Why does π appear in circle area?

Рет қаралды 15,412

Physics Videos by Eugene Khutoryansky

6 ай бұрын

Explains why the area of a circle is exactly equal to π R^2

Пікірлер: 158

@Mike-nf6nf 6 ай бұрын

My main problem with math in physics isn't so much understanding how to go through the equation, but rather, WHY that particular equation is the correct one. These videos help explain why. The color-coding and models are very helpful in making sense of the information. Thanks for all the years of work on your channel!!

@EugeneKhutoryansky 6 ай бұрын

Thanks!!!

@arinb.756 5 ай бұрын

If you're a physics student, then it is worth paying far more attention to the relationships and the why. In my experience they always give you references for tests, but more critically, in the workplace, you'll always be able to look up the math. But knowing how the world works allows you to change it and experiment with it in ways no one else has thought of.

@bo-dg3bh 6 ай бұрын

when a physics guy does mathematical proof, it feels like he’s making sense of things instead of simply stacking up equations

@soupisfornoobs4081 6 ай бұрын

Even so, these equations have their own sense behind them. There is such a thing as mathematical intuition and it's worth cultivating and applying over physical intuition sometimes

@David-bh7hs 6 ай бұрын

As someone who is a mathematician, sometimes I cringe at physics proofs 😂

@eriklopez8770 6 ай бұрын

@@David-bh7hs Congrats! Now go to your fantasy world so the physicist can cringe at you.

@carlhitchon1009 6 ай бұрын

Sounds like you've had some crappy math teachers.

@TheBrainn 6 ай бұрын

physics proof videos be like: “just trust me bro, here’s an example”

@azathoth00 6 ай бұрын

Love that you can do incredible videos on how tensors work and then do some beautiful proofs on elementary geometry

@EugeneKhutoryansky 6 ай бұрын

Thanks.

@KVI3I 6 ай бұрын

such a beautiful derivation of a very common equation in math and physics, thx!

@EugeneKhutoryansky 6 ай бұрын

Thanks.

@VlanimationTales 4 ай бұрын

Beautiful explanation! I know a few proofs for the area of a circle, but I've never seen it presented this way. BTW, congrats on one million subscribers! 🎉

@EugeneKhutoryansky 4 ай бұрын

Thanks!

@yodaqwq 6 ай бұрын

But how do we know that the ratio of the circumference and diameter is the same for all circles?

@EugeneKhutoryansky 6 ай бұрын

When you scale any object, all the dimensions of the object scale in proportion.

@IslandForestPlains 6 ай бұрын

It's like a map. The ratio of distances is the same as in reality. So if on the map street A is twice as long as street B, you know that it is likewise in the real world.

@tseckwr3783 6 ай бұрын

thank you again for your hard work on these excellent videos you produce.

@EugeneKhutoryansky 6 ай бұрын

Thanks!!!

@klumpid6097 6 ай бұрын

The music is just as awesome as the content!

@zh84 6 ай бұрын

Beethoven's "Moonlight" sonata.

@e.b.1115 6 ай бұрын

But where does pi come from in the circumference? I took those triangle areas and came up with the limit Lim n-->inf (n)(r*sin(pi/n))(r*cos(pi/n)) x=pi/n Lim x-->0 (pi/x)(r^2sin(x)cos(x)) [Lim x-->0 pi*r^2][Lim x-->0 sin(x)/x][Lim x-->0 cos(x)] (Pi*r^2)(1)(1) Pi*r^2 But the pi still comes out of nowhere lol

@EugeneKhutoryansky 6 ай бұрын

That is the definition of pi: It is the circumference divided by the diameter.

@e.b.1115 6 ай бұрын

Ah that's true I'm still not satisfied for some reason XD Love your videos!

@feynstein1004 6 ай бұрын

This seems a bit circular (heh). So in essence, this happens because the area of a circle is R/2 times bigger than its circumference.

@IslandForestPlains 6 ай бұрын

Yeah I also expected a video that explained why exactly pi is the value it is, especially after Eugene started with showing that the area of a circle is somewhat smaller than 4. An information that wasn't needed for the further explanation, as pi was then introduced as c/d. So given the question in the heading, in essence pi appears in the circle area because it appears in the circle circumference.

@feynstein1004 6 ай бұрын

@@IslandForestPlains Yeah it's a bit of circular logic 😅

@farhanhassan1865 6 ай бұрын

Always waiting for video by Eugene

@EugeneKhutoryansky 6 ай бұрын

More videos are on their way.

@farhanhassan1865 6 ай бұрын

@@EugeneKhutoryansky thanks 👍

@Mysoi123 6 ай бұрын

Absolutely beautiful! ❤

@EugeneKhutoryansky 6 ай бұрын

Thanks for the compliment.

@KaliFissure 6 ай бұрын

What's cute is that if you have a circle with radius Pi, the circumference is 2Pi² and the area is Pi³. The area of a sphere of radius Pi is 4Pi³ and the volume 4/3 Pi⁴

@lindt3787 6 ай бұрын

Interesting. Strictly speaking, length, area and volume are magnitudes expressed in different units, so comparing their raw numeric values has no meaning. But interesting nonetheless.

@KaliFissure 6 ай бұрын

@lindt3787 yes. A numerical trick. But after doing a series of investigations into sphere/circle volume area length investigations that popped out. Like a math pun.

@zacharywong483 6 ай бұрын

Fantastic explanations, as always!

@EugeneKhutoryansky 6 ай бұрын

Thanks for the compliment.

@mateuszpraseek6733 6 ай бұрын

Elegant proof :D Coincidentally I was wondering when will You upload Your next full-length video, and I am happy You did :D but its too short for me to be fully satisfied, but it's better than nothing! :D I love Your channel and hope for more videos

@EugeneKhutoryansky 6 ай бұрын

More videos are on their way. I can never predict the date of my next video. Thanks.

@VADemon 6 ай бұрын

As that other comment asking about where π comes from in the circumference, I expected some form of introduction through the ways the ancient Greeks might've derived π.

@EugeneKhutoryansky 6 ай бұрын

That is the definition of pi: It is the circumference divided by the diameter.

@chrimony 29 күн бұрын

@@EugeneKhutoryansky What people are asking for is how π can be derived, instead of just defining it as an axiom. Archimedes would be the man here.

@roaster591 6 ай бұрын

I use diameter squared times .785 for area of a circle, on the job related to pipe flow rate

@Ali2599 4 ай бұрын

Thank you very much because you are doing hard work in producing these amazing and useful videos. Therefore, I hope that this great channel will continue and we are always waiting for everything new.

@EugeneKhutoryansky 4 ай бұрын

Thanks. More videos are on their way.

@erdaly4557 6 ай бұрын

Eugene. you are a role model! Thank you so much

@EugeneKhutoryansky 6 ай бұрын

Thanks!

@vigneshsurya2504 6 ай бұрын

Very clearly explained.👏👏👏

@EugeneKhutoryansky 6 ай бұрын

Thanks.

@physicslover1950 6 ай бұрын

Wow, my mentor that was brilliant.. I am anxiously waiting for your video on gravitational microlensing... Specially the xLxS models of gravitational microlensing where x are random numbers.

@alihakimtaskran7809 6 ай бұрын

Eugene used to share videos on complex topics like quantum mechanics and general relativity. Could you share more about those complex topics?

@EugeneKhutoryansky 6 ай бұрын

Yes, I plan to make more videos like that. Thanks.

@Rationalific 6 ай бұрын

It's an amazing look to see why things are the way they are, rather than just taking them for granted as the way they are. The explanation was amazing. As for my brain, I could barely keep up, and this isn't rocket science. My mind boggles at those like the creator of this video who can not only easily understand but also explain these ideas so well. And then there are those who actually figured these things out....the giants upon which we and all of modern society stands (mostly aloofly and ungratefully).

@EugeneKhutoryansky 6 ай бұрын

I am glad you liked my explanation. Thanks.

@Rationalific 6 ай бұрын

@@EugeneKhutoryansky 👍

@skrishna6336 6 ай бұрын

Than why circumference= pi × diameter?

@EugeneKhutoryansky 6 ай бұрын

That is the definition of pi: It is the circumference divided by the diameter.

@skrishna6336 6 ай бұрын

@@EugeneKhutoryansky Perfect. Thanks for the clarification.

@anitakhandelwal307 6 ай бұрын

Wow..😊welcome mam,I have been waiting since long time..

@PabloBatistaArq 6 ай бұрын

I did calculus in college and I had forgotten about this 😅

@LawatheMEid 6 ай бұрын

C=π x diameter This equation come from arc length equation which is: A = angle of the arc in radian x radius So: C = 2π x r

@ThirdOneness 6 ай бұрын

You are the best for me , please try to demonstrate addition formula for secant and cosecant Why : secant (a+b) = sec a sec b csc a csc b / csc a csc b - sec a sec b , and so on ...

@antoniomoyal 6 ай бұрын

The proof that mathematical objects cannot be material. As matrer cannot be divided infinitely.

@LawatheMEid 6 ай бұрын

Waiting for video about subatomic world.. it will be magnificent in your way of introducing.

@EugeneKhutoryansky 6 ай бұрын

I already have many videos on that topic. They are available in my playlist below: kzfaq.info/sun/PLkyBCj4JhHt-uU7uZECW3aZx8g1klRg8_&si=Sqi1dmPghrgPe0ZH

@arinb.756 6 ай бұрын

Off topic but what is the background music used in the video on Mutually Assured Destruction? Thank you!

@EugeneKhutoryansky 6 ай бұрын

Ride_of_the_Valkyries_by_Wagner Moonlight_Sonata_by_Beethoven Both from the free KZfaq audio library

@arinb.756 5 ай бұрын

@@EugeneKhutoryansky Thanks! the music certainly makes the videos more engaging and dramatic, especially when you cover the philosophical implications of some of these topics.

@namelname2448 6 ай бұрын

Useful information.

@EugeneKhutoryansky 6 ай бұрын

Thanks.

@namelname2448 6 ай бұрын

You're Welcome!, please concentrate on Geometry,some of us need it in our work.@@EugeneKhutoryansky

@TheIvalen 6 ай бұрын

I followed you until you used pi in the circumference. It’s like defining a word in a dictionary by using the word itself.

@EugeneKhutoryansky 6 ай бұрын

That is the definition of pi: It is the circumference divided by the diameter.

@pankajtomar2358 6 ай бұрын

Excellent vedio. Nice explained. I got interest in physics due to your channel in my age of 50 . Regards

@EugeneKhutoryansky 6 ай бұрын

Thanks. I am glad you liked my video and I am glad I made you interested in physics.

@trout3685 6 ай бұрын

Using radii in a sqaure was a new concept for me.

@morkovija 6 ай бұрын

Absolutely brilliant.

@EugeneKhutoryansky 6 ай бұрын

Thanks for the compliment.

@RobertoCerv90 5 ай бұрын

Hi Eugene. Nice 2024. I'm considering your student of physics, only because I learn more deeply some terms of quantum theory. I will be incredibly grateful if you can, on your stupendous way to make us understand, more deeply the "Quiral". I can understand the spin on electrons and can be up or down, and that's because it's 1/2 to complete orbits, essential for atoms. And also haves a deal with the stable number of neutrons on atoms to completed. I understand. Also the interaction with higgs with electrons. But I don't know why that interaction, his repercution on atoms and if it's a necessary have left and right pairs of quiral particles on electron orbitals, and off course the knowledge you have of other properties unknown for most of us... It will amazing. Truly I admire your channel, and all to do for the ones who haves tis passion with the nature, and finds out all creators never go so profound like you. And you end finish knowing the same. Of all those. My best wishes from Guadalajara... A City on the state of Jalisco who belongs to Mexico 🇲🇽 Send you an “e-💐"

@EugeneKhutoryansky 5 ай бұрын

I explain why each electron orbital can accommodate two electrons of opposite spin in my video on the Pauli Exclusion Principle at kzfaq.info/get/bejne/kNKgZaqCmLWwlXk.html Thanks!

@ayushsharma8804 6 ай бұрын

Eugene do you have any plans about Classical Hamiltonian mechanics? Seems to be an empty niche on KZfaq, can't seem to find any videos

@EugeneKhutoryansky 6 ай бұрын

That is on my list of topics for future videos. Though, I already have a video on Lagrangian Mechanics at kzfaq.info/get/bejne/e8mVia17rKeqdn0.html

@TheClonerx 6 ай бұрын

Ok but now why is there a pi in the circumference

@EugeneKhutoryansky 6 ай бұрын

That is the definition of pi: It is the circumference divided by the diameter.

@Elias-dz7zx 6 ай бұрын

Good point. The video attempts to explain how π appears in the circle but is based on the definition of π that is the ratio of circumference to diameter. So the initial question and the video is pointless. It is as if it defines a word using the word in the definition. Loop!

@EugeneKhutoryansky 6 ай бұрын

No, it is not pointless. It shows why the area of a circle is related to its circumference, hence this explains why the area is related to pi.

@ayushsharma8804 6 ай бұрын

@@Elias-dz7zxthe video asks why pi appears in circle *area*, the definition of pi in respect to the circumference is irrelevant here

@Elias-dz7zx 6 ай бұрын

@@ayushsharma8804 this is exactly why it appears to area

@RobertLeyland 6 ай бұрын

Which is why we should be using TAU instead of PI, as almost all formula involving circles, trig or,rotations etc end up using 2*PI … explanations like this would also make more intuitive sense. Sadly centuries ago measuring the diameter of a circle was easier than measuring the radius, so we are stuck with PI

@RobertoCerv90 5 ай бұрын

And that's the truly reason why the Area it π*r². The curious fact is that, it's the first time I known that before. And I'm very sure, If I had seen it at school, I would have understood. And I wouldn't have hated the exercises on circle areas so much 🤭

@kv2893 6 ай бұрын

Great video!

@EugeneKhutoryansky 6 ай бұрын

Thanks!

@anton.w1b 6 ай бұрын

Thats a cool video

@EugeneKhutoryansky 6 ай бұрын

Thanks. I am glad you liked it.

@nohjrd 6 ай бұрын

Excellent video

@EugeneKhutoryansky 6 ай бұрын

Thanks. I am glad you liked my video.

@bobobricklayer 6 ай бұрын

Dude, the world of education needs you.

@EugeneKhutoryansky 6 ай бұрын

Thanks.

@chlodnia 6 ай бұрын

I kind of look like a triangle. Thanks for the video

@Singapukodama 5 ай бұрын

explaining the area of moon with moonlight sonata

@prashantsharma7788 6 ай бұрын

❤

@peshalbasnet2425 2 ай бұрын

Thank you so much

@EugeneKhutoryansky 2 ай бұрын

You are welcome and thanks.

@arandomguy777 2 ай бұрын

Physicists: Area = 3 R^2

@WFSJUBTWPTMJCFSBCJU 5 ай бұрын

what song is this again?

@EugeneKhutoryansky 5 ай бұрын

Moonlight_Sonata_by_Beethoven from the free KZfaq audio library.

@bharathreddygudibandi492 6 ай бұрын

Greatest video.

@EugeneKhutoryansky 6 ай бұрын

Thanks!

@mrhoho 6 ай бұрын

nice vid.

@EugeneKhutoryansky 6 ай бұрын

Thanks.

@samwisegamgee4659 6 ай бұрын

Great Proof! I hit *LIKE* 3 times.

@EugeneKhutoryansky 6 ай бұрын

I am glad you liked my proof.

@namelname2448 6 ай бұрын

How many perfect triangles in 1 circle?,thank you

@EugeneKhutoryansky 6 ай бұрын

As the number of slices approaches infinity, each slice approaches a perfect triangle.

@namelname2448 6 ай бұрын

I see,thank you for answering.@@EugeneKhutoryansky

@airgunslugslingers Ай бұрын

👍👍

@simpleman283 6 ай бұрын

Even I can understand that. Thanks. 1/24/2024

@user-yo5vk2bc5m 6 ай бұрын

@kagannasuhbeyoglu 5 ай бұрын

👍

@abhisheksinghyadav7887 6 ай бұрын

Hello sir I'm from India.🇮🇳

@EugeneKhutoryansky 6 ай бұрын

Hello.

@Chicky-yy7nk 6 ай бұрын

the goat

@sergiydmitruk145 6 ай бұрын

Please, explain why electricity from power bank moves only in one direction to accumulator of telephone!!! Why not in reverse direction???

@EugeneKhutoryansky 6 ай бұрын

I explain this in my video "AC to DC Voltage Rectifiers" at kzfaq.info/get/bejne/gJ5xabSG3czPaJc.html

@Lolwutdesu9000 6 ай бұрын

The first two minutes of this video are satire, right?

@ajaybisht922 6 ай бұрын

Make video on physics topics

@EugeneKhutoryansky 6 ай бұрын

More physics videos are on their way.

@ajaybisht922 6 ай бұрын

@@EugeneKhutoryansky thanks for , this immense value you have provide from very long time ❤️❤️.

@chudleyflusher7132 6 ай бұрын

You must be new around here…

@taritkumarray2614 6 ай бұрын

But please explain why circumstances of a circle is equal to 2πr. How come π fits in to solve the problem of measuring the circumference of a circle? When explaining definition of "π" You also said so diameter of a circle has something to do with ascertaining the area of a circle ? How he thought so when the person who found this formula first of area of a circle ? He could have thought of solving the problem in terms of diameter, radius, circumference only? Why the idea of π came to his mind?

@EugeneKhutoryansky 6 ай бұрын

That is the definition of pi: It is the circumference divided by the diameter.

@taritkumarray2614 6 ай бұрын

@@EugeneKhutoryansky thanks.but we all know that. The crux of the matter is how come the idea of a weird thing such as π did come in ascertaining a formula.

@lindt3787 6 ай бұрын

@@taritkumarray2614You can rephrase the question in the title as "Why does the same factor appear in the circle circumference and area formulas"

@taritkumarray2614 6 ай бұрын

@@lindt3787 Yes thank you. Please upload a new video on this question next time. Why and how on earth did come the idea of π?

@lindt3787 6 ай бұрын

@@taritkumarray2614 I was trying to help you understand the point of this video. Most people will consider that what is shown here is not as obvious as you think.

@nirmalmishra6404 6 ай бұрын

Eugene, what's your qualification btw?

@ucngominh3354 6 ай бұрын

@EugeneKhutoryansky 6 ай бұрын

Hello.

@firstnamesurname6810 6 ай бұрын

Eugene from walking dead 😂

@veryveryveryvery161 6 ай бұрын

Я понимаю так, что число пи - это характеристика самого пространства. Пока мы на прямой - работают рациональные числа. Чуть отойдем во второе измерение - появляются иррациональные - корень из двух в случае гипотенузы треугольника 1х1 или пи в случае длины окружности.

@TheDelwish 6 ай бұрын

данное значение отношения длины окружности к диаметру, которое названо пи, - безусловно характеристика евклидова пространства (в других геометриях оно просто другое). насчет отойдем в другое измерение, и да и нет, т.е. с одной стороны ничто не запрещает быть всему множеству действительных чисел на прямой, собственно есть аксиоматики чисел которые и работают на прямой, а есть типа Дедекиндовых сечений. это просто вы для наглядности континуума вещественных чисел представляете примеры с большим числом измерений. ибо проще. но строго говоря можно расширить числа на иррациональные и трансцендентые даже без всяких таких вещей. для прямой и вообще для математики нет никакой принципиальной разницы между 1 и корнем из 2. просто вам кажется что обозначение первого объекта в виде литеры "1" вам почему-то более понятно. но строго говоря непрерывность такая сложная штуку, что понять ее сложно вне зависимости что вы видите на прямой, 0.(9), 1.(0) или 1.(0)1

@robbiekavanagh2802 6 ай бұрын

Wait has this channel been an ai voice this whole time?

@EugeneKhutoryansky 6 ай бұрын

All my videos are narrated by my friend, Kira Vincent. This is stated on the screen at the end of almost all my videos, including this one.

@robbiekavanagh2802 6 ай бұрын

@@EugeneKhutoryansky I have actually been watching this channel for longer than ai voices have been good! I was mostly kidding around but honestly sometimes I don't know what's real!