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Circle Area Derivation (visual proof)
Рет қаралды 37,055
Күн бұрынThis is a classic visual proof showing how to think about the area formula for a circle.
#manim #math #mathshorts #visualproof #proofwithoutwords #mathvideo #theorem
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@Innocent.guy. Жыл бұрын
Why this is so underrated 🤬🤬🤬
@MathVisualProofs Жыл бұрын
There are many variations available on here. I just wanted to practice doing it too :)
@randompie5558 Жыл бұрын
@@MathVisualProofs I can't understand where did the pi came from??
@MathVisualProofs Жыл бұрын
@@randompie5558 The circumference of a circle is 2*pi * radius. In this case, we have radius r and we only have half the circumference.
@randompie5558 Жыл бұрын
@@MathVisualProofs thanks for the fast reply . Recently found your channel I am binging it. Great content👍
@MathVisualProofs Жыл бұрын
@@randompie5558 Thanks for checking it out!
@enekaitzteixeira7010 Жыл бұрын
Holy shit. You just caused me to have a mindgasm. We often forgets that mathematical formulas aren't random arbitrary operarions but an actual description of the universe... I wish I had seen this when I was a kid. Thank you so much for this.
@MathVisualProofs Жыл бұрын
Glad you enjoyed it!
@Gamro_ Жыл бұрын
thank God I have seen this as a kid today
@yiutungwong315 11 ай бұрын
π = 2 in Riemann Paradox And Sphere Geometry Mathematical Systems Incorporated...
@mulatinho27 9 ай бұрын
You would be surprised with the amount of people that don't understand this. That's why math is so beautiful, even artistic in some ways.
@NumbToons Жыл бұрын
Can you do a visual for area of sphere?
@edekolechowski Жыл бұрын
We do a little trolling
@drenz1523 Жыл бұрын
i dont think that exists
@elephantoChan Жыл бұрын
the formula 2pi(1-cos dx)*r comes from integrating a cone on a sphere looking out and expanding it to make a full sphere. integrating limits from 0 to 2pi radians we get the answer 4pir.
@yiutungwong315 11 ай бұрын
π = 2 in Riemann Paradox And Sphere Geometry Mathematical Systems Incorporated...
@malayali_here 11 ай бұрын
@@drenz1523but I think
@edekolechowski Жыл бұрын
Nice, now do the same for sphere...
@NumbToons Жыл бұрын
Suuuuuure
@namanlenka8595 3 ай бұрын
This is great
@gravitrax3287 10 ай бұрын
I hereby unleash the great debate: Use Tau instead of 2xPi
@xenonslash 7 ай бұрын
I just use Dπ
@sirsamiboi 5 ай бұрын
It might be a little better than π, but everyone uses π already so it would be too much work to switch over to τ
@yiutungwong315 11 ай бұрын
Master Class...
@tarunraina1454 Жыл бұрын
This makes so much sense now
@NoorazMahmud Күн бұрын
Biggest slice of pizza at a class party 💀
@KevinSamuelsKid Жыл бұрын
How is the length of the side pi r? Oh it’s half the length of the circumference. NVM
@MathVisualProofs Жыл бұрын
:)
@himadrikhanra7463 3 ай бұрын
Fringe formation....optics...most probably lamda/ 2d...de boglie?
@jakobwhaley5641 10 ай бұрын
This was devised by leonardo de vinci if im not mistaken
@MathVisualProofs 10 ай бұрын
Yes, and independently by Sato Moshun (japanese mathematician)
@jeevanandham9469 Жыл бұрын
Path of a projectile is a parabola, Derivation for this👆
@malayali_here 11 ай бұрын
It's actually hyperbola . . . . . . . . . . If thrown at 11.2 km/s or higher
@DigitalLife3000 5 ай бұрын
PYTHAGORAS WANTS TO KNOW YOUR LOCATION
@trashcan3958 Жыл бұрын
Yay, calculus...
@Zoba3301 Жыл бұрын
The edges of the rectangle will never be fully straight.
@pat9353 Жыл бұрын
If you go watch the 3blue1brown video again, you’ll see that was a problem for a sphere. This proof is correct.
@pokechannel9758 8 ай бұрын
It will as we are making infinite divisions of the circle. He couldn't show that in the video so he showed as many divisions as possible.
@Slipewater Жыл бұрын
OH
@fedoFedo-vk1qf Жыл бұрын
Proof 2Pir first
@malayali_here 11 ай бұрын
Proof of 2πr is very simple. Can be obtained from the definition of pi that 'the ratio of circumference to the diameter of any circle is a constant called pi'.
@maverickvalderrama Жыл бұрын
I got a question:
@maverickvalderrama Жыл бұрын
What is the radius equal to in the formula: A=π•r² ???
@maverickvalderrama Жыл бұрын
r=???
@MathVisualProofs Жыл бұрын
You can't figure that out unless you have the area. The formula relates radius and area. Given one, you can find the other. So if you know A, then r = sqrt(A/pi).
@Edvit40 Жыл бұрын
bro is out here inventing the most complicated ways to calculate here's how to do it pi * radius²
@MathVisualProofs Жыл бұрын
But why does that formula give the answer? This is one way to visually justify it.
@Edvit40 Жыл бұрын
@@MathVisualProofs why do we need a useless formula? the pi x radius² is exact while ur "dividing" the circle method makes bumps if you look very closely so you do not get the actual area obviously the error would be around here 0.00(here) but still, that's not the right area
@MathVisualProofs Жыл бұрын
@@Edvit40 My point is this is how one way to justify that the area is pi *r squared. This is precisely how DaVinci justified the area formula to himself. He realized you could slice the circle up like this infinitely so that in the limit you actually get the rectangle with side length r and width pi * r.
@Edvit40 Жыл бұрын
@@MathVisualProofs i dont see a single point where this is how the math works in pi x r ur using fractions
@sergioandresquirogavelarde6816 Жыл бұрын
may i ask? what part of VISUAL proof do you not understand? yes that is the formula, this is just to show why that is true
@de-ja-vu 9 ай бұрын
🤔
@user-zd2py5xi4i 2 ай бұрын
Area of ⭕=Area of rectangle 💀💀
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