"It has come to my attention that various and sundry folk have done far better approximations of the ratio of a circle's circumference to its diameter than had been possible with my excellent 96-sided regular polygon method.
"Î¼Ï€ÏÎ¬Î²Î¿," I say (or would if this calculating engine of yours could properly handle "Unicode"). It pleases me to no end to know that the great work has continued, lo these many years since that obstreperous Italic fellow with the red cloak so rudely interrupted my research.
However, with an eternity in Hades on my hands, I have endeavored to stay busy by continuing to produce more accurate approximations. (That rake Sisyphus tells me it's a waste of time, but he is not one to talk in that regard.)
What follows is the closest approximation I have made in my posthumous calcutatory diversions. "Pi," to use your modern shorthand, is about...
Hoosiers know Pi Day is actually March 20th. [wikipedia.org]
Everyone knows that pi day is the 22nd of July
Some places are big-endian, some places are little-endian, but somehow the US is middle-endian. I've never known why...
We have a history of using different endians and now we have reservations.
...yet, last year, nobody noticed the rare (little-endian) Pythagoras day on 5/12/13Sad.
..."real" Pi day is just slightly before 22/7. But close enough. :)
Tau day, the real day of celebration, is on 28 June. I'll be feasting on 2 pies on 6/28 - see you there!
pi r squared? no, pie are round!
Cornbread are square!
That's like using 48bits as a compromise between 32 and 64bit. Oh wait [wikipedia.org].
Pi Day in the rest of the world is 31/4.
The main problem with Tau is that the most mind-blowingly elegant equation in all of mathe(i.Pi) = -1doesn't look right if you put a tau/2 in there.
Covered in the Tau manifesto [tauday.com]:
e^(iθ)=cosθ+isinθevaluated at θ=tau givese^(iτ)=1+0
This formula, without rearrangement, actually does relate the five most important numbers in mathematics: 0, 1, e, i, and θNo division by two needed.
PS - I hope the tau character looks OK to other readers; on my preview Firefox shows it as just a short-looking capital T. Bad font I guess...
So ... you want to replace Pi with Tau so that it adds "+0" to the previous equation?I'd rather keep the "-1", which is not a minor concept, and throw in a free "+0" in there to satisfy your fetishist need for one more important number.Too bad I don't know how to make proper math equations on this comment system, I'd throw in a freee(i.Pi) = -1 + (0 x integrate(o, infinity, infinite sum (1 /square root (length (vector multiplication))))Just so you can get more math symbols.
I thought I stated "elegant". Don't pull a "+0" on me.
bob_super wrote:So ... you want to replace Pi with Tau so that it adds "+0" to the previous equation?
No, I want to replace it with Tau because it preserves the meaning of the relationship better than the standard form. kinda the same as I like the circular area formula better with tau:A=1/2 τr^2because the form helps me remember how to compute areas of sectors with arbitrary angles.
bob_super wrote:I'd rather keep the "-1", which is not a minor concept, and throw in a free "+0" in there to satisfy your fetishist need for one more important number.
Apparently you're in the minority there, most pi fanatics prefer the version without the minus sign; save your "fetish" accusations for them.
Honstly, the aesthetic choices made by mathematicians baffle me. For me, elegant means simple, useful, and instructive. I find that beautiful. I'm OK with you not agreeing, but there's no need for abusive language.
Theta is not a number.
Yep. should have been another tau. Missed it until after I submitted.
The largest turn you can make is to go back from where you just came. So what is the angle you have to turn for that? Yes, that's right, it's pi. Not tau.
Also if you look up spherical coordinates in n dimensions, you'll find that all but one angle covers only a range of pi. So why does that one remaining angle cover a range of 2 pi? Well, because unlike in 1 dimension (where nobody would think of adding a discrete angle), people decided to restrict the radial coordinate to nonnegative values. If the radial coordinate covered the full real axis, all the angular variables would cover a range of length pi (which can be chosen as going from 0 to pi), and the irregularity for the one angle would vanish. Anyway, even as it is usually done, it is the irregular angle which goes through a range of length 2*pi, and the regular ones cover a range of just length pi (and BTW, instead of the range [0,2pi), it usually makes more sense to use the range (-pi,pi] for the irregular angle anyway).
Now you don't see the latter as clearly in 2 or 3 dimensions because in 2 dimensions the only angle is the irregular one, and in 3 dimensions, there's just one regular angle. Therefore you don't clearly see which one is the regular one until you go to higher dimensions (or put serious thought into what goes on in just one dimension).
Boy, you tau guys are almost as bad as those GNU/Linux guys used to be.
Happy Ï€ day Friday, everyone!
Happy Π, π, ᴨ, ℼ and ℿday
Now how the heck did you get pi to show up in there? I tried several things and the only one that showed in preview ended up as unicode spludge :)
I had tried this π but it didn't work, however, I think I forgot the # when I was trying to diagnose the subject filter being different on preview vs submit issue :) It actually DOES work! Wheeee!
You need a 2 digit uid for it to work :(
You can use a Unicode to HTML entity converter, such as this one. [rishida.net] Works for Chinese, Japanese, and Greek, but apparently not Cyrillic.
ἐν ἀρχῇ ἦν ὁ λόγος. πの日
Maybe the converter fails for Cyrillic? Or maybe you just don't have a Cyrillic font installed on your computer?
The following displays just fine for me:
It's the actual number with infinite precision :D
Start the countdown to the next major holiday on the 17th!
Hmmm ... on my monitor, I only get a finite (and very low) precision! ;-)
You scream? Why do you scream?
'In space, no one can eat ice cream.'
I think Archimedes would have gone to his rest in Elysium [wikipedia.org] and he'd not be hanging out with the likes of Sisyphus who was thrown into Tartarus as punishment for his crimes.
Why do we have holidays such as Presidents Day (US) celebrating politicians and explorers but not thinkers such as mathematicians and scientists. I would argue that the technology created by thinkers is as influenctial or more than the contributions of even civil rights movement leaders. Why not make pi day a holiday celebrating math and science an official government holiday everywhere? Get loud. Contact politicians. Convince your friends.
Rant Alert. We talk a lot about problems and issues here, but what are we doing about it?
Oh god, I hope not.You just know that the first "math and science" holiday lawmakers come up with would end up being "Steve Jobs Day".
I should really implement a +1 Horrorifying moderation for posts like this ...
I've always said we need a "+1 scary"
And a "-1 wrong", because that's what many /. posts are, without necessarily being trollish/flamebait, and "overrated" doesn't convey the point that some statement is just plain based on demonstrably incorrect data.(sorry for replying to myself)
I award you no points, and may God have mercy on your soul.
In theory, the idea is that, if they're demonstrably incorrect, someone should post a reply demonstrating that they're wrong. Then everybody with modpoints mods up the correction to +5. The original, wrong post? Leaving it alone is good enough, really, so all who pass by with threshold=1 may point and mock at the idiot displaying his wrongness in public.
The bigger problem, IMO, is when those with mod points, but without knowledge of the field in which the wrongness occurs, don't realize it's wrong, see what looks like an expert sharing his knowledge, and mod it +1 informative. Getting in a mod up/down war isn't the answer -- a reply demonstrating the wrongness is absolutely key here, as that shows would-be upmodders that any existing downmods are likely correct, rather than accidental mismods, or abuse of the mod system for a personal vendetta.
Finally, turn up the gain on your troll detector. Blatant but seemingly sincere wrongness is an effective trolling tactic.
Great idea. Humanity has benefited from science, math, technology for thousands of years, so maybe it is time to celebrate this.
Pi day, in particular, has some advantages over a generic 'yay knowledge' day. The ratio of dimensions of a circle is easy to show to the general public, even if the deeper concepts and implications are not. Focus on the concept, rather than a person, also avoids the philosophical debate as to whether mathematics is created, or merely discovered, by the individual.
Also, consider that pi day is Albert Einstein's birthday!
I love this idea.
Unfortunately, "e day" doesn't fit nicely with a date. Nor does "h day." Or "phi day."
What are some other well-known science/math constants we think deserve a holiday?
I sort of like "Hubble Constant Day," which would whizz back and forth through the year based on the best current understanding of cosmology...
We could have several Phi days, a sequence, if you will: January 1, February 3, March 5, May 8, and August 13.
While researching pi day today, I found the following literary masterpiece:
Poe, E. Near A RavenMidnights so dreary, tired and weary. Silently pondering volumes extolling all by-now obsolete lore. During my rather long nap - the weirdest tap! An ominous vibrating sound disturbing my chamber's antedoor. "This", I whispered quietly, "I ignore".Perfectly, the intellect remembers: the ghostly fires, a glittering ember. Inflamed by lightning's outbursts, windows cast penumbras upon this floor. Sorrowful, as one mistreated, unhappy thoughts I heeded: That inimitable lesson in elegance - Lenore - Is delighting, exciting...nevermore.
Poe, E. Near A Raven
Midnights so dreary, tired and weary. Silently pondering volumes extolling all by-now obsolete lore. During my rather long nap - the weirdest tap! An ominous vibrating sound disturbing my chamber's antedoor. "This", I whispered quietly, "I ignore".
Perfectly, the intellect remembers: the ghostly fires, a glittering ember. Inflamed by lightning's outbursts, windows cast penumbras upon this floor. Sorrowful, as one mistreated, unhappy thoughts I heeded: That inimitable lesson in elegance - Lenore - Is delighting, exciting...nevermore.
That continues on the page it came from [c2.com]. So, what's that got to do with pi day? If you're stumped, see the linked page.
PI day is old hat now. I can't wait for "e day." Now that will be a trip.
I am waiting for LSD Day; that will be a trip.
While LSD is (like pi and e) transcendental, it's not a number ;)
Sounds like an Indian celebration...
I'll just leave this here.
Why do I never have mod points when I want them?
As a mathematician, I do not celebrate "Pi Day" (or Tau/2 day). One should not have to bribe people with pie to get them to think about math. But more importantly, a celebration of a number just emphasizes the long running misconception that math=arithmetic. Unfortunately, the vast majority of people never actually do any math; what is taught as "math" in schools is arithmetic and algorithm following. There is no thinking involved, no discovery, no room for beauty. That is what we should instead be celebrating.
tl;dr: theoretically, in a physical application: approximately 61 digits.
Thought experiment: how many digits of Pi can we use? In this discussion, I explicitly ignore any number-theoretical application of pi being a transcendental number [wikipedia.org].
Let's imagine calculating the circumference of something really big with as precise a unit of length as we can.
What is the biggest "thing" that has a circumference that we can measure? Let's use the diameter of the observable Universe [wikipedia.org]. This is approximately: 8.8 x 10^26 m.
What is the smallest unit of linear measure? Let's use the Planck Length [wikipedia.org] or approximately: 1.6 x 10^-35 m.
According to Wolfram Alpha [wolframalpha.com] this is 5.4 x 10^61 Planck lengths.
Granted, there is no current means by which we could actually measure something with anywhere near the precision of a Planck length, never mind on the scale of the observable universe. But, assuming we could, approximately 61 significant digits of Pi would suffice to compute its circumference.
Footnote: As a young teen, a challenge by my geometry teacher led to my memorizing Pi to 10 decimal places. A year later, I found a book enumerating Pi to 40 places, which I also took to memorizing. When I got to college, I discovered a guy across the hall from me in my dorm (Hi Rob!) had memorized it to 50 places. The battle was on. We'd one-up the other 5-10 digits at a time. After about 4 months, we called a truce at 200 decimal places. That was quite a while ago, yet I can still recall it to 120 places.
Oh 61 eh? I thought it was 42...
Joking aside, it's an elegant thought. Thank you for this! This is why I come here.
Universal expansion has outpaced the change in the dynamics underlying Planck Length. At some point in the past, 42 digits would have been the required precision. ;)
... which sadly means that sometime in the future - probably on or about next Tuesday - we will need to go to 62 digits for "good enough" calculation.
I guess until then we can, for objects a tad smaller than the entire universe, go with just 6 digits of precision. If you ever get stuck having to use a vanilla calculator that does not have Pi built-in, just remember "113355". Split that in the middle into 113 and 355. 355 / 113 = 3.1415292 .. close enough for many applications.Practically though, if you memorize or use Pi to 31 places where the first zero appears - past that it really cannot mater all that much. We aren't all Daniel Tammet's who can recite Pi to 20,000 places.
Could you explain why it makes sense to remember six digits in order to get an approximation of pi that's only valid to 4 digits?
The 5-digit approximation 3.1416 is more accurate and easier to remember; or you can memorize it to six digits as 3.14159. (The latter is both a correct rounding and a correct truncation, which is nice so if you ever want to learn more digits, you don't have to unlearn the final one.)
You really don't see the structure in "113355"? If you have to remember that as an arbitrary sequence of six digits, I honestly feel sorry for you.
Don't know how, but I totally missed that. Thanks for pointing it out.
The incredible bit was that I realized it was a non-strictly monotonous sequence, but didn't think the implication of that (w/r/t recovery from transposing adjacent digits) was worth mentioning, because that doesn't make it much easier to remember. (I assumed this property was why the AC concatenated it in denominator:numerator order instead of the usual.) And yet I missed the two elements (odd numbers in sequence, and each number repeated) that were obviously the real point.
I agree with you that it seems easier to just remember the digits.
However, I believe the AC made a mistake in the arithmetic. The given fraction agrees with pi to more than 4 decimal places. I suggest you check it yourself, but I believe the first few digits of 355/113 are 3.1415929. This is a better approximation than the AC indicated.
355/113 is 7 digits of accuracy in only 6 digits. It's also more convenient if your calculator doesn't do floating point.
It also seems to get you accuracy within 1/1000th of a millimeter per meter - which scales to about 1 millimeter of inaccuracy per kilometer.