 + y^2)^2 = x^2 - y^2 \) is n… |
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Post #ApVjr6jPoOBTH1m9ya by [email protected] |
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@mattmcirvin @TobyBartels - I find this article irritating because it's inc… |
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Post #ApVk0uzkIqVflk5mqG by [email protected] |
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@johncarlosbaez @TobyBartels ...This reminds me that I keep forgetting I can pr… |
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Post #ApVk0v8FnDJcC84a6S by [email protected] |
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@mattmcirvin - I've taken to using JSTOR for studying the history of scienc… |
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Post #ApVkCvQ2YHcAYk7I7U by [email protected] |
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@johncarlosbaez @TobyBartels ...some of this stuff from Leibniz makes me really… |
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Post #ApVkCvbjqmyL91adM0 by [email protected] |
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@johncarlosbaez @TobyBartels ...e.g. (my translation): "I forgot to say ab… |
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Post #ApVkCvlfFsubdoEYpE by [email protected] |
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@mattmcirvin @TobyBartels - as a physical principle, "everything happens i… |
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Post #ApVkzSHZfZjoNqIWB6 by [email protected] |
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@johncarlosbaez @TobyBartels "...the machines of nature are machines throu… |
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Post #ApVlX9p8nwpqyt4K1Y by [email protected] |
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@TobyBartels @gsrdzl - yes, the lemniscate r² = cos2θ is analogous to the cir… |
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Post #ApVmVNNxVnlmPt4L44 by [email protected] |
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@johncarlosbaez @TobyBartels OK, the crucial bit here is on page 79, but it doe… |
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Post #ApVn1IstmXPDivlUXo by [email protected] |
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@mattmcirvin @TobyBartels - thanks for the translation! The great thing about … |
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Post #ApVoBkg7OqFam6KiGm by [email protected] |
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@johncarlosbaez @TobyBartels ...The only real further clue *this* article gives… |
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Post #ApVvpUG8Z1nR7A4hd2 by [email protected] |
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@johncarlosbaez @gsrdzl @duetosymmetry : The circle is \( r = \cos \theta \), … |
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Post #ApW1qW0CAXIUXCUXke by [email protected] |
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@TobyBartels - whoops! My slide showed Leo's actual generalization. |
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Post #ApW3OHEJhLFqWFl9Wa by [email protected] |
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@johncarlosbaez : Good, it's the same (except that my n is Leo's k, an… |
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Post #ApXsq6YOH7WAKu8Ski by [email protected] |
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@digitalgreenery - ϖ is just a script version of a lower case π. @CptSuperl… |
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Post #AprjnEPJbchHOne0A4 by [email protected] |
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@johncarlosbaez Thanks for reminding me to get back on with a little project of… |
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Post #ApsVwkUkTBPdK5n1EG by [email protected] |
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@liuyao - here's a way to compute pi using AGM - not the most practical, bu… |
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Post #Apt1nI8dj6jnIsyzCa by [email protected] |
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@johncarlosbaez yes, I remember your posting about it on the other site. |
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Post #AqQWspsDEjx6As6Gie by [email protected] |
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@johncarlosbaez @Danpiker these two functions are special cases of Jacobi ellip… |
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Post #AqQXmBMf2DwqkrjX1M by [email protected] |
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@paulmasson - nice! Thanks! |
