11 ms·
The number pi has an evil twin
- BeetleB 2y agoI follow John on Mastodon. He never fails to disappoint.
- hinkley 2y agoThen why do you follow him?
- barrell 2y agoOddly enough, “never fails to disappoint” can have the meaning “never disappoints” as well as “routinely disappoints”. I’ve never thought about that one before
- jrmann100 2y agoHere's a StackExchange thread on this exact mix-up (a "misnegation"): https://english.stackexchange.com/questions/139448/never-fail-to-disappoint https://english.stackexchange.com/questions/139448/never-fai...
- heresie-dabord 2y agoNative EN parser here. I would never consider this usage correct except as a rhetorical (facetious) insult. People may well repeat it without understanding the original nor their mistake. Although if enough people bust the syntax, it may attract descriptivist reporting, as with the widely observed malapropism "irregardless". https://english.stackexchange.com/questions/139448/never-fail-to-disappoint https://english.stackexchange.com/questions/139448/never-fai... https://en.m.wikipedia.org/wiki/Irregardless https://en.m.wikipedia.org/wiki/Irregardless
- kazinator 2y agoI've never failed to win a game of mahjong against a bunch of grannies a Chinatown back room joint. I've never tried such a thing; therefore, I've never failed.
- barrell 2y agoIt’s not a matter of correctness, but of understanding. OP definitely intended to imply the content does not disappoint, and used a colloquialism most native speakers would understand
- slippy 2y agoI am a native speaker and got the gist and saw the paradox, and found the phrasing a bit tortured by the triple negative. Thank you for explaining that this was a colloquialism. Now I have to go look up the etymology... And upon further inspection, this usage is actually a misnegation. "It is a veiled insult: an ironic form of insult delivery which is misinterpreted as flattery to the buffoon who is targeted by it, much to the entertainment of anyone else within earshot who understands the true meaning."
- hinkley 2y agoOnly in the same sense that “could care less” is understandable but also means the opposite of the intention.
- ftmch 2y agoThere are East European languages, mostly Slavic ones, that have these weird double negatives which are grammatically correct and mean the opposite. A sentance such as: "I haven't never been there" means you've never been there.
- scubbo 2y agoFrankly, I could care less
- hinkley 2y agoI have only ever heard it used as a high brow burn, and a wickedly hard one at that.
- reshlo 2y ago> can have the meaning “never disappoints” How?
- kazinator 2y agoA complete stranger who has nothing whatsoever to do with you, who has never tried to do anything for you, nor has been expected to, has never disappointed you. They've also never failed to disappoint you, because they have not failed in any regard whatsoever. This is an example of a vacuous truth. I've never failed an airliner landing. While that may sound like I'm boasting of being a good pilot, in fact I'm not a pilot at all, and I've never attempted such a thing. Another vacuous truth. Every crow in an empty set of crows is white. Also, every crow in an empty set of crows is black. Propositions universally quantified over an empty set are all vacuously true. Statements with always and never are universally quantified over some set of events. If that set is empty it leads to vacuous truths. "Every time I've seen a crow, it has always been white" is vacuously true if I've never seen a crow. I.e. the set of crows I've seen is empty, and consequently is a true statement that they're all white.
- seba_dos1 2y ago> A complete stranger who has nothing whatsoever to do with you, who has never tried to do anything for you, nor has been expected to, has never disappointed you. They've also never failed to disappoint you, because they have not failed in any regard whatsoever. "never failed" != "never fails"
- reshlo 2y ago> A complete stranger who has nothing whatsoever to do with you, who has never tried to do anything for you, nor has been expected to, has never disappointed you. They've also never failed to disappoint you, because they have not failed in any regard whatsoever. Nobody who uses the phrase ever means it in this way. The point of using the statement is to convey that you are familiar with the person’s history. As another commenter has already pointed out, “has never failed to disappoint” is not the same statement as “never fails to disappoint”. The habitual present can’t refer to empty sets, as it is only used to refer to repeated actions.
- ykonstant 2y agoWhat a country!
- jacknews 2y agoNever heard that one, but maybe it's like 'could care less', which has acquired the opposite of it's actual meaning (the phrase should be 'could not care less') by repeated incorrect use.
- hinkley 2y agoI’d say that’s more tolerated than embraced. We know what you meant, you just didn’t say what you meant. Not everyone tolerates it.
- Agingcoder 2y agoThis is the first time I come across this mistake / non-mistake so I misunderstood your comment. Are you sure it’s a common enough misnegation for people to understand what you meant ?
- barrell 2y agoI didn’t use the expression, I don’t think I would have myself, but it didn’t even strike me as odd until I read the comment by hinkley. Did you read the original comment and think BeetleB follows John and thinks all of his content is disappointing?
- BeetleB 2y agoHeh. This comment blew up on me. Yes, it was a typo.
- metaphor 2y ago> This ∞-shaped curve is called a 'leminscate', and ϖ is called the 'lemniscate constant'. I'll show you the leminiscate in my next post. Two of these...do not belong?
- brookst 2y agoEven the word has evil twins
- saghm 2y agoIt's so evil that it defies spelling
- thaumasiotes 2y agoLemniscate. https://en.wiktionary.org/wiki/%CE%BB%CE%B7%CE%BC%CE%BD%CE%AF%CF%83%CE%BA%CE%BF%CF%82#Ancient_Greek https://en.wiktionary.org/wiki/%CE%BB%CE%B7%CE%BC%CE%BD%CE%A...
- adrian_b 2y ago"Lemniscate" is the correct spelling. All the other variants are mistyped.
- yard2010 2y agoIt's quite funny imo that someday english people were like "forget about latin or german, greek is lit! Let's use greek"
- laurent_du 2y agoWhat makes you think it was the English? I am pretty sure it comes from continental Europe.
- cgio 2y agoLatin is lemniscus, so someday Latin people were like “let’s use Greek”
- sapphicsnail 2y agoIf I saw ϖ in the wild I would have assumed it was an omega (ω) with a macron over it. Makes me wonder how many more varient Greek letters are out there.
- wombatpm 2y agoAncient, Ancient Greek had three additional letters: an F like character, a double lambda character, and P sounding character that looked like a lollipop. In case you need some additional symbols
- rsynnott 2y agoConsiderate of them; very helpful for future mathematicians.
- perihelions 2y agoI guess these are the letters? https://en.wikipedia.org/wiki/Archaic_Greek_alphabets https://en.wikipedia.org/wiki/Archaic_Greek_alphabets Ϝ Digamma Ͱ Heta Ϻ San Ϙ Koppa Ͷ Tsan, Digamma Ͳ Sampi
- Pinus 2y agoAny actual Greeks around here? I always wondered what π looks like when jotted down in, say, a shopping list...
- xico 2y agoThis is actually a normal manuscript π as taught in Greek school. See https://www.typotheque.com/articles/modern-handwriting-a-historical-survey-5 https://www.typotheque.com/articles/modern-handwriting-a-his...
- nuancebydefault 2y agoAs psted now and then on HN:our alphabet has a variant as well: ampersand (per se: and).
- notpushkin 2y ago> I'm not enough of a cultural relativist to believe there's a civilization that cares more about the shape ∞ than the shape ◯. Rumor has it there is one civilization of lizard-people out there. One is in fact running a company here on Earth with this shape as a logo! /s
- kvdveer 2y agoYou mean Arduino is ran by the Illuminate?
- ta988 2y agoyes you can blink leds
- notpushkin 2y agodun-dun-dunnn! But I was actually alluding to Meta and the memes about Mark Zuckerberg being a lizard: https://www.youtube.com/watch?v=jiudBq7z8wk https://www.youtube.com/watch?v=jiudBq7z8wk
- big-green-man 2y agoYou just blew my mind. I'm taking a dive on this.
- Morizero 2y agoIs there an abstraction of a leminscate/consonant with 3+ center points?
- fisian 2y agoYes, the Lissajous https://en.wikipedia.org/wiki/Lissajous_curve https://en.wikipedia.org/wiki/Lissajous_curve which also can be turned vertical (to look like an 8 instead of ∞).
- mandarax8 2y agoBut this doesnt have the property that the product of the distances to the focal points is constant no?
- mandarax8 2y agoHeres two examples for 3 and 6 points in 2D, 3D respectively: https://en.wikipedia.org/wiki/Cassini_oval#Generalizations https://en.wikipedia.org/wiki/Cassini_oval#Generalizations These are symmetric as well though.
- marginalia_nu 2y agoKinda looking like hydrogen orbitals.
- SubiculumCode 2y agoIs there an evil twin to the set of prime numbers?
- block_dagger 2y agoEvery even number?
- ralusek 2y ago2?
- pwdisswordfishz 2y agoWell, this one is pretty evil as prime numbers go.
- fisian 2y agoThere are the anti prime numbers (also called highly composite numbers).
- OscarCunningham 2y agoThere are the Lucky Numbers https://en.wikipedia.org/wiki/Lucky_number https://en.wikipedia.org/wiki/Lucky_number. Generated by a variant of the Sieve of Eratosthenes, they're believed to have a similar distribution to the primes while not having similar multiplicative properties.
- amai 2y agoThe opposite of prime numbers are https://en.wikipedia.org/wiki/Highly_composite_number https://en.wikipedia.org/wiki/Highly_composite_number But I'm not sure if these ones are evil.
- GistNoesis 2y agoAnd to protect you from it, you can use the following lucky clover charm (polar plot r=cos(2theta) ): https://www.wolframalpha.com/input?i=+plot+r%3Dcos%282theta%29 https://www.wolframalpha.com/input?i=+plot+r%3Dcos%282theta%... whose perimeter can also define a constant 4*E(-3) ~ 4 * 2.4221 https://www.wolframalpha.com/input?i=plot+r%3Dcos%282theta%29+from+theta+%3D+-pi%2F4+to+pi%2F4\ https://www.wolframalpha.com/input?i=plot+r%3Dcos%282theta%2...
- divbzero 2y agoπ is derived from the circle, which is defined by distance from a single point. ϖ is derived from the lemniscate of Bernoulli, which is defined by distances from two points. Is there an analogous constant that is derived from a shape defined by distances from three points?
- clort 2y agoit sounds like you are suggesting it might be turtles all the way down?
- deleted 2y ago[deleted]
- VHRanger 2y agoI mean the concept of distance from 3 points introduces a mess of metrics or even measure theory. 2 points always have a shortest path between each other, so the constant is about this fact. For 3 points you have the whole universe of possible triangle shapes to contend with.
- jovial_cavalier 2y agoIt's easy to generalize this to more points. https://www.desmos.com/calculator/fo7tqlfjgo https://www.desmos.com/calculator/fo7tqlfjgo
- vitus 2y agoShortest path between two points still depends on your metric. For instance, if you're constrained to travel along the surface of Earth, your shortest path is going to travel along a great circle, rather than pass through the interior of the sphere. That said, you could, for instance, pick the three vertices of an equilateral triangle (using the Euclidean distance as your metric of choice, as we do in order to derive the lemniscate and the circle), and again deal with the product of the distances from each vertex. You again start with small circles around each vertex, which eventually expand to a single looping curve, and then into ovals encircling the entire triangle. https://en.wikipedia.org/wiki/Cassini_oval#Generalizations https://en.wikipedia.org/wiki/Cassini_oval#Generalizations https://en.wikipedia.org/wiki/Polynomial_lemniscate#Erd%C5%91s_lemniscate https://en.wikipedia.org/wiki/Polynomial_lemniscate#Erd%C5%9...
- veltas 2y ago[flagged]
- yukioikeda 2y agoIt seems obvious that these are not twins. We can only say that π and ϖ are two among the infinite multitude of siblings ϖₙ.
- efortis 2y agoInfinity symbol with Lissajous curve: x = Asin(at + delta) y = Bsin(bt) https://ericfortis.github.io/lissajous/?preset=Infinity https://ericfortis.github.io/lissajous/?preset=Infinity
- jan_g 2y agoInteresting! I can see it in two ways: (1) as elongated U-shaped ellipsis that rotates sideways and (2) as bent lemniscate that rotates vertically.
- divbzero 2y agoThe Fourier transform is composed of trigonometric sines and cosines. There must be an analogous transform composed of lemniscate sines and cosines?
- ttoinou 2y agoYou could try to make a transform based on a sum of lemniscates in the complex plane
- TomK32 2y agoAm I the only one who expected the evil twin to be 3 ?
- incognito124 2y agoFor some reason, I imagined a number where every digit of pi was transformed into a [9-digit] and that it has special properties. This one is more magical, though.
- nthingtohide 2y agoChange pi to ϖ in this setup. 2022 - Non-Euclidean Doom: What happens to a game when pi is not 3.14159… https://youtu.be/_ZSFRWJCUY4?t=406 https://youtu.be/_ZSFRWJCUY4?t=406
- seba_dos1 2y agoSuch a promising yet disappointing talk.
- AlecBG 2y agoThe lemniscate really looks like a homoclinic orbit in a 2d dynamics problem
- deleted 2y ago[deleted]
- doffen 2y ago[flagged]
- mongol 2y agoYes, that is when I stopped reading. I left Twitter recently, but I would not call it a Nazi bar. It is just not for me, any longer.
- nthingtohide 2y ago> Hence neither a man's contemporaries nor the man himself can form any final estimate of him or of his fitting position, because their knowledge is too imperfect. History often reverses the decision of contemporaries. Probably true about Elon.
- I_complete_me 2y agoBut I think mainly in the direction of demotion. Offhand I can't think of examples of someone ... oh, wait Van Gogh.
- nthingtohide 2y agoBaruch Spinoza is another. He was excommunicated.
- Johanx64 2y ago[flagged]
- mnsc 2y agoCuriously that made the thread better for me and the author's opinion about Twitter is exactly as true as the opposite opinion, that it is now the unfiltered source of objective truth. Or do you believe your opinions on the threads value or twitters reputation is special?
- veltas 2y agoI also found it extremely helpful that the author virtue signalled to agree with me, so I know whether I am supposed to like it or not.
- slippy 2y agoHmm. Why only 2? Why not 3 points? Can you find an interesting curve produced by a constant product of distances from N points? Maybe even in higher dimensions, for 1 point, you have a sphere. What is the shape for 2 points? Is it more like an hourglass-like double droplet?
- amelius 2y agoThere is a generalization: > Back before Twitter became a Nazi bar, I issued a challenge there: find a whole series of numbers like pi, each with its own bunch of formulas. @duetosymmetry took me up on this and invented the numbers ϖₙ: (...)
- plank 2y agoYes. But the question remains: is there a geometrical analogue?
- knappa 2y agoOn the 3 points bit: One and two points are special. In each of these cases, there is, up to translations and uniform scaling, only one configuration. When you have three points, though, there are as many configurations as there are similar triangles. You could probably get a number for each similarity class of triangle, but you shouldn't expect to get a constant across all classes.
- Bengalilol 2y agomupi (mutant pi) or piet (pi evil twin) would be better names
- Qem 2y agoPizarro = Pi + Bizarro. Also there was an evil person that beared this name, Francisco Pizarro, the conquistador that kickstarted the genocide against the Incas. See https://en.m.wikipedia.org/wiki/Francisco_Pizarro https://en.m.wikipedia.org/wiki/Francisco_Pizarro
- mst 2y agoHaving that shape become more important to a civilisation than the circle because it has something to do with the geometry of hyperspace seems like it could be an interesting conceit for a sci-fi setting.
- sourcepluck 2y ago> This ∞-shaped curve is called a 'leminscate', and ϖ is called the 'lemniscate constant'. I'll show you the leminiscate in my next post. I think others have commented, but this three-way spelling certainly got a chuckle from me.
- deleted 2y ago[deleted]
- yason 2y ago[flagged]
- NoboruWataya 2y ago> Up/down arrows jump to the next post and page up/down isn't too helpful for reading. I didn't experience this at all on Firefox, up/down and page up/down scrolled in the normal way.
- RobotToaster 2y agoIt kinda happens to me on firefox, one press of the down arrow scrolls so "Here's a formula for the lemniscate in polar coordinates" in the first reply is at the top of the screen, not helpful.
- davorak 2y agoThe issue existed from me in both firefox and chrome. Click on outside columns will result in normal scroll. Click or highlight in the center column will result in the jumpy scroll that does not quite scroll one comment at a time with up/down arrow.
- kuschkufan 2y agohere's a nickel, get a new browser. no idea why i even go for bait like this. because i like doing unpaid support work i guess. i tested in firefox and chrome. both work fine and don't do it like op decribes - no keybinds, keys behave normal. maybe one of the dudes from yesterdays thread that had his own chatgpt programmed browser extensions installed that break the web for him.
- pwdisswordfishz 2y agoSame here. I have to install a userscript to restore usable scrolling: // ==UserScript== // @name Mastodon: don't fucking hijack the keyboard // @grant none // @match https://hachyderm.io/* // @match https://mastodon.social/* // @match https://mamot.fr/* // @match https://queer.party/* // @match https://social.treehouse.systems/* // @match https://infosec.exchange/* // @match https://jawns.club/* // @match https://mastodon.gamedev.place/* // @match https://mathstodon.xyz/* // @run-at document-start // ==/UserScript== window.addEventListener('keydown', ev => ev.stopPropagation(), true); window.addEventListener('keyup', ev => ev.stopPropagation(), true);
- soneca 2y ago> ” This ∞-shaped curve is called a 'leminscate', and ϖ is called the 'lemniscate constant'. I'll show you the leminiscate in my next post.” This got me confused, so I went to check. Apparently ”lemniscate” is the correct spelling.
- johncarlosbaez 2y agoFixed - thanks.
- thechao 2y agoHey, John — Matt Parker mentioned in one of his ellipse videos the fact that every elliptical ratio has its own pi-like constant. He just quickly rattles the fact off, but never delves into it. Do you know of any research into trying to characterize the family of pi? I mean, beyond its evil cousins.
- klodolph 2y agoFor a circle, pi is the ratio of the circumference to its diameter. Every ellipse also has a circumference-to-diameter ratio. Well, two ratios, since ellipses have both major and minor diameters. You might think that there would be some kind of clever formula that let you calculate this ratio, but there isn’t! Instead, these pi-like numbers for ellipses are expressed as integrals: https://en.wikipedia.org/wiki/Elliptic_integral https://en.wikipedia.org/wiki/Elliptic_integral Scroll down to “Complete elliptic integral of the second kind”. That is your search term for looking it up. It is kind of a surprise that there isn’t some neat formula for calculating the circumference of an ellipse. The formula given is: C = 4 a E(e) The function E(e) here can be calculated in a few different ways, but it is really just defined as an integral that measures the length of a single ellipse arc. Here, e is eccentricity. E(0) therefore gives π/4 since a circle has eccentricity 0. E(1) also therefore gives 1. So the E(e) function goes from π/4 to 1 as e goes from 0 to 1.
- candlemas 2y ago>On our planet, it was Bernoulli, Euler and Gauss who discovered this math. You don't say. Newton must have been sick that day.
- cl3misch 2y ago> I'm not enough of a cultural relativist to believe there's a civilization that cares more about the shape ∞ than the shape ◯. Maybe these are "logarithmic" beings, as opposed to us "linear" beings? The lemniscate is based on geometric mean, which is basically multiplicative mean and/or mean in log-space -- as opposed to the additive mean in linear space. If we assume we are linear beings good at intuitive addition but somewhat bad at intuitive multiplication, there could exist beings which live in log-space and whose minds are based on multiplication. Their circle would be the lemniscate.
- tibbetts 2y agoHumans are actually intuitively log scale thinkers. That is, humans without the kind of early arithmetic training that Westerners get will think more in terms of ratios than differences. There are theories it is more evolutionarily adaptive. https://www.scientificamerican.com/article/a-natural-log/ https://www.scientificamerican.com/article/a-natural-log/
- jcelerier 2y agoIsn't it also related to our physical perception? Both hearing and vision at least have somewhat logarithmic properties (e.g. response to point-source brightness, and hearing frequency response)
- dustingetz 2y agofibonacci retrace shows up in liquid markets a lot
- nayuki 2y agoHumans have quite a few logarithmic responses: Brightness of light, loudness of sound, musical octaves and relative pitch.
- bnetd 2y ago[flagged]
- d_burfoot 2y ago[flagged]
- ryanmcgarvey 2y agoIs it a political statement if it's also a statement of fact? Sure, the comment has some color to it, I'll concede that, but one can no longer post these kinds of things on Twitter and get the honest engagement from community members one used to. It's no longer a welcoming place for this kind of discussion.
- BearOso 2y agoWith no account, I can no longer read comment chains on Twitter. It will only show the direct comment linked to. If you go to the user's page, all you see are the promoted tweets. There's no way to access the timeline sequentially anymore. With those restrictions, you're writing only to a captive audience if you post on Twitter. So you are technically correct, you literally cannot post these things on Twitter.
- foogazi 2y ago> Why does this guy think it's acceptable to bitterly insult so many people, Won’t someone think of the people? My mom is on X - I don’t see how that offhand remark insults her > I think HN should have a policy for submitted content that is along the lines of the policies in place for comments We can already flag and vote - what more censorship do you want ?
- cluckindan 2y agoSide by side, there is a clear parallel to monopolar and bipolar fields. Is this found in any version of Maxwell’s equations?
- layer8 2y agoIs there something like ThreadReaderApp for Mastodon?
- BearOso 2y agoI thought it might be e. e is often used to model unbounded growth, so it's chaotic, while pi is harmonic. Plus, evil starts with 'e', so why not. "Laugh with me Jocko!" "Eeeeeeeeeeeeee!"
- anyfoo 2y agoCan’t have harmonics (i.e. harmonic oscillations, or any oscillations really) without e, though. sine and cosine are both sums of e, and if you look at the beauty of analytical sinusoid signals (which only have one component in the entire spectrum, lacking their negative frequency one) it’s just one exponential and nothing else.
- aap_ 2y agoWow, pomega is such a terrible name for it!
- dclaw 2y agoThis discussion helped me discover my new favorite map. https://en.wikipedia.org/wiki/File:Peirce_Quincuncial_Projection_1879.jpg https://en.wikipedia.org/wiki/File:Peirce_Quincuncial_Projec...
- _steady 2y agooh wow that's a lot like a maximally extended penrose diagram
- thih9 2y agoMore projections in a friendly pdf: “An Album of Map Projections”[1], the one above is on page 190. For a more festive example see Berghaus star projection on page 156. [1]: https://pubs.usgs.gov/pp/1453/report.pdf https://pubs.usgs.gov/pp/1453/report.pdf (1989)
- dclaw 2y agoOK, that's fucking awesome. Thanks
- deleted 2y ago[deleted]
- extraduder_ire 2y agoI believe I have seen the same projection used in a mod for quake 3 for dramatically increased POV.
- waldrews 2y agoSeems like a fine number, but I bet there's quite a few more irrational computable numbers out there.
- dxbydt 2y agoaside: As the Professor points out, the ratio of pi to its evil twin is ~1.198, the arithmetic-geometric mean of sqrt(2) and 1. The geometric part involves a square root, and square roots are expensive. So I was like, well, if the AM converges to GM, then due to AM-GM-HM inequality, it must converge to the harmonic mean as well. And the HM does not need an expensive square root! https://imgur.com/a/UkxkPzW https://imgur.com/a/UkxkPzW Its quite wild that the AM GM convergence is almost immediate - in just 2 steps, whereas to get a decent convergence for the Gauss's constant via HM, you need like 15 steps.You can dispense with expensive operators like square root but you end up paying for it with numerous iterations.
- Chinjut 2y agoThe c value you compute depends on computing the b value, though. It's not a recursion carried out in a way which avoids square roots. It's just carrying out the same AM-GM sequence computation, and then taking a certain weighted harmonic mean over that sequence, which converges just because that original sequence converges anyway. Note that the arithmetic-harmonic mean I think you were going for is just the geometric mean (not the arithmetic-geometric mean, just the geometric mean simpliciter; see https://mathworld.wolfram.com/Arithmetic-HarmonicMean.html https://mathworld.wolfram.com/Arithmetic-HarmonicMean.html).
- ComputerGuru 2y agoThe post mentions that ϖ is called “varpi”; I just wanted to add that this is actually short for “variant of pi”, also known as an “archaic form of pi” from old Greek writing.
- flatline 2y agoI read it as “omega-bar.”
- initramfs 2y agohttps://en.wikipedia.org/wiki/Bizarro https://en.wikipedia.org/wiki/Bizarro
- avalys 2y agoI thought this was going to be about tau, which is not pi's evil twin, but rather, the One True Circle Constant. https://tauday.com/tau-manifesto https://tauday.com/tau-manifesto
- ssalka 2y agoupvote for tau, the one really running the show while pi gets the fame & fortune
- TaurenHunter 2y agoOther notable constants and where they show up: Euler–Mascheroni Constant (integrals and sums involving the harmonic series, Gamma functions) Catalan’s Constant (certain trigonometric series, lattice Green’s function) Feigenbaum Constants (logistic map, chaos in dynamical systems) Khinchin’s Constant (partial quotients in simple continued fractions) Glaisher–Kinkelin Constant (asymptotic expansions of the Barnes G-function, combinatorial limits and certain product expansions) Ramanujan’s Constant (complex multiplication of elliptic curves) Omega Constant (Omega times e to the power of Omega = 1, Lambert W function, x^x^x^... = 2)
- ctrlrsf 2y agoHow do you even know this?
- ska 2y agoSpend some time doing math and you'll pick up a few without noticing. Somewhat path dependent, but they do crop up. See also: https://en.wikipedia.org/wiki/List_of_mathematical_constants https://en.wikipedia.org/wiki/List_of_mathematical_constants
- rak1507 2y agoWhat do you mean by x^x^x^... = 2? Isn't the solution to that sqrt(2)?
- 77pt77 2y ago
- mettamage 2y agoSo are there an infinite amount of constants like this? In terms of pi, e and this number? Just wondering, there are an infinite number of shapes I suppose? But does that mean there is an infinite amount of constants?
- dwaltrip 2y agoThere are infinite integers [1]. So even if we just look at basic polygons — shapes formed by connecting some (integer) number of points with straight lines — we easily get infinite shapes. Math is crazy. The universe is crazy. Happy holidays! ——— [1] At least, that’s what they tell us… :p
- whamlastxmas 2y agoWish people wouldn’t inject weird social jabs into stuff like this
- kolbe 2y agoJust like advertising--if they have earned my attention by saying things I want to read, then they have the right to dilute its quality with whatever else they want, up until it net doesn't interest me anymore. In this case, the jab is tiny and the quality content is bountiful.
- whamlastxmas 2y agoThe author isn’t going to convince anyone or change anything with a random jab and it detracts from what they’re communicating
- kolbe 2y agoSounds like his problem
- babbledabbler 2y agoWoah it even has a w for wa-pi-rio.
- nektro 2y agohow close is ϖ to e?
- thoughtcritical 2y ago"figure of eight" curves .... perhaps the simplest is the lemniscate of Gerono, which has the parametrization: x = cos(t); y = sin(2t) / 2; and looks like this: Lemniscate of Gerono animation https://i.sstatic.net/VKBgs.gif https://i.sstatic.net/VKBgs.gif However, the lemniscate of Bernoulli may be visually more pleasing; it has a parametrization very similar to the lemniscate of Gerono, except that both axes are scaled by a factor of 1/(sin(t)^2 + 1) = 2/(3 - cos(2t)): scale = 2 / (3 - cos(2t)); x = scale cos(t); y = scale * sin(2*t) / 2; It looks like this: Lemniscate of Bernoulli animation https://i.sstatic.net/nOPMx.gif https://i.sstatic.net/nOPMx.gif per: https://gamedev.stackexchange.com/questions/43691/how-can-i-move-an-object-in-an-infinity-or-figure-8-trajectory https://gamedev.stackexchange.com/questions/43691/how-can-i-...