8 ms·
How Pi Almost Wasn't
- deleted 2y ago[deleted]
- gerdesj 2y agoLooking at the list of 10 equations. For me 2,5,8,9,10 being simplified with Pi=3.141 is the best outcome, especially 5. I'm definitely: e^{i \pi} + 1 = 0
- tonyarkles 2y agoI agree with you on the absolute beauty of e^{i\pi}+1=0, but I think I would also see a different beauty in e^{ik\pi}=1 for all integer k (if we had \pi=6.28... instead)
- orangecat 2y agoI would argue that #2 is better with tau; yes there's a factor of 1/2, but it should be there for the same reason that kinetic energy is 1/2mv*2 and distance traveled under constant acceleration is 1/2at*2. All of those are the result of integrating a linear function.
- yen223 2y agoFor all integers k, e^(i k\tau) = 1 This is way more beautiful to me than the pi version e^(i 2k\pi) = 1
- jmclnx 2y agoMost of the article was over my head, but it hit HN because tomorrow is PI Day. It is a nice article though. A Quote: >we celebrate Good-Enough Pi Day in honor of the approximation 3.1, which is close enough for most purposes. It could be celebrated on either the 3rd of the 1st month ... or on the 1st day of the 3rd month... at the end it went to the fact in other countries there is no month 14 :)
- deleted 2y ago[deleted]
- ahazred8ta 2y agoApproximate Pi day is in July: 21/7. 1 Kings 7:23 describes a basin in Solomon's Temple as ten cubits across and a cord of thirty cubits encircles it. The word for 'cord' has two spellings with two numerical values: qvh (111) and qv (106). Now, 3 × 111/106 = 333/106 = 3.1415
- leereeves 2y agoShouldn't that be 22/7?
- dekhn 2y agoI'm still surprised that Pi isn't considered a universal physical constant, given Buffon's needle depends on (IIUC) the physical curvature of nonrelativistic space.
- mitthrowaway2 2y agoUp until 2019, it sort of was, via the magnetic constant mu_0 = 4 pi x 10^-7 H/m exactly. Unfortunately the 2019 revision of SI redefined it.
- IHLayman 2y agoIs it because pi isn’t measured, but calculated? The wikipedia article (https://en.m.wikipedia.org/wiki/Physical_constant https://en.m.wikipedia.org/wiki/Physical_constant) makes a distinction between a mathematical constant and a physical constant, stating that the latter cannot be calculated but instead needed to be measured experimentally… Pi could be measured experimentally, but it has an exact definition and can be calculated outside of any experiment.
- illini1 2y agoBuffon’s needle assumes a flat space, while a non-Euclidean space or geometry would affect the probability leading to a different value other than pi. You can treat the space around us as Euclidean, but that isn’t true for every part of the universe.
- not2b 2y agoEven in a non-Euclidean space with positive or negative curvature, the limit of the ratio of the circumference to the diameter of a circle as the diameter goes to zero is pi.
- ants_everywhere 2y agoIf you run Buffon's needle a lot you come to the conclusion that we live in a locally Euclidean space. That's fine and good. We also live in what you might consider a "locally Newtonian" world, but when things get very big or very small, the Newtonian approximation breaks down. The ratio of a circle's circumference to its diameter (or equivalently the sum of triangle angles) has the same problem. If you want general relativity to work, then we need to live in a curved spacetime. Depending on whether that spacetime is positively or negatively curved, the angles of a very large triangle may add up to more than or less than pi radians.
- readthenotes1 2y agoI usually hold that the only sensible date ordering is yyyy-mm-dd So that files sort properly. I'm happy to see that this enabled pi day, whereas the Europeans would prefer it not exist.
- Etheryte 2y agoISO 8601 is the standard date format in a number of European countries, but you do you.
- roelschroeven 2y agoIt is? I've only ever seen dd/mm/yyyy or dd/mm/yy as standard date format, with different separators instead of / depending on the country.
- dspillett 2y agoIt isn't used on any official forms and such that I'm aware of, at least outside technical circles, but people don't tend to have a problem with YMD ordered formats when they are used.
- johnisgood 2y agoYYYY-MM-DD+Z is pretty much the standard.
- 2y ago
- thaumasiotes 2y ago> William Oughtred, in his 1631 work Clavis Mathematicae (The Key of Mathematics), used the notation “π/δ” where π is the circumference of a circle and δ its diameter This notation would make more sense if you described it as referring to the "perimeter" of a circle, which it seems almost certain is what William Oughtred had in mind. (Though maybe he was thinking "periphery", which is a more exact match to "circumference". I don't know where "circumference" came from; there is no conceptual difference to explain the difference in word use, and it's strange for a Latin word to be used in geometry anyway.)
- jszymborski 2y agoThe far superior constant, Tau, mentioned. I am glad Mr. Propp has heard the good word.
- djmips 2y agoHe's got it wrong. People don't support tau like he supported the Red Sox, the support tau because it's actually a handy constant. Pi still exists! Tau is not an inconsequential lost cause. I think it will slowly win over everyone.
- abnry 2y agoThe real nerds celebrate octal pi day on 3/11. The crowds are too big on 3/14 anyways. https://imgur.com/a/gczeqkz https://imgur.com/a/gczeqkz
- twiceaday 2y agoThe real nerds celebrate Tau day on 6/28.
- abnry 2y agoThat's just controlled opposition.
- hgomersall 2y agoOnly in America though.
- lern_too_spel 2y agoTo be clear, the real nerds celebrate octal pi day on the octal date 3/11, which is 3/9 to the decimal date partisans.
- nokun7 2y agoAryabhāta, an exceptional Indian mathematician born in 476 CE, left a lasting mark on mathematics and astronomy. At the age of 23, in 499 CE, he calculated pi to be approximately 3.1416 and suggested its irrational nature, relying on insights from Vedic traditions. He’s also widely recognized for introducing zero as a numeral and developing various mathematical and astronomical concepts. That said, the value of pi had been explored even earlier by another Indian mathematician, Baudhayana, around the 6th century BCE. Baudhayana not only worked out pi but also laid out what we now call the Pythagorean Theorem, long before it reached European scholars.
- theamk 2y agoI've read Tau Manifesto [0], and I am now convinced that 3.14... is not the best circle constant, "turn" (tau, τ) with value 6.28... would be a much better choice. How many radians in full circle? 1 tau (turn). What about 1/3 circle (120 degree)? 1/3 tau. What about euler's constant? e^i*tau=1, or in other words rotate vector by 1 turn and end up at start position. So beautiful. So unreachable - pi has so much legacy, there is zero chance of changing it. [0] https://tauday.com/tau-manifesto https://tauday.com/tau-manifesto
- brookst 2y agoArea of a circle?
- deathanatos 2y agoYes, even that one gets more beautiful, too. Look at the usual equation: A = πr². Why is there no "2" there? Let's derive it, and in particular, let's derive it from the onion proof, which is that a circle's area is composed of many small circles, arranged concentrically, like a 2D onion: A = ∫_0^r 2πt dt There's that blasted 2 again. The tau form is more beautiful: A = ∫_0^r τt dt Integrate it, and you'll get A = τr²/2, the constant being a result of the integral. That is, to me, the usual equation is more properly A = 2πr²/2, the two 2s being different in their origins, and we just usually use & memorize the simplified form.
- hinkley 2y agoUnfortunately the ancients didn't invent calculus. Pi had been in use a long time when Liebniz and Newton came along.
- deathanatos 2y agoAnother way to look at that would have been visible to non-calculus bearing ancients: A = πr² C = πD … why do we arbitrarily use r in one equation, and D in the other? (… because we're using the wrong constant, and it bugs us, and we're sweeping that under the mathematical rug.)
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- smallstepforman 2y agoThis is the first time I encountered the quarter pi formula: 1 − 1/3 + 1/5 − 1/7 + … Amazing …
- rottc0dd 2y agoThere is a playlist by 3b1b for different interesting derivations of Pi: https://www.youtube.com/watch?v=8GPy_UMV-08&list=PLZHQObOWTQDMVQcT3414TcPMeEYf_VtPM https://www.youtube.com/watch?v=8GPy_UMV-08&list=PLZHQObOWTQ...
- adrian_b 2y agoThis kind of sloppy writing is too frequently encountered and it is annoying: "Archimedes didn’t think of 22/7, 223/71, or pi as numbers; to him, they were ratios of magnitudes". This has nothing to do with "thinking". This is just about (incorrect) language translation and mathematical terminology. In Ancient Greek and Latin and in any other old languages, the word "number" designated the result of a counting operation, i.e. it corresponds to what in modern mathematical terminology is named "natural number", so it must be translated as such in a mathematical context. In Ancient Greek and Latin, the word "magnitude" (or "measure") designated the result of a measurement operation, like the measurement of a length with a standard ruler or the measurement of a weight with weighing scales, i.e. it corresponds to what in modern mathematical terminology is named "real number", so it must be translated as such in a mathematical context. There is no difference between Archimedes and a modern mathematician, both distinguish natural numbers and real numbers, but since they speak different languages, they use different words for these 2 concepts. Whenever you read an ancient mathematical text, "number" must be understood as "natural number", while "magnitude" or "measure" must be understood as "real number". The names do not matter, this is just a problem of language translation (which is done usually incorrectly for texts with mathematical terms, like also for texts with specialized terms from physics, chemistry, biology or mineralogy, because the translators have little knowledge about those domains). The important difference between ancient mathematics and modern mathematics is that the ancients did not have a method of construction of the real numbers from natural numbers, which has been conceived only in the 19th century, by the time of Cantor, Dedekind etc. The ancients also did not have the method of abstract algebra, where you prove something for a set of axioms of a given form (e.g. of group, of ring, of field etc.) and then the proof is valid for any set where that set of axioms is satisfied. Abstract algebra is also a creation of the 19th century. Because of that, the ancients had 2 independent sets of axioms for natural numbers and for real numbers, even if many of them were identical in form. The consequence of this was that many theorems and demonstrations had to be duplicated for natural numbers and for real numbers, because something proven for one of them could not be applied directly to the other.
- johnisgood 2y agoRight, I read Aristotle's metaphysics, the terms used refer to concepts for what we use a different word, today. So what you said is very important to take into consideration.
- kazinator 2y agoVery Eurocentric article. This dude https://en.wikipedia.org/wiki/Zu_Chongzhi https://en.wikipedia.org/wiki/Zu_Chongzhi found in the fifth century AD that π lands between 3.1415926 and 3.1415927, using Liu Hui's algorithm on a 12288-gon: https://en.wikipedia.org/wiki/Liu_Hui%27s_%CF%80_algorithm#Later_developments https://en.wikipedia.org/wiki/Liu_Hui%27s_%CF%80_algorithm#L... He also discovered the 355/113 approximation over a millennium before the Europeans: "[H]owever milü π = 355/113 could not be found in any Greek, Indian or Arabian manuscripts, not until 1585 Dutch mathematician Adriaan Anthoniszoon obtained this fraction; the Chinese possessed this most extraordinary fraction over a whole millennium earlier than Europe." (First article above quoting scholar Yoshio Mikami) Also: https://en.wikipedia.org/wiki/Liu_Hui%27s_%CF%80_algorithm#Significance_of_Liu_Hui's_algorithm https://en.wikipedia.org/wiki/Liu_Hui%27s_%CF%80_algorithm#S...