@@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?
@@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.
@@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.
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".
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.
@@AdrenalineL1feInteresting. Would you say that you found them more confusing than, less confusing than, or equally as confusing as the conventional notation?
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.
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.
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.
@@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
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.
@@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.
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
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
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!
its not about which formulas look 'cleaner' its about what makes more sense. it is inconsistent to treat the radius fundamental property of a circle, and then use a number defined by the diameter
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
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!
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.
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.
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.
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.
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.
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.
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
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.
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.
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).
Using pi for perimeter and tau for pi/2 would make a lot of sense. Like you said, Euler probably used pi because perimeter starts with a "p", but also the Greek letter tau looks like half of the Greek letter pi.
Yes, but imo that is, if anything, an argument in favour of it being a joke comment: If you are from, say, Europe, and write dates as dd.mm.yy or dd.mm.yyyy, 31.4. immediately looks wrong to you, just as 4/31 would to you (I assume).
Never enough, when the chinese got it way more accurate hundreds of years before him, he should be laughed at for trying to prove something using a vastly incorrect value.
@TheSearchingTruth I can't tell if you're joking or not, but if you're serious, then it's because if we approximate pi, calculation using it won't be exactly correct.
The real lesson is that we celebrate everyday as a circle constant day if we are flexible and creative enough to do so. No need to limit yourself to 3.14 or 6.28. Celebrate forever.
+TheOofGod Yeah, it seems to be pronounced "oiler" by German pronunciation rules (one of them being that "eu" is read "oi", hence "Deutsch" is read "doitch" for example) since he was born in Switzerland, a German-speaking country.
*i like how he used it to represent whichever constant was the most efficient, but i think that concept would be hard to teach to kids in highschool and middle school, so if anything, i think it would be good to teach that concept in advanced math in college and universities.*
I agree - we should be celebrating both! Because why only celebrate one when you can have two, right? Thanks, Euler! 😍 And happy half τ day to everyone! 🙃 P.S. R.I.P. Stephen Hawking.
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?
Trying to blur out the author of the "early calculus book"? didn't work, there was a split second written "LEONHARDO EULERO". I first thought it was L'Hopital.
![Chicken P - People's Favorite (Remix) [Feat. 42 Dugg] (Official Video)](http://i.ytimg.com/vi/a6Bn8FEtxmY/mqdefault.jpg)
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?
"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
"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))
"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
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.
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 -/-
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
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 :)
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
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
@@AdrenalineL1feInteresting. Would you say that you found them more confusing than, less confusing than, or equally as confusing as the conventional notation?
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)
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
Of all days, RUclips chooses to recommend me this on June 28th. I got your message, algorithm.
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.
Why is this even a thing? Just use tau when you want 2pi and use pi when you want tau/2
"...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 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
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
2:27 CHAD Euler VS NPC Euler
I often wondered where you stood on the PI vs TAU subject. Thanks for this interesting look at Euler!
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
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.
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)
Even Laplace was like, "Read Euler, he is the master of us all."
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...
I really like when videos make me start thinking about things in a new way. This was a very well made video.
RIP Stephen Hawking, 1942- Pi day 2018
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. 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.
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!
Until I watched this I never heard of tau being 6.28... I only heard of it as torque.
Ooh, Ben is quite the piece of eye candy. He can bisect my diameter whenever he wants ...
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
This guy Euler was nuts. He pops up everywhere in algebra, geometry, cryptography.....everywhere
R.I.P Professor Hawking
R.I.P
Euler is a mathematical poet. He uses notation to convey things, but isn't bound by it.
Euler is bae
*Gay
Thx
Euler came out ❤❤
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]*
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
its not about which formulas look 'cleaner' its about what makes more sense. it is inconsistent to treat the radius fundamental property of a circle, and then use a number defined by the diameter
Happy Pi day! Happy Birthday A. Einstein! RIP Stephen Hawking....
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
A fitting story to a fitting day. great content as always :), but unfortunately we lost a genius this day :/
As it turns out, ‘π with three legs’ is how τ is written in many Cyrillic handwriting styles (ᲅ or most italic т).
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!
Good one! (PS - You produce my favorite RUclips channel. Thx for the stellar work.)
Even knowing beforehand who the mystery person is, the look he gives you at 2:28 is priceless.
0:40 I am sold. tau’s my favorite now
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.
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.
3:51 A breath came out of my nostril.
I actually started hating Math due to the very lengthy exams in ny university but thanks to 3Blue1Brown love for it has resurfaced again!
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
These videos are just so perfectly animated, really. I love these videos.
You put succinctly into words what had bothered me for the last couple years and I couldn't put my finger on!
Great video. Great way of thinking about mathematics. Happy pi day!
This video was particularly enlighten. Well done!
I think the fact that Euler spoke in term of the radius means he'd be a Tau supporter in the present day.
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
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 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.
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.
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
I humbly touch your feet since in Indian Tradition that is the way to respect the Guru who imparts knowledge -With much gratitude.
I'm less used to it yet tau makes more sense.
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
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
I love you.
I wouldn't enjoy maths to the fullest extent without you. Huge respect bro.
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...
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).
Our definition of pi will be the law straw for aliens deciding to wipe us out
Using pi for perimeter and tau for pi/2 would make a lot of sense.
Like you said, Euler probably used pi because perimeter starts with a "p", but also the Greek letter tau looks like half of the Greek letter pi.
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
Congrats on trending. You always have thought provoking content.
Yes, we should use the constant that makes the most sense for the problem at hand. And most of the time that's Tau, not Pi.
This is so analogous to programming. I will think of this whenever someone brings up standards or stuff like OOP vs FP from now on.
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.
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
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
Brilliant. Thanks for the service.
Actually Pi should be celebrated on the 31st of April (31.4)
Some Person, not if you're in America. mm/dd/yyyy
RubixB0y The joke is that April only has 30 days.
Franz Luggin I'm not sure they noticed that. I assume they live in a country where the date is formatted dd/mm/yyyy
Yes, but imo that is, if anything, an argument in favour of it being a joke comment: If you are from, say, Europe, and write dates as dd.mm.yy or dd.mm.yyyy, 31.4. immediately looks wrong to you, just as 4/31 would to you (I assume).
Franz Luggin it's the opposite, if you're from Europe than its 04/31 who looks wrong to you (typo error maybe?)
This video is a piece of art! Stunningly good, also the atmosphere and the music… ❤
well there is one thing we can all agree on, the guy who almost made Pi = 3.2 is dumb and should be made fun of.
www.strawpoll.me/15269888/r
That was many decades ago. I think we've laughed at him enough.
Never enough, when the chinese got it way more accurate hundreds of years before him, he should be laughed at for trying to prove something using a vastly incorrect value.
@TheSearchingTruth I can't tell if you're joking or not, but if you're serious, then it's because if we approximate pi, calculation using it won't be exactly correct.
Cranberry Crackle It’s a fairly common joke, like how engineers “think” sin(x)=x=tan(x) and cos(x)=1
Simply the most brilliant guy on u tube
I never expected a video about Pi vs Tau to actually be deep and meaningful but since it's a 3blue1brown video, I guess that was kinda expected...
The real lesson is that we celebrate everyday as a circle constant day if we are flexible and creative enough to do so. No need to limit yourself to 3.14 or 6.28. Celebrate forever.
The tau creature is freaking me out, man. It doesn't look right.
直径に対する円周の比を採用したのは、例えば太い木の円周の長さを求めるのに便利だったという実用的な理由が大きいと思います。
え、日本人？ 同じだ！
So Euler is pronounced as "Oiler".
I've been reading it as "Yuler" wtf
Back when I was a teenager I couldn't figure out how to pronounce "Fibonacci".
+TheOofGod
Yeah, it seems to be pronounced "oiler" by German pronunciation rules (one of them being that "eu" is read "oi", hence "Deutsch" is read "doitch" for example) since he was born in Switzerland, a German-speaking country.
The right way is 'Oiler' but many lecturers of mine still pronounce it 'Yuler'
i've been reading Euler as Euler.
Éuler
*i like how he used it to represent whichever constant was the most efficient, but i think that concept would be hard to teach to kids in highschool and middle school, so if anything, i think it would be good to teach that concept in advanced math in college and universities.*
I agree - we should be celebrating both! Because why only celebrate one when you can have two, right? Thanks, Euler! 😍 And happy half τ day to everyone! 🙃
P.S. R.I.P. Stephen Hawking.
actually pi day is celebrating the area
We should also celebrate Jan 57! Wait.
You are the best maths teacher in the whole entire f*@&ing world. Period.
Seriously its the 21st century, we gotta go Metric and fix Pie. Its the least we could do :)
Euler himself wanted 6.28 to be the standard.
The debate is over, pi people.
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?
Grant Sanderson has made many videos about multivariable calculus for Khan Academy.
This channel makes me a better math teacher every video!
Trying to blur out the author of the "early calculus book"? didn't work, there was a split second written "LEONHARDO EULERO". I first thought it was L'Hopital.