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.
@@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.
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.
@@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
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.
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
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.
@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 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.
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 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?
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
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.
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.
@ the more accurate you try to measure a coastline, the longer it gets. And because of the complex shape of coastlines and the ever changing tides, everyones coastline is theoretically infinite. This is called the Coastline Paradox.
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
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.
Good visualization but the permeter the ngon can be represented pretty easily using trig. N is the amout of sides and the perimiter is 2n*sin(180/n), assuming the radius is one half which is whats shown in the video
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 RUclips 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
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
Amazing visualization
Still it's hard to understand 😂😂😂
No lmfao?@@Educatedindian123
just a random comment
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
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
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 IS 1/2.
Math before you comment
@@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.
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
8 years of math classes summed up in one RUclips short
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
Длина окружности равна диаметр окружности умноженный на π. L = ∅ × π
This is one reason why i love math.
This is actually beautiful for so many reasons. This is the old way. Geometric proofs.
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
This also is a good explanation of the concept of calculus actually… nice video
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!!!
Amazing, very well done... great perception
I 100% thought this was a mobile game ad for a second at the beginning
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.
Really beautiful. I never saw this way of evaluating pi.
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
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 😊
A great and direct way of showing approxiamation too.
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
At some point of my life i was EXACTLY pi years old..
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
Some random person will strap an image of Albert Einstein and add flashing light
I have never seen such a brilliance animation for math
this is the most satisfying way of math ive ever seen
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
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
This is the most understandable video about the number pi
😢 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?
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
I like this and the Spirograph of pi being unreasonable
This is the coolest thing I've seen in awhile
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...
This is so satisfying to watch 👍
Others...discovery of 3.14
Me......designs of arc reactor😅😅
Same😂
I wonder who created this animation. Truly a masterpiece
Amazing sound
Ngl, it’s kind of ingenious. Consider me impressed 👏👏👏
Wow 👌🙏
I'm stupid
The radius is visibly 1/2
Yeah it showed that the diameter is 1 at the start
Wow, simply beautiful presentation. Kinda mind-blowing when you consider that centuries of thinking inspired this video
its cool how it exponentially goes closer and closer to pi..
It hits an infinite amount of points on the circle, which is why we will never have a true number for pi.
"tick, tick, tick, tick..." Will be in my mind forever 😅
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.
My dad was an engineer. He explained this.. but seeing it visualized, it is amazing!
This is amazing. I never thought about it this way,
I need a longer version of this
An actual educational yt short. Wow. That's really rare
What is really interesting to test out are the angles of the laser divided by the perimeter
pardon?
I actually just learned something new
I wish they would have showed more stuff like this in school
This visualisation is effectively a summary of centuries of mathematical development. Amazing!
And this is why everyones coastline is theoretically infinite
what does this have to do with that?
@ the more accurate you try to measure a coastline, the longer it gets. And because of the complex shape of coastlines and the ever changing tides, everyones coastline is theoretically infinite.
This is called the Coastline Paradox.
@@duncanmcgee13 its not theoretically infinite it's undefinable.
Круто! Спасибо за визуализацию👍
This is actually an insane visualization of diminishing returns..
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
This is the best visualization I have ever seen, of finding PI!
Eureka! There is no limit!
Pi is like that one cousin who is everywhere and when you wanna talk to him or smt then they aren’t there, or like a DLC for Math…
Пи это отношение длины окружности к диаметру.
А видео прикольное
Oh now I get it, i thought they just chose a random number
This actually it's pretty interesting and thought provoking
It was slowly building the titanic 😂
They explained in a way even my school maths teachers couldn't explain this clearly 👍🏻
The universe and its perfect fractal nature represented here. Just like in the Vitruvian man. This says so much more than it seems
Thank you, the visuals help a lot
Thanks that helped understand a lot of things
It's like a graph function!
My reaction while watching the video:- 🤨🧐🤔☹️?
I learn more from this than my teacher with that 1 hour class
They should put this in schools
This is how the PS2 was created. Great visualisation by the way
Jogo when he shows his limitless power while saying "between Heaven and earth, i alone am the honoured one"
First time in my life I understood what’s pi!!!!
I had no idea what pi actually meant and everything google explained was just useless... this visual presentation really cleared up all my questions!
❤Gods creation
Whoever made this, God bless you ☺️
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.
Good visualization but the permeter the ngon can be represented pretty easily using trig. N is the amout of sides and the perimiter is 2n*sin(180/n), assuming the radius is one half which is whats shown in the video
Nice gun shorts, brilliance.
It is intuitive and easy to understand. 굿!
This is actually pretty accurate to one of the earlier methodologies to determine pi.
Wow that's actually really cool now that is been visuslized
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
If I was taught like this since elementary school, I think I'll be the next Einstein
That first bit was just straight up Iron Man.
gonna pretend that i understood all of that
thanks newton that we don't have to do it that way, it take so much time to converge.
A worthy example.🦾
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
Nice representation, though the only thing I learned was an equilateral hexagon equals 3
Great men you explain the concept of π very easily
reminds me of the bookstacking problem or something like that