How pi was almost 6.283185...
ฝัง
- เผยแพร่เมื่อ 19 มิ.ย. 2024
- In some of his notes, Euler used π to represent 6.28... So why did we adopt 3.14...?
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Home page: www.3blue1brown.com
The idea for this video, as well as the live shots, came from Ben Hambrecht, with the writing and animating done by Grant Sanderson.
Special thanks to:
- University Library Basel, for letting us rummage through their historical collection
- Martin Mattmüller from the Bernoulli-Euler center for helpful discussion
- Michael Hartl, author of the Tau Manifesto, for pointing us to obscure references
- Library of the Institut de France
Cinematographer: Eugen Heller
Music by Vincent Rubinetti:
vincerubinetti.bandcamp.com/a...
Thanks to these viewers for their contributions to translations
Hebrew: Omer Tuchfeld
Korean: tebaioioo
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The people who fight about tau and pi just go in circles
nice one, haha
@@Yolwoocle If Tau was mainstream, every kid's life (on average) would be a little easier; so would every physicist's life, every engineer's life, every mathematician's life, so on and so forth. Hell. If Tau had been mainstream from the beginning, we might already have made it to Mars by now. Who knows?
@@arielhernandez1638 I agree with you! But there are loads of other things that would be very convenient. It'd be a lot better if we used base-12 instead of 10, for example. But it's too late to change!
@@arielhernandez1638 Well, I've seen a few equations with pi squared but none of them had it in "four pi squared" so this would be where tau no longer makes it simpler.
Here's a spanner to throw in the argument: the hyperbolic version of angle (associated with Minkowski geometry, split-complex numbers) is 2x the area between a given line, the x-axis, and the unit hyperbola, but this is not equivalent to the arc length. So should we even be discussing circular angle in terms of cirumference?
"have you ever heard of Euler's formula?''
" *which one?* "
Deserve more likes!!
@@vismaydharod313 Isn't that Heron's formula?
V-E+F=2
@@tomkerruish2982 Yup .... but im not sure...
ζ(s) = Π (p : prime) (1 / (1 - 1/p^s))
"It's often joked that formulas in math have to be named after the second person to prove them, because the first is always going to be Euler."
LOL!!!
John Chessant Euler is badass
I really laughed out loud alone lol
Felipe What is math? Euler don't hurt me, don't hurt me, no more.
420 likes, blaze it
Gauss was also a badass
"So which topic of maths did Euler influence?"
"Yes"
Topic in math-
M A T H
that is correct
@@DawnshieId Makes no sense. When math is „a field of science“ it’s reasonable to say it can be influenced. Math as a toolkit for solving problems can reasonably said to be developed. Math as „true sentences within a axiom system“ is obviously only discovered, if we mean by that that those truths donor rely on anyone knowing them or not (they are a priori) and thus „discovering them“ will not have any „actually new“ information. So, depending on what one is talking about, influencing, developing and discovering math are all reasonable things and not mutually exclusive.
*but they are distinct
@@sebastianlenzlinger9291 Influenceing in this sense means expanding, which Euler did. I agree with the idea that mathematics is not invented, but rather discovered. You could say that the symbols are invented, and that's true, but the idea is what nature follows.
I still think we should define 🍕 = π/4 = τ/8.
🍕 can be defined as:
- the ratio of crust length to side length in an idealized pizza slice
- the ratio of pizza to box, given a perfectly circular pizza fit snugly inside a perfectly square box
I know it was a joke and your slice example depends on how big a slice is, but I always thought that this was the only way that made sense because of a slightly different argument.
π/4 is the ratio of a circle to its outlining square. It works both for circumference and for area. And that's the only definition that plays nicely with areas. For the ratios of circumferences we get 2πr/8r = π/4 and for the area πr²/4r² = π/4.
If you want, we can call it 🍕 (pronounced "pi-pi" for "pizza pi") and define once and for all that a slice of pizza is 1/8 of a pizza.
@@emulgatorx nope, pronounced pee-pie
@@emulgatorx PIZZA PASTA PUT IT IN A BOX
Modern JavaScript developer should use this. Awesome.
Ah yes. πzza
The true definition of pi is at 3:14
Spooky.
Genius
🤯😯
Woah!!😮
What hate you is sit part is 360 . 1.53 40° and null dollar 360 : 1.53 40° -/- _10 -/-
Can you eat Pi? Yes.
Can you eat Tau? No.
Therefore we celebrate pi day.
People have baked taus before, too.
I would be seriously disappointed if we discarded the usefulness of tau as an educational tool because of some pie memes.
Memes TV Genius lol
Pie memes rule the math world.
Demauscian yeah, but today no one will know what your talking about when you say the number pee.
John Sherfey In Brazil everyone do.
Pi Day is now both Einstein's birthday and Hawking's deathday. :(
John Chessant Hawking died yesterday
It was today, in his local time (UTC)
Iluminati and :(
It's a sad day to be sure, but while Stephen Hawking, the man, is no more, his intellectual and cultural legacy is permanent. A hundred or even a thousand years from now, physics students will still learn about Hawking radiation and black-hole entropy.
As V for Vendetta put it, "ideas are bulletproof".
Too bad his magic wheelchair didn't save him
tau should be for 3.14... and pi for 6.28... because of the # of legs
Tau being 6.28 and pi 3.14 still makes sense if you think the # of legs is number tau is divided by
Tau stands on one leg because it's twice as strong! :)
Or you could think that since pi has two legs it should weigh twice as tau
Tau = T = 6.28
Pi = TT = 3.14
Tau/3 = TTT = 2.09
Tau/4 = TTTT = 1.57
I think that idea may have legs :)
Tau > Pi literally
Xano Trevisan Kothe well you are right
Welp, can't argue with that!
Xano Trevisan Kothe 🤯
pi × 2 = tau
Pi^2>Tau>Pi
5:22 unexpected factorial
YellowBunny You mean you don't celebrate the holiday on June 304,888,344,611,713,860,501,504,000,000th?
I don't think such a date exists :)
He did the math
6 divided by 28 factorial or (6/28) factorial? Alright, we got an answer for the first one but we need the continuous version of the factorial function to answer what (6/28)! is.
Well, you have the gamma function, e.g. www.wolframalpha.com/input/?i=gamma(6%2F28+%2B+1)
Of all days, TH-cam chooses to recommend me this on June 28th. I got your message, algorithm.
Euler was one of the few actually concerned and engaged with math. My, to this date, favourite video of yours is the triangle of power, because it shows how to handle a problem, not the notation, while still hinting at how confusing bad notation can be.
those triangles were confusing indeed
Let me blow your mind. I would define: O = 6.28... D = 3.14...
So now O/2 = D. Which any child can learn in minutes. O defines the radius of a circle.
@@dangi12012 looks like 0=6.28
In Physics, pi almost never appears alone in formulae. It's 2 pi pretty much all the time.
Same with 3d graphics programming, it would be more efficient to calculate directly with Tau (instead of having to do one more additional multiplication: 2pi vs tau). Also I find Tau more natural and cleaner, if one values that formulas should be as small and simplistic as possible.
As a physics student, I have to agree with this statement; although, I am partial to the three-legged pi because of the other variables already using tau(most notably torque and time constant). Also specifically the area of a circle would add an extra 1/2.
@@KimTiger777 As far as I know, compilers will pre-calculate constant values, so in the compiled code, 2*Pi will be stored as Tau. Or, if that is then multiplied with another constant, the result of that whole thing.
Otherwise you would be right, because it would cause millions of additional multiplications. So far, everyone has told me that compilers are incredibly smart, and will always optimize as far as they can, so you should first write readable code over everything else, and only then try to optimize the relevant parts.
Yeah but now you have two meanings of tau in physics, one for the circle and the other for the torque. It's gonna be confusing.
There's a reason particle physicists often use -h- instead of h. It saves them having to write h/2π
Pi is useful in Engineering because you measure pipes with calipers which gives the diameter.
Tau is useful in Mathematics because you draw circles with a compass which is set to the radius.
Eta* is useful in Electronics because the minimum and maximum absolute amplitude of a sine wave occur 1/4 way around a cycle.
* I think Pi/2 (Tau/4) is called Eta, but I am not sure.
Engineers have to convert to radius constantly anyway. You can't calculate that surface area or moment of inertia without using radius.
η! η! η! Ο Messi não tem copa, quem tem copa é o Vampeta.
@@cptant7610 Yes you can. For example area of a circle = (pi/4)*d^2, but doesn't matter anyway. I've also seen moment of inertia of circular cross section using diameter too. etc etc
I can also just as easily divide by 2 after measuring. My digital calipers can even do it for me.
What about 3/4 Tau? I don't really know why they'd have a name but 2 of them equals 3 Pi so it's pretty interesting imo.
3.14 has had a regular adoption due in part to the nature of practical engineering and manufacturing. I can accurately measure the diameter of a sphere or rod using a micrometer or calipers, I have to Infer the radius from that measurement. Additionally I have no practical way to find the center of a physical sphere or rod in such a way that I can take a direct measurement. I'm with grant on this one, it's not about what's right, it's about the problum at hand.
@@murilodesouza416 I thought it was about constructing a circle in the old days. You use a compass, which is set to the radius of the circle. So the radius should be more important to them. Yet the Babylonians and Archimedes all tried to find pi (3.14...), so who knows why it really turned out that way.
This is largely irrelevant too due to the fact that there exists literally thousands of equivalent definitions for π, many of which are not directly related to circles even if those definitions explicitly are founded on Euclidean geometry axioms instead of, for example, calculus.
Besides, even the analytical process of expressing what π is when talking about the ratios of circumference and diameter lends itself to becoming a definition that is very generalized to all sorts of applications that may not directly involve geometry. For example, even if we acknowledge that claiming that C(r) = 2πr is somewhat outlandish of a notation, this is resolved by the what becomes the analytical definition of C(r) when using calculus. What is C(r)? It is the *arclength* of a circle of radius r. Therefore, πr is the *arclength* of a circle of semicircle of radius r. The difference is that the curve for a semi-circle is a function, the curve for a circle is not. Hence the semi-circle lends itself to a manipulation with derivatives and integrals. y(x) = (r^2 - x^2)^(1/2) ==> y'(x) = -x/(r^2 - x^2)^(1/2) ==> 1 + y'(x)^2 = 1 + x^2/(r^2 - x^2) = r^2/(r^2 - x^2) ==> s(x) = [1 + y'(x)^2]^(1/2) = r/(r^2 - x^2)^(1/2). Therefore, πr is equal to the integral of r/(r^2 - x^2)^(1/2) from x = -r to x = r. This is the same as the integral of 1/[1 - (x/r)^2]^(1/2) from x = -r to x = r. Performing the variable change t = x/r implies dx = r·dt, and the interval of integration has -1 < t < 1 instead. Therefore, πr is equal to the integral from t = -1 to t = 1 of r/(1 - t^2)^(1/2). Therefore, π is equal to the integral from t = -1 to t = 1 of 1/(1 - t^2)^(1/2). In fact, from the construction of the problem, this can and should be taken as the definition of π. As it happens, this is an integral that occurs frequently in applications, justifying the usage of the constant.
I can just as accurately divide a diameter by 2 after measuring... My digital calipers can even do that for me.
@@Grauenwolf That... is not easier. No.
@@error.418 To divide by 10 you just move decimal point one position to the left, that's why it's easier than divide by 2. For the rest of the world that uses decimal system, that is. For US that cuts inches in half inches, than in quarter inches, eights and sixteens of an inch, well, yes, divide by 2 is more natural than divide by 10.
I often wondered where you stood on the PI vs TAU subject. Thanks for this interesting look at Euler!
"...and writing a letter to the Bernoullis to boast about doing so afterwards!"
Hahahahaha
smh, bro made 3 comments all of which got in the top five comments about basic very ordinary things
@@zacharycarter5917 it's pretty much what all youtube attention whores do, they quote the video
I just realized that Euler probably used π=e at some point.
Oh shit
Hmm...... clearly im missing something so please explain, why is pi = e worth mentioning?
@@Dravaek There's a common tongue in cheek joke about engineers approximating pi=e=3
Scotty it’s also because both Pi and e are important mathematical constants
That is engineering, Euler is a mathematician
I wish I had a circle of friends where on Pi day, they said "we should actually be celebrating 28th June"...
lol. A 'circle' of friends.
i'm 2 days late but happy Tau day!
well yes, but actually no.
you see, if have a solid circle of friends, they would prb celebrate on the tau/2 day
My favorite channel on youtube. I do not say that to be nice. It is what I think.
Your graphs are amazing, your explanations are clear and profound, and your conclusions are always well adjusted. Congrats and keep up the amazing work. Thanks a lot!
Why is this even a thing? Just use tau when you want 2pi and use pi when you want tau/2
I really like when videos make me start thinking about things in a new way. This was a very well made video.
This video was particularly enlighten. Well done!
We should have an epic rap battle of history between Euler and Gauss.
Make this happen
Nice Peter see this
Lol
We need to have such rap battles on more academic matters like this anyway, ppl insulting each other at a personal level is just so cringe...
@@comparatorclock Lighten up man. It's just a bit of fun
We should celebrate on 27/1 for _e_ day.
In America we celebrated e day back in february (2/7/18). I hope modern medicine steps up its game enough within my lifetime that I'll live to celebrate another one
What's _e_ called?
Euler's number
*_E_*
@@toebel reminds me of the special pi second, 3/14/15 9:26:53
27/1 it's an intenational day for remember those who died for the Hitler's madness (shoah)
What an all around great episode :)
So Euler thought of Pi as a variable and we basically mistakenly have taken the Pi = 3.14159 variant as a constant?
How unworthy we all are of Eulers work...
I've noticed that many math classes these days focus much less on solving problems and more on simply cramming your head with formulas, so it's no wonder that most people will completely ignore the actual math aspect of them.
Mistakenly? Not really. Just because he didn't think of it as a constant doesn't mean that it isn't helpful to - in fact, I'd argue it's necessary - it's so obscenely common that it doesn't make sense not to define pi as a constant
As I understand it, it's not that Euler thought of pi as a variable; it's that he used the symbol pi to stand for different things in different contexts. Which is something that mathematicians do all the time, just not so much with that particular symbol nowadays (although it is also used for the prime-counting function).
Well, to be fair. Pi does pop up quite often in all branches of math and in many different applications.
I don’t blame those for wanting to give a reoccuring number like that a name
2:27 CHAD Euler VS NPC Euler
I love how you drew Tau just like Pi, but with only one "leg", but still with eyes.
Tau to Pi: Back in my day sonny, i lost my leg because of the war...
Pi should be equal to 1/sqrt(3.141...), then it can be defined as the radius of the circle with area 1.
Late, but thats a terrible idea
But what if someone decides to use the diameter as reference? We came back to where we started. But interesting concept anyways!
@@lih3391It's a joke.
These videos are just so perfectly animated, really. I love these videos.
Brilliant video. I love your search for understanding the essence of the problem.
Awesome Video! Your videos are best. They always make me glad that I am subscribed to you :D
RIP Stephen Hawking, 1942- Pi day 2018
Brilliant. Thanks for the service.
This video is a piece of art! Stunningly good, also the atmosphere and the music… ❤
Euler+Euler+Euler+......=Euler
Are you saying Euler = 0?!
*[TRIGGERED]*
Or Euler equals infinity.
You cannot sum infinity, it's not a number.
kkkllleee, well, actually you can but that will just be infinity...
0*infinity = 0?
*[TRIGGERED]*
Top 10 Anime plot twists
Anime > real life
Number τ will shock you.
Shyam Murugan lysergic acid diethylamide+AFK .i.e away from keyboard a.k.a real life =< anime
Number 3.14 will shock you
Congrats on trending. You always have thought provoking content.
Great Pi video, and good Pi day to you too 3B1B! I especially liked the part "we should focus on the task at hand", it makes 'silly' questions like can something be divided by 0 feel like 'philosophy of math' sort of, not actually solving a problem.
I love your videos! Could you possibly make one about Curl and Divergence, they at the core of many physics equations but rarely described in a purely mathematical since?
R.I.P Professor Hawking
R.I.P
Thanks for yet another truly wonderful video! And to you a happy pi day!
I must say that most of the times i don't compreend what you are saying because my somehow little understanding of maths, only the basics, but usually try to understand if what you are saying makes sense with what i know. Either way your work is good, keep it up!
This is my first pi day since i moved out of my parents place. My love for math came from being homeschooled, and trying to find the "shortcuts" to the problems at hand. Now, it's less about the results, and more about understanding the solution. Happy pi day < 3
Great video. Great way of thinking about mathematics. Happy pi day!
Good one! (PS - You produce my favorite TH-cam channel. Thx for the stellar work.)
Normally I would have left once I had surmise what the video was about. But you had so much truly Unknown information to me, that I had to subscribe
Why is he allowed to touch those old books with his hands?
Because everyone trusts him.
Gloves take away sensation from your fingers and make it easier to rip pages. Different institutions weigh the pros and cons of wearing gloves, based on the kind of item you're handling
Euler is bae
*Gae
*Gay
Thx
Euler came out ❤❤
You put succinctly into words what had bothered me for the last couple years and I couldn't put my finger on!
Appreciable efforts to deliver knowledge. 👍👍
Until I watched this I never heard of tau being 6.28... I only heard of it as torque.
Happy Pi day! Happy Birthday A. Einstein! RIP Stephen Hawking....
Thank you for that!
Your videos are inspiring, they always make me love math a bit more :')
Numberphile did a quite funny debate weather we should use pi or tau, w Matt Parker.
"funny"
Numberphile is like the Kardashians of Mathematics...
impagic1 nice whether we’re having today
Lucky Abat lel rip
*and Steve mould
Great video. We should definitely celebrate both 3/14 and 6/28 for the sake of it though
Yes eat more pie
pi day is coming soon
Yep. We should celebrate both tau and half tau day.
Great video! With all the buggery around the choice axiom, certain people would benefit greatly from thinking like this. Great job
I actually started hating Math due to the very lengthy exams in ny university but thanks to 3Blue1Brown love for it has resurfaced again!
Euler is a mathematical poet. He uses notation to convey things, but isn't bound by it.
A fitting story to a fitting day. great content as always :), but unfortunately we lost a genius this day :/
This channel makes me a better math teacher every video!
I think this is one of the best math videos I have ever seen ... the way you solved all the non-sense Internet arguments ... thanks alot
Even Laplace was like, "Read Euler, he is the master of us all."
The whole argument is moot, because if you want to use τ, it's not like anyone can stop you. Some formulas are cleaner with τ, some are cleaner with π, so why not use both? Euler had it right: explain your notation, and there's no problem.
The argument is not just to use tau, but to teach the use of tau as the default instead of pi.
I've thought about this and what I came to think was best would be to use tau in any application where it does not conflict with another usage of the symbol. For example, in physics and engineering, tau may refer to torque or to a time constant; in that context, using pi would be suitable, just as electrical engineers use j for the imaginary unit instead of i since i is taken as referring to (instantaneous) current, even though in all other contexts i is typically used. Outside of those contexts, I'd say to always use tau, and that includes in beginning trigonometry and then up - radian measures for common angles are given as fractions of tau, which makes it far easier to work with.
@@eduardolarrymarinsilva76 And TomatoBreadOrgasm's argument is that the idea of a "default" is flawed to begin with.
@@NoriMori1992 How so? Default settings are essential in every aspect of life. It is specially important in education. Imagine if different schools in your country taught their students arithmetic with either infix, prefix or postfix notation. That would A LOT of confusion, which would only get worse if you tried to teach more than one. But everybody agrees that "infix is preferable" and so you can do arithmetic and your math can be checked by most of the world.
That's the power of defaults, it just happens that pi is a BAD default.
Eduardo [Larry] Marín Silva Pi’s not a “bad” default, just arguably not ideal. It’s like tipping in the U.S., it’s a bad system that we don’t bother changing because it would be very inconvenient. Likewise, telling everyone *worldwide* to swap circle constants is very inconvenient and there’s no real authority to make the call. It’s just not something you should push to change because it’s a very uphill battle with very little to gain.
I love you.
I wouldn't enjoy maths to the fullest extent without you. Huge respect bro.
Ooh, Ben is quite the piece of eye candy. He can bisect my diameter whenever he wants ...
As it turns out, ‘π with three legs’ is how τ is written in many Cyrillic handwriting styles (ᲅ or most italic т).
I used to prefer pi over tau simply for the angle sum theorem, but getting into electronics has only made it more appealing given that tau already has functionality in concert with pi as a time characteristic of distributions.
Your videos are very helpful in gaining concept. So please create a series on Random Variable and Probability distributions
One of your best videos on MATH
I think the fact that Euler spoke in term of the radius means he'd be a Tau supporter in the present day.
yeah yeah blame it on euler
Damn Euler! He ruined Euler!
who would win?
* Leonard Euler, the early hero if tau-ism
* one naughty Euler boi
Great video! I love pi so much! The beginning of pi is the ray.
Love this video!!
3:51 A breath came out of my nostril.
Even knowing beforehand who the mystery person is, the look he gives you at 2:28 is priceless.
Hello, 3blue1brown, I was wondering if you would consider making a series of videos regarding the introduction to topology. I think it is a very interesting topic, which is also quite abstract like linear algebra. The series of videos you made about the latter were very helpful. It would probably be a great help to many if you made a similar series on topology.
It's interesting to look at Pi and Tau side by side.. For the most part, the only digits that they seem to sometimes share/overlap exact positions, are the 9s, and 0s.. And Tau has it's own, even longer, Feynman Point! (Same goes for the quarter-circle constant, 1.57.. Tho I can't find much info out there on whether there's any significance to these overlaps..)
So basically Euler is to math in the same way that Newton is to physics
Both r mathematian but Newton did more to mathematics
@@jakkaxn5513 No Newton invented calculus but Euler literally improved every area of mathematics. So it's really Euler who did more.
@@createyourownfuture3840 Newton did a whole lot more than just calculus
Our definition of pi will be the law straw for aliens deciding to wipe us out
Thats crazy the university library your friend went to is in my home town where i just graduated (university of basel). I mean i know i shouldve expected that given that euler lived in basel and was a student of bernoulli but i was still somehow surprised to see the front steps of the library (literally 5 minutes from where i live).
I like the "pi-with-three-legs" notation because it stands out so well in modifying long-familiar equations, and also in switching back and forth from using pi to using its double in equations, using whichever is simpler and more convenient. However, connecting tau and pi by the number of legs will mentally help students. If the value of pi weren't already established and found in every book to date, it would make a bit more sense if the values of pi and tau were swapped -- but dividing by the number of legs is just as valid as multiplying by the number of legs.
It's Stephen Hawkings memorial day now, pi might have to take a back seat from now on
Rip stephen hawking
Godammit, I had no idea.
F
It's also Einstein's birthday.
He died on March 13, not 14. So not Pi Day.
I'm less used to it yet tau makes more sense.
Every time I watch one of your videos it gives me a fresh perspective on mathematics
Great video!!!
A lot of people seem to completely misunderstand the real point of τ.
It's completely uninteresting whether it makes formulas "look cleaner" or not, that's an extremely trivial point, and I have no idea why people even care about something that utterly pointless.
The REAL purpose of τ is that _it would make more sense for beginners._
It's much easier to grasp the fact that it actually represents a full revolution instead of half a revolution, and this will make people who are starting out in Trigonometry feel more comfortable with that subject right off the bat.
Intuition for beginners is like rewriting a confusing textbook so that it's easier to follow - "cleaner formulas" is like changing the front cover of that book without rewriting it.
By far the most important argument in favour of using tau.
Correct. It makes radian measure simple and intuitive. If I want to give you a third of a circle - cut the pie into three pieces, I take (1/3) tau radians in each. Cut to 6 pieces, (1/6) tau. Cut in half, (1/2) tau. Very simple and easy, no?
Whatever benefits you see to that, you should weigh them against the costs. There is a cost of confusion of having both pi and tau, and the cost of having to unlearn it anyway if the student has any use for math at all at a later stage. Given how trivial the matter is, it's just not worth it.
@@AlexanderShamov First, when it comes to adopting a new standard, you don't need to roll out that standard for all grades at the same time. Older students who had already started down the old track could continue that track, while new students could be taught with the new symbol. over time the old system would be phased out. Second, I think you're underestimating the value of intuitive notation, but I guess in the past you'd have been in favor of keeping the roman numeral system rather then that new and strange arabic numerals, It would just confuse students already used to doing math the old way
@@grrrlag No, as a mathematician myself I can appreciate very well how imporotant intuitive notation is. Language and notation is everything when it comes to mathematics. It's just that, again, multiplying a constant by 2 is a trivial matter. Comparing that to the difference between Arabic and Roman numerals is just dishonest, since that difference is highly nontrivial both conceptually and practically.
Let me give you an example of a similarly trivial but even better change in notation: namely, changing the order of function and argument in a function application notation from f(x) to (x)f, motivated by the fact it's more intuitive (you start with something, then act on it), and that the implied left-to-right composition is more intuitive than right-to-left (fg meaning apply f first, then g, currently it's the other way around), and it combines better with diagrammatic reasoning, as diagrams mostly flow from left to right and top to bottom. In fact some even do that from time to time - that is, change the order of composition, warning the reader in advance. And again, in my opinion it is a trivial change, with a small benefit (still better than that of multiplying pi by 2, in my opinion), outweighed by the cost of adoption.
And I stress that there is no such thing as starting to teach students differently without having them interact with both standards at the same time. Transitions like that take decades, i.e. multiple generations of students, so they better be worth it.
I must say I rarely find myself arguing on the conservative side, but this particular issue is just ridiclulous enough.
14.3 --> Einsteins Birthday, Hawkings day of death, and Pi day. Lets call it the PHYSICS DAY :D
As a student in physics, I agree, but I have some math students in my friend's circle who would not agree to include the Pi stuff in it ;) ...
you certainly dont understand either math nor physics.
Math is the language of physics. and physics is the descrition of reality. Many math phenomenons surprisingly describe things in reality. like the rieman zeta function. it had no real world application until we found out that it perfectly describes quantum effects like the Casimir-effect.
But dont forget the 28th June
Ginkoman2 damn European dates
Ginkoman2 😂 just joking
Congrats on trending!!
Using tau rather than pi certainly simplifies many equations, and I like that. I also like fundamentals which are easy to remember. I find it easy to remember that pi is the ratio of the full distance around a circle (circumference) to the full distance across the circle (diameter). More generally, pi is the ratio of a given proportion of the circumference to the same proportion of the diameter. That seems tidy. If we prefer the simplification of equations, then using tau seems like a great idea (in most cases, where tau is not already used as a conmon variable in the equation (or related equations).
0:58 I think you can truthfully say THE most influencual.
Edit: as you basically pointed out later
Edit 2: yes im fun at parties
MrLikon7, I'm *
Hey, I'm fun at parties too!
Its arguable between him or gauss. Both have merits in regard for there influence.
Time to make a pie and pretend that i just made two pies. Then i have to throw half of it away because it is 3/14
ABSOLUTELY LOVED IT!!!!!!
thank you oiler, very cool!
The reason pi became the standard was because vernier callipers existed, it was very easy directly get the measurement of a diameter but no such tool existed for the radius
The first person to represent the ratio of radius to circumference as the symbol pi was very likely William Jones, a mathematician from the isle of Anglesey, Wales, UK in Synopsis Palmariorum Matheseos published 1706. Euler likely did get this directly from Jones as he studied Newton. Jones was befriended by Newton who liked his book and worked as his editor and publisher.
wikichris Yes, but Euler popularized the notation, since he popularized most notation.
does that mean newton stole jones' work? :thinking:
Why not? He stole everyone else's...
Make sense, if you think for it.
I personally would use τ in circles and trigonometry because of the relation between the radius and circumference and a full period of a sine wave but π also appears on its own in some solutions like the Gamma function where Γ(1/2) = sqrt(π). And even then, arcsin(θ) and arccos(θ) are only defined between -τ/4 and τ/4 (or -π/2 and π/2 if you prefer it that way) and arctan(θ) with θ -> ∞ becomes τ/4 (π/2) too, hence the definition of π = τ/4.
However - and I've just noticed this thinking about your comment - Γ(1/2) = (τ/2)^(1/2), which is kind of beautiful.
I love your channel!