How many radii fit around a circle?

In this short, we investigate how many radii of a circle would fit if you lay them in arcs around a circle. The method of laying a single radius around the circle creates an angle subtended by that arc - that angle is known as 1 radian. So in this video we see that there are more than 6 radians and less than 7 radians in a circle. The full measurement is actually around 6.28 and is the constant 2*Pi.
#short #math #manim #radian #circle #radius #tauday #tau

[@alu4807]

And thats the reason why "pi" almost was 6.28

[@MathVisualProofs]

And is now called "tau" :)

[@themusicking4365]

@Dwight Schrute did you read his comment? edit: This reply has more likes than all but one of my comments

[@RoboMuskVsLizardZuckerberg]

It's using r. Not diameter Since it actually 2 * r * 3.14 or 22/7 2 * 3.14 * r 6.14 * r Oo wait. Is this there a joke that's I miss? Oh well, another one flew by my head r/woosh

[@gabrielbarros493]

​@@RoboMuskVsLizardZuckerberg Maybe it's a historic thing

[@DoomRutabaga]

@@RoboMuskVsLizardZuckerberg you forgot the multiply the things after the decimal. you multiply 3.14 by 2 and it gives you 6.28

[@KaliFissure]

Tau , you fit TAU radians

[@MathVisualProofs]

Uh oh. I didn’t want to unleash the tau v pi argument here :)

[@KaliFissure]

@@MathVisualProofs if it starts to get heated we take down the thread. 🙂🖖

[@RubyPiec]

2pi = tau

[@RubyPiec]

@@MathVisualProofs there's an argument?

[@MathVisualProofs]

@@RubyPiec yes. A sort of argument for fun’s sake - should we use tau instead… I’m sure there are good videos out there

[@gyuuyomi]

if only math lessons was shown and explained more visually like this

[@sammarks9146]

I would have done SO much better in class.

[@O_79]

@@sammarks9146thats your fault bro

[@O_79]

your fault

[@pyrite2060]

@@O_79 they would have done better if theyd worked harder yes, but dosnt disprove their statement. everyone learns in a different way. mabye if theyd had this visual they may have understood math better

[@wednesdaysmith922]

IN 58 seconds this short taught me more about Pi than all of the math classes I've taken. Very memorable now that i understand how to visualize Pi. Thanks, I love this channel!

[@MathVisualProofs]

Glad it helped!

[@ProSquidGaming]

How? It barely said anything All it said was there are 2pi radians in a circle I love the visuals and everything, but if this taught you the most you’ve ever learned about pi, try watch khan academy or something, you’ll be astonished

[@hikari1690]

​@@ProSquidGaming I don't think he has the capacity to stay aware that long. This is exactly what's taught in math class after all just faster. Wait till he remembers division. And, god forbids, what pi signifies! Mind will be so blown you'd think it was mostly vacuum like space 🤣. P.s. sorry OP. I just felt like being mean cause youtube is being mean to me by censoring my jokes

[@ProSquidGaming]

@@hikari1690 😂 I think every person here that has a interest in maths knew all of this before

[@wednesdaysmith922]

Yeah. I guess having shitty math teachers my whole life and going to a terrible public schools in a state with the some of worst education in my country makes me an inattentive dumbass that must not pay attention or like math. I took and have notes from all my math classes and guess what, visualizing what pi actually represents or even a basic explanation behind what the formula means NEVER happened once in my school experience. I wrote my original comment because understanding this visualization makes the whole formula make sense instantly the first time i heard it.. Obviously the formula implies as much but it's not immediately obvious to people who have never been told that or had to think deeply about the construction of this formula. Glad you two truly lovely gentlemen wanted to display your superiority as bean counters while showing the world you're unpleasant nerds. You both definitely would make WAY better bean counters than me.

[@Geocentric-videos]

Pi Is literally just how many times the diameter fits into the circumference

[@furioussnackmonster2043]

Yes, so the radius is double

[@marcusvale]

Exactly, so the radius will be 2 times pi....

[@FitSS369]

Therefore , pi is a constant for any circle with a ratio of c/d where c= circumference and d= diameter

[@sajtosbaguette9220]

@@FitSS369 there is no ratio to count pi brother... That's why it is irrational...

[@universenerdd]

​@@sajtosbaguette9220 bro, but there is. It's c/d always

[@driftliketokyo34ftw35]

Circles are pretty rad aren’t they?

[@SamHe-nm8sz]

Was this a radians pun

[@Dawn_Aramoana63]

Aha! A comment that makes sense.

[@TbV-st8ef]

That was so unfunny I laughed Sorry if this sounded mean, I actually laughed

[@georgeofhamilton]

They’re 2π rad, as a matter of fact.

[@turkey_sandwhich]

AGHHHHHHHHHHHHHHHH

[@GraemePayne1967Marine]

74+ years on this planet, and FINALLY I understand what a radian is!

[@josorr]

Ha! It only took 62 years to understand.

[@SylviusTheMad]

How did no one ever explain this to me in school? I was good at math. I'm still good at math, and routinely use geometry to solve real world problems. I studied Astrophysics at university. I can do spherical trigonometry. But this explanation for radians I did not know.

[@jeschinstad]

So you get twice as many half diameters as you get full diameters? Radical.

[@TorGNorge]

Hahahaha

[@DuolingoWrath]

👍

[@agnostic47]

I never understood why they use 2pir instead of pid.

[@everythingisscience658]

​@@agnostic47 Atlernative answer. The area of a circle is pi times r squared. And area tends to be more useful than circumfrance. Additionally lots of mechanics place the origin of the system at the centre of the circle. In that situation it is more useful to take the radius as it is now the distance between a point and origin.

[@decibel333]

​@@everythingisscience658 ok that's a good answer. I'm still in the πD camp because perimeter is not area. But to your point the volume 4/3πr^3 ... More consistent

[@andrewtate8792]

Its just 2 pi cuz thats how pi is defined: diameter * pi or radius * 2 * pi

[@MathVisualProofs]

Yes, exactly the point here is why we use radians :)

[@raiden8929]

This motherfucker tryna pretend to be andrew tate.

[@TacoBellYoutube]

Duh nigga

[@utk__]

Or just TAU

[@alexflosho]

I thought it was asking "How many radii in a circle?" and my answer was "all"

[@tom_something]

How did I not know that a radian is just the angle that projects an arc length that is equal to the radius of the circle? the math was always right there, but I wasn't curious enough I guess. Any time I'm looking at radians, I'm just in a big ol' hurry to convert it to degrees so I can "get" it better.

[@LukaDoncicFitnessOfficiaI]

SAME I GOT GEOMETRY EOC SOON

[@tejara01]

This is how math should be shown

[@MathVisualProofs]

👍

[@plasticelephant1969]

Yeah, we had this in a test somewhere to obtain this number

[@ilovecairns5181]

Maths*

[@tejara01]

@@ilovecairns5181 depends where in the world you are mate

[@timagarmaza9511]

Bro it’s basics. I have a bad news for you If you can’t come up to this with your imagination.

[@Losjo4093]

Radian is 180° devided by pi 3,14 that becomes around 57°

[@MathVisualProofs]

But then what is a degree? ;)

[@philliphine1401]

​@@MathVisualProofs You're evil HAHAHAH

[@MathVisualProofs]

@@philliphine1401 :)

[@philliphine1401]

@@MathVisualProofs But I'm actually curious, make a video about that please!

[@MathVisualProofs]

@@philliphine1401 I'll see what I can do. It might not be that interesting. The idea as that the number 360 is nice because it is divisibly by a lot of numbers (like 2, 3, 4, 5, 6, 8, 9, 10), and perhaps was thought to be the length of a year, so the circle was cut up into 360 equal pieces, and that is called a degree. It is less natural than a radian because we chose 360 for the number of equal pieces, whereas a radian is part of the circle, so wondering how many radii fit around a circle is a more natural measurement.

[@terrencetunnock9046]

I understand radians now, this is such an intuitive explanation/visualization, thank you very much

[@mihfrunze]

When i was in high school just memorize radian to degree formula to solve questions but i was a pathetic and i search why radian exist and what it is. When you learn It gives you a great pleasure but in sametime your friends are ahead of you with solving questions.

[@totallynotcozmo510]

I've always loved trigonometry.

[@bennyyt7726]

Trigonometry?

[@ShivSingh-io5eh]

@@bennyyt7726 in the education system of my country, we were first introduced to the concept of radians in trigonometry. In other chapters of geometry, we simply use degrees instead of radians. From trigo, we were introduced that 2π = 360°, So that in the graph of sin, cos, tan etc, we can mark 90° as π/2 and 180° as π. So I'm guessing the same might me the case for the person who wrote the original comment. So that must be why they mentioned trigonometry

[@curiositypiqued6573]

This is more algebraic geometry

[@AliHassan-hb1bn]

Visualisation is better than just a mental approach.

[@TechTrader108]

This video gave more basic knowledge pf a radian than the maths we learnt in all of school

[@adamlasry5225]

Beautiful explanation. Simple. Powerful. Thanks 🙏

[@duckified.]

this would've helped things make so much more sense in advanced math class

[@gamechep]

wtf is advanced Maths? Maths is maths!

[@AngryEgg6942]

Literally just take 2πr which is the circumference of the circle and divide it by r. You get about 6.28. So you can fit 6 whole radiuses.

[@brightblackhole2442]

oh right, of course the formula that shows how many radii fit around a circle shows how many radii fit around a circle. genius!

[@rubentuting525]

​@@brightblackhole2442 😂 circular reasoning😆

[@windy8395]

2πr divided by r is literally just 2π so it doesn’t do anything new

[@samrad1745]

@@brightblackhole2442 in a round about way

[@nickybritain3661]

Is that thinking outside the box? Er, circle! 🤪

[@Nictator42]

A nice demonstration for why Tau is more fundamental than Pi, and why 2pi shows up so much in maths.

[@nerofl89]

Ah yes, tau the fundamental particle also called the tau lepton...no wait maybe tau the proper time in relativity...or tau the torsion of a curve...no, then maybe tau as in torque...or maybe the time constant tau...wrong again, maybe tau the golden ratio...crap, why don't just use 2 pi. Considering the fact that less than 1/5 of all formulas containing pi rely on 2 pi, tau is objectively inferior and would require a bunch of rewriting equations to appease a minority of equations simply for aesthetic purposes.

[@isavenewspapers8890]

⁠​⁠​⁠​⁠​⁠​⁠​⁠​⁠​⁠​⁠​⁠​⁠​⁠@@nerofl89​​⁠​⁠​​⁠I'm not sure what point you're making by listing all those uses of τ. (Wait, the golden ratio? Who doesn't use φ for that?) Probably the most favorable interpretation of your statement is, "Aren't we lucky that allllll these current uses of τ don't collide with each other! But if we try to introduce a new τ usage, then *that* one is gonna manage to collide with a bunch of the other ones." Which, fine, maybe there's some truth to that. The circle is quite a fundamental shape, so stuff related to it is going to naturally spring up all over the place. But it's not too hard to alter our notation in these cases (e.g., N for torque, τ_p for proper time). Failing that, we can just mark τ the circle constant with a little subscript circle. "less than 1/5 of all formulas containing pi rely on 2 pi" Where did you get that statistic? 2π shows up all over the place in formulas, counting cases like 4π and 8π, which you logically should. When you call τ "objectively inferior", I don't know what you mean by "objectively". In terms of the actual correctness of the math, there's obviously no difference. If you mean that you actually have factual evidence that the usage of π is better than the usage of τ, I'd like to hear it.

[@armanghasemi1494]

To summarize, we know that for any circle, our circumference is going to be 2pir. Now that we want to fit this space of 2pir with a bunch of our radii, we can write: r * x = 2pir, where x is the number of radii that fit into the circumference. Thus, we divide 2pir/r = x to get 2pi (about 6.28 as said), which is why we can fit 6 but not 7 radii into our circle.

[@stephengibbons4680]

Hey, just wanted to share a counter narrative to a few of the comments here. I'm currently 4 years into studying for a mathematics degree. While I have known for over 5 years that the answer is 2π, and knew we had good reason for why radians are better, I didn't really understand that reason. Seeing the 6 radi fold onto the circle unlocked a deeper understanding. I've (only) just realised why they're called radians (I think gradians having a similar name made it seem arbitrary for so long), and seeing everything fold onto the circle, and connecting sine, cos and tan waves with their circle derivation, it makes much more sense as to why we have to us radians in trig calculus. I found out last week that I have aphantasia, which may explain why my brain never made this connection itself. As someone who is studying mathematics, I really appreciate this channel for providing the visualisations my mind can't. Thank you.

[@MathVisualProofs]

Thanks! I think that lots of people never see what a radian is. There are lots of videos out there showing it, so maybe another wasn't needed, but I liked the idea of folding out six radii at once and hadn't seen that. So I am glad you liked it and appreciated it. Glad to hear you are continuing your math studies! Keep it up :)

[@IceNinja-vq9el]

POV: You watched Animation vs Maths 😎

[@StarryNightLover]

We were learning about this topic 😅thanks

[@platnumspoons]

As soon as I saw this, I thought about Vihart

[@mybetterhalf6373]

All this talk about PI~ Now I'm hungry. 😋

[@ColinRichardson]

And this is why I like Tau..

[@HotKeys2021]

Best explanation of radians I’ve come across

[@MKJ8888]

Ok, when I heard between 6 and 7 I'd already known this is 2 pi

[@regulusberdin8619]

You can put 6.283184 (tau) radii in a circle wothout any overlaps.

[@matthewtallent8296]

I knew the math like the back of my hand, I just kept watching for the animation 😍 I've never seen it shown this way before, well done +sub 👏

[@MathVisualProofs]

Glad you liked it! Thank you!

[@moritzhexagon]

Bro out here bending the radius like its nothing 😅

[@gamer9smith]

Because it isnt?

[@SpooxyCowboy1911]

I’ve taken so many math classes and not one of them ever made this clear. Thanks for the visual!

[@RogersGaming07]

I just remembered that one Alan Becker video "Stickman vs Math"

[@krishna.vineet]

And that's remaining arc of Circle after 6 radian is π, discovered and estimated centuries ago in India. Edited: the remaining arc want π, it was the reason too calculate π.

[@MathVisualProofs]

Yes. I think still the first documented instance of it is Archimedes though...

[@krishna.vineet]

@@MathVisualProofs I am not a historian, and not even care about it much, but just can't see the ignorance of world toward ancient Indian mathematicians. Whole world is using the results, still doesn't even know them. Now read this out, sir. Archimedes (Greek) gives the concept of π, basically the meaning and value upto 2 decimal digits (3.14) in around 250 BC. But the concept was already given by the people of Egyptian, Sumerian and Babylonian. And even before it, Sulbha Sutra (Budhayana, 800BC, value 3.14), Shatpath Brahman (700 BC or older, value 3.1), Yajurveda (1000 BC, value 3) are some Indian known texts where concept of π is given in much clear way. It's wrong that we say, Archimedes discovered π but when head toward other civilizations, we say, that's just the concept. Archimedes was great, but it doesn't mean that he did everything. It's clear ignorance to 4 different civilizations. Okay, after the concept, it was time to calculate the value. I will not go hyper that we Indian give π like no other civilizations, and not also will be too woke to ignore the work of my ancestors. Many mathematicians around the globe have contributed to give us the actual value, most of them are still ignored, mainly Chinese and Indian. But, I will mention 3 Indian Scientists in this race. 1. Aryabhatta(6th century): first person who Gives upto 4 decimal digit 3.1416 and said that it's not true, it's approximation, the true value will be slightly less then it.. which actually is like 3.14159... 2. Madhava(16th century): It was the real game changing step. *HE SHOULD BE CALLED AS DISCOVERER OF π.* He was the first person to give infinite series. Though process of Archimedes and Madhava are same, but Archimedes did it geometricaly, he did it arithmetically. His series was infinite, depends on you how far you calculate. 3. The legend Ramanujan (20th century): he gives single formula which was the fastest way to calculate π. His formula is still the bedrock of all discoveries happens now for π. Super computers use it. And a fact here, I said Archimedes and Madhava had same mindset, so why this much difference in values? It's not because of different methods, it's because of digits. Archimedes took Circumference = 22, and diameter = 7. But Madhava was on whole another level, his circumference was 2872433388233, and diameter was -9 × 10¹¹. Yes, negative, I don't know why and how, but he has written it. His calculations were smooth enough to create an infinite series. And looking into his series, we can understand why diameter was negative.. it was also a clue of ramanujan paradox.

[@MathVisualProofs]

@@krishna.vineet Thanks. I have a deep appreciation of the mathematics done by both the ancient (and not so ancient) Indian civilizations (and others). As you noted, I agree that many civilizations (probably starting with babylonians) had an understanding about the circle constant. But I still think that Archimedes is the first instance of someone proving that the circle constant is in fact constant. I, too, am not a historian of mathematics, but I had read the article mentioned in this post some years back (divisbyzero.com/2013/03/05/circular-reasoning-who-first-proved-that-cd-is-a-constant/) and was referring to that. I am not trying to offend anyone. You can see in my "Pascal's triangle" videos, I refer to the arithmetic triangle as "Halayudah's triangle" because I do think that was the first place the array was described in triangular fashion (I may be wrong on that, and I think there is some reference to the numbers by Pingala). Anyway, thank you for your comment, and I agree that Archimedes was not the first to approximate Pi; I meant he was the first to demonstrate it as a constant, which is what is implied by this video and the definition of a radian.

[@krishna.vineet]

@@MathVisualProofs It's not bad in ignoring the legacy of ancient Indian texts, because even 99% of Indians knows nothing about it and why do we expect it from others. There are very few who want to understand it and just some can master it. Ramanujan & Vivekananda were 2 of them. I don't care whether the Europeans their respect to it or not, at the end we are one in this universe and the teachings should be delivered to masses, not the teacher, teachings are more important. But I keep doing it because the teacher still has much things to teach that are coded and need to be understand. We(India) have lost many teachers into darkness through Regular attacks, loots, slavery, colonization, English education system, and are still loosing due to the current secular fabric of country. Some of us are trying to bring remaining teachers to stage but don't know where it gonna end up. Our ancient text describes much work of Archimedes, Aristotle, Pythagoras, Vinci, Tesla, Wright Brothers, Computer Programmers, AI, Einstein, Edison and others even before they born. We don't want the credit, we just want to tell that there maybe the much things with which we can proceed. Pingla was just one branch of this tree. However, moving to topic, from Yajurveda, what I understand is that they could do.. Inter-transform a square, circle, semi circle and triangle keeping area constant. Calculating area of circle without π. Given Budhayana Sutra (later Pythagoras). Calculation of square roots. Geometric calculations of squares. Doubling of cubes. Now, why I believe that π was told as constant in it. They calculate area of Circle as area = 1/2 × circumference × diameter/2. Then they try to write circumference in form of diameter. And end up as Circumference = (diameter × 3) + something. Yes, nothing clear here, and that something also seems to be variable for different sized circles. But, after 2 shlokas, it is written that Circumference = diameter × (3+something). Thats it in Yajurveda. they didn't say it as constant, neither π.. But we see, it clear that "something" is a constant. But still there is a doubt, "whether they know that circumference/diameter is constant?, because even then, that 'something' can be said as constant." And the answer is YES, it was constant for them as they were using this constant relation to transform a circle into other shapes but without knowing the value of that constant. So in Yajurveda, the value of what we call as π was (3+something) and it was indirectly said as constant. Later in Katyayani Sulba Sutra, they proceed to calculate that "something". And taking about how ancient it was, well in Google and by many historians says to be 1000-1200 BCE. But some Indian historians deny it. It's because Yajurveda gives us some Astrological and Geographical evidences which dates back atleast 60,000 years ago. I am not going there, just maths part was mine 😅. And thanks to look into it, have a good day ahead. And if you want to know ancient Indian maths, I will advice you to start with 4 main Sulba Sutras.

[@kojiyaw]

I had no idea wtf radians are until now

[@Nancy-uq1ki]

Same buddy 😅

[@architislive9654]

this is basically an example of wolfrachs theorem

[@RuloKobashikawa]

I know the pi definition but I also like this exploratory perspective

[@Jopie65]

And that's why pi actually is about half a pie.

[@tzbq]

wait that's right you can make a pie with diameter e

[@baibhav11]

I knew the calculation, today I learnt the meaning

[@nvraman]

At 58, this visual image made me a toddler learning fun

[@maxumProductions]

This explains radians much better than any high school or college class I’ve ever taken

[@victorlaurent2978]

Probably not true. You just didn't care.

[@maxumProductions]

@@victorlaurent2978 i mean, in college i did.

[@victorlaurent2978]

@@maxumProductions isn't college where you get a bachelor degree?

[@skymanflyman6610]

Damn that was crazy

[@MathVisualProofs]

:)

[@Bacon2000.]

And pi said "throughout trigonometry to calculus, i alone am archemidas constant"

[@Grumppool]

Damn, you made this so easy, now I hate every math teacher that failed to get this through my head.

[@14megasxlr]

ohhhh ,so that's where Pi comes from....

[@MathVisualProofs]

Yes! In particular Pi is the number of diameters that fit around the circle.

[@carultch]

Pi comes from a constant Euler used for representing special case angles around the circle, that he'd define uniquely for every problem. He'd start with statements like, "let pi equal the circumference of the unit circle", or "let pi equal the semi-circumference of the unit circle". So in a way, Euler used pi, more like the way we use theta in modern times, where it is a variable in radians instead of a constant. Somehow, his semi-circumference definition is the one that stood the test of time, even though modern proponents of tau think it should've been the full circumference definition.

[@muhammadfitranramadhan2212]

Many people still don't know that pi is the ratio of half a circle and it's radius

[@forward876]

now i finally know what a radian is

[@nothindu..kattarhindu8848]

Thanks man for clearing all childhood concepts which were mostly memorized for marks. 😅

[@kylerenglish5698]

Π = diameter / circumference, therefore since radius is ½ the diameter, the number of times the radius fits around the circumference is 2π

[@diamond_player]

Or just tau

[@ecstasyofgold888]

I took a lot of geometry and trig in the past and no one ever told me that a radian is the arc length of one radius. C'mon that makes so much sense! I always thought it was some random nonsense chosen as a weird standard.

[@MathVisualProofs]

Glad this helps!

[@cmmndrblu]

Language can obscure things which should be obvious.

[@Atmatan_Kabbaher]

You make me like math, and I had trauma-induced math anxiety until literally a few months ago. Dang.

[@Raj-sz9pg]

I totally forgot the concept of Radian

[@chakraace9823]

That's why the circumference of a circle is 2πr. 6.28×r 6.28 arcs of the length of radius

[@kirkclarke7396]

No such thing as circumference though or pi

[@PixelCraftEdits]

​@@kirkclarke7396perimeter of a circle is circumference

[@freerobux49]

@@kirkclarke7396 what??

[@kirkclarke7396]

@@freerobux49 what has convinced you that circles are possible? There isn't a machine in the world which can draw a tiny fraction of one.

[@freerobux49]

@@kirkclarke7396 microsoft paint

[@mattb5816]

Tau do you make such good videos?

[@MathVisualProofs]

🙃

[@user-zl9gd3mf9g]

I don't know why I watched this till the end 💀

[@TheStriked]

Thank you so much, it made it much more clearer than just using a unit circle's circumference

[@jordisimon1451]

Bro explained the perimeter of a circle in the longest way possible

[@MathVisualProofs]

No, I explained what a radian is in the longest way possible to fit in a short :)

[@smiledawg]

The perimeter was just the setup to explain the radian

[@Ricardo_S]

The circumference of a circle is equal to πD D=2r If the Radian's lenght is the radius then are 2π radians

[@MathVisualProofs]

For sure!

[@SABRANGHARYANA]

The Graphic Art is so beautiful. Just chumeshwri.

[@GevinTheIdiot]

Fun fact: diameter (the a straight line from one side of the circle to the other or 2 radiuses) times equals the circumference. So if you use radius instead of diameter then it's very easy to see that because radius is half a diameter then you multiply pi by 2.

[@hudsonator7259]

Now I understand why 2pi is the whole circle, and now understand when people say that radians are easier for computers, because I never knew this relationship and that 2pi was chosen arbitrarily to be the full rotation (or I thought that)

[@baivaokumar1886]

Diameter is double of radius And the number of diameter that take to fill the circle is called π Radius is half of the diameter so it's π × 2.

[@saltedjules_]

or, τ

[@saltedjules_]

or, τ

[@Bob-gm4bb]

7 = thala for a reason MSD Love from India 🇮🇳

[@Smart_Chick_]

As a medical student who won't use this at any point in my career, I'm still thrilled

[@pold111]

i finally get why people use 2pi

[@KeyesAnthony]

When you’re a college senior STEM major and you just now learned what a “radian” actually is 😅

[@joshuaohuka7719]

This is me...I am said STEM major...

[@ZA-lv8ba]

@@joshuaohuka7719You are the people I cant stand sharing stem with. You’re just in it for the money

[@reminderIknows]

tau vs pi 6.28 - 3.141592653589793238462643383279502884197169399375105820974944592307816406286208998628034825342117067 looks like tau is winning 😂 i memorised pi to 100 digits and this is the only use case i have for it

[@the-boy-who-lived]

You can fit the *radius* around the circle approximately *_6.283185307179586_* times You know the circumference of a circle is 2πr If you want to find out how many times the radius (r) can go around the circle, 2πr/r = 2π This means the radius can fit around the circle approximately 6.283185307179586 (2π) times.

[@mayzar8646]

“First draw a circle” You see that’s the hardest part

[@user-bt6gd9bt5q]

interesting because 6.28 is double 3.14

[@yourmum69_420]

wow noshit sherlock

[@r.a.6459]

Arc length = radius × angle If angle is 2π, which makes whole circle, then Arc length = r × 2π = 2πr You got the circumference formula!

[@MathVisualProofs]

:)

[@samiksha8018]

Wow, used this formula for millions of times, and here you derive it..

[@Cobalt_Spirit]

​​@@samiksha8018 Actually that is not correct. The formula c=2πr is derived directly from the definition of π. π is defined as the ratio between the circumference of any circle and its diameter. π=c/d π=c/2r 2rπ=2rc/2r 2πr=c The arc length formula is then derived from this one. An arc covers a fraction of the circumference which is equal to the angle the arc covers (which we'll call α) divided by the angle of the whole circle (2π). From that: l=c·α/2π=2πr·α/2π=rα Indeed: l=rα

[@samiksha8018]

@@Cobalt_Spirit oh thanks for letting me know abt this, I won't forget this 😀

[@dhanisac966]

Did I just understand what he said? That was well explained. I doubt, I will forget the numbers anymore

[@christiand.4979]

Good explanation!

[@AdityaSingh-sb5ez]

Thankyou very much for clearing my concept about radian 🥲

[@divyanshumishra24136]

nice vid

[@MathVisualProofs]

Thank you!

[@--Fenix--]

If you know what pi is, this question is answered instantly. Pi is the amount of diameters that fit the circumference.

[@ItsCoa]

Thank you, verry good video and simple explanation❤

[@metalmagerin3]

Dang, imagine a whole video just to say the circumference of a circle is 2πr, couldn't be this guy

[@chinmayeelenka9589]

Wow 😲 nice explanation

[@hammy_and_britney]

Thank you, Math Visual Proofs

[@jadengabban8370]

i wish i had these when i was in school, my teachers were never able to explain why formulas worked or give insight into it and so i never was able to learn a lot of math because i just didnt understand how to use formulas when i didnt know why it worked

[@juampii500]

Thanks you for explanation i needed it 😊

[@cyanideonfire5924]

2π is what came to my mind when I saw 3 was about half.

[@curiositypiqued6573]

Just when I'm starting to understand that damn pi always fucks it up again for me 🤯🤯🤯

[@keithking1985]

Wow you just explained pie. Awesome 👍

[@arunchaturvedi1960]

Beautifully explained with visual aid! Wish we had these when I was in school :(

[@anojhanparameswaran9234]

That's an amazing explanation

[@ropeyarn]

How to trivialize one of the most fascinating puzzles of geometry.

[@andymcneil7085]

I love this type of puzzle and can happily sit and work things out.

[@langstonreese7077]

You can use this trick to measure curves!

[@nelsonleonardogarciaeslava7978]

Muchas gracias bro felicidades hecho pa'delante saludos desde Bogotá Colombia

[@s.muller8688]

my life completely changed after seeing this.

[@MathVisualProofs]

Hah!

[@s.muller8688]

@@MathVisualProofs ;P

[@vijaygopal7150]

Not many math teachers even know this. I wish I knew this 30 years back 😢

[@mrreemann3739]

Pi is the ratio of the diameter to the circumference. The diameter is twice the radius. If pi is a little more than 3, then twice that would be a little more than 6.

[@pranav3151]

No it's the ratio of circumference to diameter not vice versa

[@alial-qassab9186]

Best explanation of rad I ever seen ❤

[@mnverma7455]

In Aryabhatiyam which is an Indian text, it is written that the circumference of circle is approximately 3.14 times of the diameter of circle