Circumference = diameter*pi This visualization is horrible using some internal polygon with the number of sides approaching infinity is infinitely more complicated than just taking the damn circumference
@@StellaNoxFr its not exactly exponential. The actual formula is a bit complicated. The formula is n*sqrt(0.5-0.5*cos(2pi/n)) where n is the number of sides,
@@Lord_LindaThePhilosopher Archimedes did this with a 96 sided shape. William Shanks computed 527 digits of the thing by hand. that is more accuracy than you will ever need.
A beautiful representation of how to reach pi you would need infinite subdivisions meaning pi is also infinite, a function that converges at both infinity and a set value which itself is an infinite value a set of infinity
4 int dx/(1+x²) [from 0 to 1] Let x = tanu then dx= sec²u du we get int 4sec²u/(1+tan²u) du (from 0 to π/4) we get int 4 du = [4u](from 0 to π/4) = π-0 = π.
I like the visualization of the asymptote. No matter how close you can make a polygon to look like a circle, you’ll never get to the exact circumference of a circle
@@jtmckend6741 So ironic. Firstly, it's not called a perimeter it's called a circumference. Secondly, no, the equation for the circumference of a circle is 2πr meaning for this visualization to work the radius has to be 1/2. Think before you comment.
Till now i was not knowing anything about pi.. i regret for not having this kind of teaching when i was studying my school. This is tremendous way of teaching. Iam thankful to u let my children learn this properly.
@@HeckYeahRyan Alas, no. If the circumference is pi, then the diameter must be one, and the radius is 1/2. After some working out, we find the side of the triangle is (√3)/2 ... and therefore the perimeter is 3(√3)/2, or about 2.598
This is a great video to find the near value of Pi When video starts , 2 green lines are shown which 1 unit apart A triangle is drawn such that it is less than the circle circumference. It basically means the triangle perimeter is roughly around 2+ You then add more sides. 4 sides. Now the perimeter increases. You continue to add more sides. And the. You realise the perimeter of new polygon approaches 3.10+ but always remain 3.20- You conclude perimeter or circumference of a circle is approximately 3.10 (3.14 to be more precise ) If a diameter of 1 circle has 3.14 circumference And if a diameter of 2 circle has 6.28 circumference , then you can conclude a common factor should be around 3.14 Let’s call this number 3.14 as Pi. Pis is born
Not this one ......but , That old video of 3 connected lines rotating and making infinite circles & yet not touching is the best representation of Pi.....i have ever witnessed.
Each angle is 360°/n for n>3, so the change in ° is 360°/(n+1) - 360°/n = -360°/(n²+n). If you're talking about the laser cannon's angle change and not the angle change of the n-gon's corners, then you halve that result.
Schools should just make compilations of videos like this, I swear every 20 minutes concept will take 45 seconds and more intuitive understanding might actually help them
This is a crucial point that should be mentioned in the video. Do people really don't remember the formula of the circumference? I was surprised to see that no one else mentioned it.
@joelbarker421 I mean 0.5 units So when u multiply it with PI then only u will get the output as mentioned in video Else if u assume 2 which is .5 of 4 will be given u greater output than PI which will falefy the video content BTW u put gr8 point, nice point to view 😊
I am 36, i only know this visual explanation today 🙏 Your children will learn this at the age of 12 🙏 Because of technological advantage 🙏 So don't cribe 🙏
What fact? - what happens when the circle is bigger? What does this prove ? I dont unterstand Why not rolling out the circle kn the beginning? Why does the approximation show us?
Nicolas of Cusa reinvigorated the exploration of the classic Greek paradox, often termed, "The Squaring of the Circle," in his De Docta Ignoratia, or, "The Learned Ignorance." Think about it like this. The polygon becomes more "circle-like" as you add faces because the length of the sides approaches the circumference of the circle. Yet, as it does so, it becomes paradoxically less "circle-like" as it gains faces and vertices because a circle has no faces nor vertices. Another example he gives is the reverse, attempting to find the straight line from the circle. You can increasingly make the circle larger and larger, and at a certain point, from a fixed perspective, the circle will appear as a straight line, much like the horizon looks flat from our position on the Earth, because the Earth is so large. Really fascinating stuff, geometry is the heart and soul of mathematics. Everyone should read Cusa.
Pi is the ratio between the diameter and the circumference of any circle hence C = (pi)(radius * 2). Pi = how many diameters it takes to match the length of the circles circumference.
Unfortunately it doesn't. This is why visual proofs can be dangerous to teach. This exact same behavior would be observed if Pi was just 3. You're visually seeing a series of better and better approximations of Pi, not a demonstration that it's a transcendental number.
I never thought I could relate to a number before. But perhaps there's a lot in life that you're really close to but never really get to see it. Goes for people you might love as well.
![[MV] A leap of faith...ความเชื่อใจครั้งสุดท้าย (From "Petrichor the series")](http://i.ytimg.com/vi/U1piZH2CNXA/mqdefault.jpg)
I’ve never we seen this visualization before. This is brilliant.
Isn't pi length of circumference divided by diameter? Here i see only length of circumference ...
@@wini7886Diameter is represented by the green lines
This is how they did it before Isaac made the binomial theorem. Billions of sides just to get less than 40 decimal digits of pi
@@wini7886 Radius is 1/2 so the circumference is pi
Circumference = diameter*pi
This visualization is horrible using some internal polygon with the number of sides approaching infinity is infinitely more complicated than just taking the damn circumference
Its like an asymptote. It forever reaches closer and closer and closer to a apecific number, but never actually meets it
Or... a limit
ye its more of a limit
Yeah, I'm wondering what the exact function behind. It looks like exponential...
It’s an asymptote definitely
@@StellaNoxFr its not exactly exponential. The actual formula is a bit complicated. The formula is n*sqrt(0.5-0.5*cos(2pi/n))
where n is the number of sides,
Finally TH-cam becoming knowledgeable again
1 video aa gaya saamne toh knowledgeable again? 😂
@@Atiurrahman27"becoming".
Right??? so sick of AI generated garbage content.
nice ignoring literally any other knowledgeable youtuber skills
Love it
Very nice visualization, and extremely satisfying too!
Never have I ever seen someone post something one hour before I saw a video.
@Kaya-zp4yh see that preaty often tbh
just a random comment
Amazing visualization
Still it's hard to understand 😂😂😂
No lmfao?@@Educatedindian123
just a random comment
@@Educatedindian123 how?
This is the most understandable video about the number pi
Love it, how a work of centuries elaborated in few seconds.
This comment had 69 likes but now I made it 70.
@@sps123star unforgivable
Centeries? I mean in the end a computer figured it out cause we couldn't lol
@@Lord_LindaThePhilosopher Archimedes did this with a 96 sided shape. William Shanks computed 527 digits of the thing by hand. that is more accuracy than you will ever need.
And then Newton was bored one day and found a new way to calculate pi way faster with calculus
A beautiful representation of how to reach pi you would need infinite subdivisions meaning pi is also infinite, a function that converges at both infinity and a set value which itself is an infinite value a set of infinity
It is not infinite. It is transcendental.
@@SGD2718 like The God
@@razibran1494? Mathematically a transcendental number is an irrational number that is not the solution to any polynomial with integer coefficients.
Integrating 4/(1 + x^2) dx from 0 to 1 with Simpson's rule is more computationally efficient.
ramanujans pi series is pretty fast too
🎉
4 int dx/(1+x²) [from 0 to 1]
Let x = tanu then dx= sec²u du
we get int 4sec²u/(1+tan²u) du (from 0 to π/4) we get int 4 du = [4u](from 0 to π/4) = π-0 = π.
Why you mixing alphabets and numbers bro. Can we talk in addition subtraction divide multiplication?
@@vinayakpatil355if you dont understand Integration why reply
This also is a good explanation of the concept of calculus actually… nice video
Oh my god. This MAKES SO MUCH SENSE!! Should be shown in every classroom! Why cant teachers just explain this!!!
It’s simpler to visualize that circumference is 3.14 times the diameter of a perfect circle
…because you really don’t need to know this in order to remember that pi=3.14?
@@tfan2222 it's important to understand why you're expected to know about things, both for motivation and for gaining insight into the subject.
@@PerfectYarnexcept this videos doesn’t do what you said. It’s just showing the old method of approximating pi.
Cause they don't know
I 100% thought this was a mobile game ad for a second at the beginning
I like the visualization of the asymptote. No matter how close you can make a polygon to look like a circle, you’ll never get to the exact circumference of a circle
Exactly what our math teacher told us back in the day. Think about a circle as a polygon with infinite corners.
This is actually beautiful for so many reasons. This is the old way. Geometric proofs.
U meant radius of circle is 1/2 units.🎉🎉
Yups its only possible that way, since pi is the ratio of circumference and the diameter
just a random comment
Bro the perimeter of a circle with a radius 1/2 IS π.
Math before you comment
Edit: fixed brain fart "_ IS 1/2" to "1/2 IS π"
@@jtmckend6741 So ironic. Firstly, it's not called a perimeter it's called a circumference. Secondly, no, the equation for the circumference of a circle is 2πr meaning for this visualization to work the radius has to be 1/2. Think before you comment.
@@Carter9007You're right, I meant to say "1/2 IS π" but didn't bother to reread my comment before I posted.
Till now i was not knowing anything about pi.. i regret for not having this kind of teaching when i was studying my school. This is tremendous way of teaching. Iam thankful to u let my children learn this properly.
Really beautiful. I never saw this way of evaluating pi.
This is INCREDIBLY informative of a visualization. Top notch.
The fact it starts with 2.71(e) is amazing af.
What it's mean..?
Rulers number
shouldnt the first one be 3 since its a triangle and 3*1=3
Ummm actually, it’s 1.5 times sqrt(3)
Approximately 2.598
@@HeckYeahRyan Alas, no. If the circumference is pi, then the diameter must be one, and the radius is 1/2.
After some working out, we find the side of the triangle is (√3)/2 ... and therefore the perimeter is 3(√3)/2, or about 2.598
A great and direct way of showing approxiamation too.
This is a great video to find the near value of Pi
When video starts , 2 green lines are shown which 1 unit apart
A triangle is drawn such that it is less than the circle circumference. It basically means the triangle perimeter is roughly around 2+
You then add more sides. 4 sides. Now the perimeter increases.
You continue to add more sides. And the. You realise the perimeter of new polygon approaches 3.10+ but always remain 3.20-
You conclude perimeter or circumference of a circle is approximately 3.10 (3.14 to be more precise )
If a diameter of 1 circle has 3.14 circumference
And if a diameter of 2 circle has 6.28 circumference , then you can conclude a common factor should be around 3.14
Let’s call this number 3.14 as Pi. Pis is born
Hell! I don't even know tables 🙂
And I'm seeing this video like a fool.
We start somewhere right!!@@GanpatKevane
Why the shift of the machine after the first drop of the black line?
NERD!!!
Heading toward calculus and limits. Beautiful.
Not this one ......but , That old video of 3 connected lines rotating and making infinite circles & yet not touching is the best representation of Pi.....i have ever witnessed.
Ik what you are talking about but that doesn't explain the value of pi
Thats phi not pi
There is a mistake! It's 2pi
Wow, simply beautiful presentation. Kinda mind-blowing when you consider that centuries of thinking inspired this video
This is one reason why i love math.
The universe and its perfect fractal nature represented here. Just like in the Vitruvian man. This says so much more than it seems
Длина окружности равна диаметр окружности умноженный на π. L = ∅ × π
Да тихо вы
Не ломайте кайф!
Не зная химии-
Волшебный лайф.
This visualisation is effectively a summary of centuries of mathematical development. Amazing!
Nice effect. Good choice of sounds 👌
One thing id like to see, is the ° in change
Each angle is 360°/n for n>3, so the change in ° is 360°/(n+1) - 360°/n = -360°/(n²+n).
If you're talking about the laser cannon's angle change and not the angle change of the n-gon's corners, then you halve that result.
@TimeFadesMemoryLasts thanks for taking the time
Maravilloso!! Muy contundente 👍🏻👍🏻👍🏻👏👏
I have never seen such a brilliance animation for math
Wow, I've been using this formula for a long time and only now found out the origin of the calculation..👍
Schools should just make compilations of videos like this, I swear every 20 minutes concept will take 45 seconds and more intuitive understanding might actually help them
Only true when the radius of circle is 0.5
is it not?
This is a crucial point that should be mentioned in the video.
Do people really don't remember the formula of the circumference? I was surprised to see that no one else mentioned it.
@@syeddaniyalali7788yes, if radius is 1 the length represents 2pi… it pisses me off to see this much people being scammed
You dumb 0.5 what??
@@syeddaniyalali7788 exactly 💯 I was looking for this comment
My dad was an engineer. He explained this.. but seeing it visualized, it is amazing!
Back in elementary school, when I first learned about pi, the teacher didn’t explain why it was used. Now I understand.
I was wondering why we used pi for a very long time. It's crazy how this answers that question
I like this and the Spirograph of pi being unreasonable
Amazing, very well done... great perception
This video is correct only when the radius of the shown circle is 0.5
I suppose that every circle in the universe is .5 if you never say .5 of what.
@joelbarker421 I mean 0.5 units
So when u multiply it with PI then only u will get the output as mentioned in video
Else if u assume 2 which is .5 of 4 will be given u greater output than PI which will falefy the video content
BTW u put gr8 point, nice point to view 😊
This is amazing. I never thought about it this way,
😢 i am 25 only now i came to know this fact
same or mujhe bhi aaj pta chala😂
I am 36, i only know this visual explanation today 🙏
Your children will learn this at the age of 12 🙏
Because of technological advantage 🙏
So don't cribe 🙏
Bro (only 25 ) mtlb km lgra h apko 😅
What fact? - what happens when the circle is bigger?
What does this prove ?
I dont unterstand
Why not rolling out the circle kn the beginning?
Why does the approximation show us?
This may the the coolest animation I've ever seen
8 years of math classes summed up in one TH-cam short
Nicolas of Cusa reinvigorated the exploration of the classic Greek paradox, often termed, "The Squaring of the Circle," in his De Docta Ignoratia, or, "The Learned Ignorance."
Think about it like this. The polygon becomes more "circle-like" as you add faces because the length of the sides approaches the circumference of the circle. Yet, as it does so, it becomes paradoxically less "circle-like" as it gains faces and vertices because a circle has no faces nor vertices.
Another example he gives is the reverse, attempting to find the straight line from the circle. You can increasingly make the circle larger and larger, and at a certain point, from a fixed perspective, the circle will appear as a straight line, much like the horizon looks flat from our position on the Earth, because the Earth is so large.
Really fascinating stuff, geometry is the heart and soul of mathematics. Everyone should read Cusa.
Pi is the ratio between the diameter and the circumference of any circle hence C = (pi)(radius * 2). Pi = how many diameters it takes to match the length of the circles circumference.
Yes. The video shows that if the radius of the circle is 0.5, pi = 3.1415...
it's amazing for who have founded this formula.
This explains why the true value of pi has no end
Yep. It is an asymptote, it will get infinitely close to 3.? But never reach yhere
@@cheetahman515 its past 3. its 3.1
Unfortunately it doesn't. This is why visual proofs can be dangerous to teach.
This exact same behavior would be observed if Pi was just 3. You're visually seeing a series of better and better approximations of Pi, not a demonstration that it's a transcendental number.
@satoastz 3.14 > 3.1 the point it approaches is undefined as the last digit can never be known
1/x approaches 0 as x approaches infinity, therefore 0 is irrational
thats what you sound like
This is nsin(180/n) where n is the number of sides of the polygon inside the circle
Others...discovery of 3.14
Me......designs of arc reactor😅😅
Same😂
this is the most satisfying way of math ive ever seen
Wow 👌🙏
Ngl, it’s kind of ingenious. Consider me impressed 👏👏👏
Amazing sound
This is so satisfying to watch 👍
Actually real reason is that whenever you divide diameter of circle by circumference of corcle the answer is always 3.14 and something
what?
@sydssolanumsamsys sorry it was misinformation
@@Mr_lemon0909 okay lol
This is the best visualization I have ever seen, of finding PI!
I'm stupid
The radius is visibly 1/2
Yeah it showed that the diameter is 1 at the start
I actually just learned something new
I wonder who created this animation. Truly a masterpiece
Its basically circumference of circle with 0.5 unit radius , and when it touches value of pi the polygon made in that circle with have infinite sides.
its cool how it exponentially goes closer and closer to pi..
This actually it's pretty interesting and thought provoking
Today I understand why pi value is continues❤
This is the coolest thing I've seen in awhile
I wish they would have showed more stuff like this in school
I feel like high school kids would understand this more than what they teach in a text book about pi and circles.
An actual educational yt short. Wow. That's really rare
Would be interesting to see the exact functions of this. What comes after? What happens before? Why does it converge?
Thanks that helped understand a lot of things
Explaining limits to non mathematicians. Good job.
First time in my life I understood what’s pi!!!!
Thank you, the visuals help a lot
I learn more from this than my teacher with that 1 hour class
This is actually pretty accurate to one of the earlier methodologies to determine pi.
This is actually an insane visualization of diminishing returns..
Whoever made this, God bless you ☺️
The Best video on pi..
I need an hour long version of this now
視覚的にすごい分かりやすい
外角も見てみたいな
What is really interesting to test out are the angles of the laser divided by the perimeter
pardon?
It's like a graph function!
Круто! Спасибо за визуализацию👍
simple yet best way to explain π
Пи это отношение длины окружности к диаметру.
А видео прикольное
This also represents how reality gets more and more complex the more humans examine it and you can never truly catch up
Go watch a video about the double slit experiment if you really want to see something complex
It is intuitive and easy to understand. 굿!
At some point of my life i was EXACTLY pi years old..
This is beautiful!! 🥹🥹
Jogo when he shows his limitless power while saying "between Heaven and earth, i alone am the honoured one"
A worthy example.🦾
Interesting, like it's making a logarithmic curve, maybe the asymptote is true pi
I never thought I could relate to a number before. But perhaps there's a lot in life that you're really close to but never really get to see it. Goes for people you might love as well.
thanks newton that we don't have to do it that way, it take so much time to converge.
I took calculus a zillion years ago but I still love it when a limit approaches infinity or whatever tf it is
when a series converges
If only I knew this a few years ago so I could draw it on the paper as my answer 😮
You showed me something my teachers couldn't teach me in 12 years
Yeah you're right. This is exactly how they actually searched for pi
"tick, tick, tick, tick..." Will be in my mind forever 😅