This is is the best explanation of pi I've seen so far, that too the explanation was by one of the best artists. And the drawings were simple yet elegant, I'm impressed and you have caught my attention
@@СофияИванова-х6й If the circle was smaller then both its diameter and circumference were smaller, and they would be smaller by the same factor. So for a circle of any size its circumference will always be 3.14 times its diameter.
I figured this out in 4th grade by experimenting with various coins as my “wheel”. We hadn’t learned fractions yet so all I could say was “the distance around a circle is a little bit more than three times the diameter.” Well actually I didn’t know the word diameter yet so it was “A little bit more than three times across the circle.”
Same time here 😂 maybe 3rd, same way as in the video half, half, half!? 15 is Pretty (and known), so 3,15 😂 Pretty disappointed that 2x15=30 and 3x30=90 damn!😂 3,25 !? Ugly .. third x quarter..dang 😂
I always learned: "Circumference = π • diameter" I always thought everyone understood pi as being the ratio between the circumference and diameter of a circle, but this video brought back a memory. When I first saw someone write C=2πr, I was so confused why they used a more complicated and abstract formula. C=πd is so much simpler and tells you explicitly what you showed in this video. It makes sense if you learned C=2πr, you wouldn't get the same intuitive understanding of what pi is. By the way, I would recommend you measure the diameter instead of the radius, because measuring the diameter gets you a smaller relative error of the measurement.
Think of it this way: if I asked you to sketch the circumference of a circle, π would get you only halfway there. You need 2π radians for a complete circle. Now that you have your 2π radians, what's the circumference? Well, that's easy, 2πr. Sure, 2πr and dπ will get you the same circumference, but that's an answer to a single question. The deeper you go into math and physics, the more important the radius becomes. But besides all of that, what would be a more intuitive way of finding the circumference, going all the way around the circle and multiplying by the radius, or stopping halfway and multiplying by the diameter?
We did this in school. We were told to make cardboard discs and to use a piece of string to measure the circumference. Then measure the diameter and divide the first number by the second. No matter what the size of the disc was, the result was always close to 3.1.
This is a really nice explanation of what Pi is / where it comes from. It is NOT a demonstration of how Archimedes determined a more precise value than "a little more than 3". Pi is only approximately 3.14, and Archimedes didn't have access to numbers written in decimal form anyway - they hadn't been invented yet. He was able to work out (using a very brilliant geometric method) that the number of diameters it takes to equal the circumference has to be between 3 10/70 and 3 10/71. That was enough precision for him, and it gives us 3 1/7 (22/7) which is about 3.148. Would love to see you make a video showing that method!
Thanks - It's really for the visually minded and mathematically challenged. For some people the maths only makes sense when there is a practical demonstration behind it. 😃
Yes, I read that he used hexagons inside and outside a circle and doubled them until he got to 96 sides. Then he found out the perimeter that way into the fractions you described.
@@shooraynerdrawing I enjoyed your explanation. I always thought of pi as "just a number," but now I "see" that it's 3.141592... DIAMETERS of a circle!
Nice video. If you do this again, right around the six minute mark of the video, when you were getting three and a half and a then three and a quarter, measure the line with your ruler... to that mark... and divide that by the diameter of your circle. Use that as your decimal. You wrote down 3.14 out of nowhere because that was what we were told pi was in school. The straight line distance divided by the diameter of your wheel is the way to go, if you don't know about 3.14 ahead of time.
22/7 (3.1428) was Archimedes upper boundary for PI not PI itself. Archimedes said PI lies between 3.1408 and 3.1428 which is approximately 3.141. Of course he stated it in fractions not decimals. 223/71 < π < 22/7 or 3.1408 < π < 3.1428 So pi must be ~ 3.141_
@markphillips3341 Years ago, a dear friend, who had been to different schools than I had, insisted it was exactly 22/7. We looked at what the calculator showed when we hit the pi key versus 22 divided by 7. It's different at the 1000ths place: 22/7 is 3.142857 (right-of-decimal digits repeat) rather than 3.14159265... So 22/7 is slightly too large. I'm not sure my friend was convinced; irrational numbers can be a hard concept to wrap one's head around.
Archimedes didn't do any of this. This was known *long* before him. Whoever first noticed that the ratio of the circumference of a circle to its diameter was the same no matter how big the circle is lost to pre-history. Understanding why this was so came from the Greeks, but also well before Archimedes - though they didn't have a rigorous concept of arclength, so couldn't fully prove it (that only came in the Renaissance). What Archimedes did was show that the *area* of circle is half the product of its circumference and radius (thus deriving the pi r squared formula). He used an approach of refining approximations that must later would develop into calculus. He then also used similar methods to find formulas for the surface area and volume of a sphere, which was his proudest accomplishment.
The 3.14 constant comes from: whenever you divide the circumference of any circle to its diagonal from the center; no matter how big or small the circle is you always get 3.14
The story is a bit more complicated. The Egyptians and the Babylonians understood this ratio too. But it was Archimedes that determined the ratio more precisely. Archimedes did not name it however. According to Petr Beckmann's A History of Pi, the Greek letter π was first used for this purpose by William Jones in 1706, probably as an abbreviation of periphery.
Indeed, associating Pi with mathematics results in a form of Code ... it is not the True symbol for what it claims to represent. For some unknown reason, the true symbol has been lost to modern thought... but it is something that can be 'rediscovered' if someone is so inclined)
I am 63 years old from Bangalore,India. And I am an Engineer. Till now I thought pi was just a ratio. This is the first time , I saw this kind of explanation. If my primary school teacher had taught me something like this , I am sure I would have been a better student and an Engineer. Thanks and God bless you 🙏🙏🙏
Also "5 eh? So let's call it 2 squared, for really large values of 2. That's close enough for what we're doing". I heard that one pretty much verbatim from a couple crusty old engineers. ;)
Archimedes is said to have built odometers for the Roman's. He based it upon the method shown here but he was a little cleverer. He marked of points on a road ar 'diameter intervals into the distance. He started of as You but only stopped when the wheel arrow was on a 'diameter point'. His first fix gave him 7 whole turns for 22 diameters thus giving Pi a ration of 22/7. He foud a better one on a longer road where he got a better fix of 113 whole turns in 355 diameters giving Pi a more accurate ratio of 355/113 .... this is the value he probably used in his odometer designs. Some consider is possible that He designed The AntiKythera Mechanism.
Truly you are one of the best teachers i have ever come across. Very useful video sir. I would like to have this book in India . Pls tell me how may can I purchase it from you ??
Archimedes calculated π by drawing a regular hexagon inside and outside a circle, then successively doubling the number of sides until he reached a 96-sided regular polygon.
Archimedes didn't have sophisticated tools, all he had was an old wooden cartwheel. Luckily, we have sophisticated tools like, *Kellog's Crunchy Nut Cornflakes*
-Take the first three odd integers: 1,3,5 -Double them thusly: 113355 -Divide the last three by the first three thusly: 355/113 There ya go, Pi accurate to 6 decimal places!
I am an engineer so of course I've used pi in my calculations, but this explanation is fascinating! And the fact that pi is also an irrational number impresses me even more! Then there's the calculation of e, imaginary numbers, . . . (sigh).
I have seen that animation many times on Wikipedia, but I never thought, it was the origin (not to mention, that Archimedes wasn't the only, but the most accurate Mathematician)
I finally understood what pi is .. incredible and it is soo simple! like all genius things it is simple. Do you think that anyone would explain in this way in elementary? Everyone would have understood.
Nice video. If you do this again, right around the six minute mark of the video, when you were getting three and a half and a then three and a quarter, measure the line with your ruler... to that mark... and divide that by the diameter of your circle after you measure your wheel. Once you have that answer to the division problem, use that as your decimal. You wrote down 3.14 out of nowhere because that was what we were told pi was in school. The straight line distance divided by the diameter of your wheel is the way to go, if you don't know about 3.14 ahead of time.
A common memory aid is 22/7, which gives 3.1428 - Not accurate past the three digit approximation. However, 355/113 = 3.1415929, which has 7 digits right, and is also an easy-to-remember sequence.
This is is the best explanation of pi I've seen so far, that too the explanation was by one of the best artists. And the drawings were simple yet elegant, I'm impressed and you have caught my attention
Ditto!
Hello ! Please tell me if the circle was smaller and stopped to say 2 and something ? What happen ?
@@СофияИванова-х6й If the circle was smaller then both its diameter and circumference were smaller, and they would be smaller by the same factor. So for a circle of any size its circumference will always be 3.14 times its diameter.
You have to be seriously innumerate for this to be amazing.
Pi x D = C was simple enough...
I figured this out in 4th grade by experimenting with various coins as my “wheel”. We hadn’t learned fractions yet so all I could say was “the distance around a circle is a little bit more than three times the diameter.”
Well actually I didn’t know the word diameter yet so it was “A little bit more than three times across the circle.”
Eureka! 😆
ua-cam.com/video/hfIhPaNKxN8/v-deo.html
Same time here 😂 maybe 3rd, same way as in the video half, half, half!? 15 is Pretty (and known), so 3,15 😂 Pretty disappointed that 2x15=30 and 3x30=90 damn!😂 3,25 !? Ugly .. third x quarter..dang 😂
Yeah? Well, I "discovered" the Mobius strip at 10 years old. So there! 😊
Really? Fourth grade and you hadn't had fractions? Wow! As for your comment, good for you!
This is the most logical explanation of pi
This is put together very well! You always sound so happy while talking about all this which makes it feel very welcoming
Glad you think so! 😃
For a GENIUS, deriving the the value of PI was A PIECE OF CAKE…
That really is truly astonishing... I had no idea Pritt Stick was even around in Archimedes time...
Yeah! it's been going forever! 😂
I always learned: "Circumference = π • diameter"
I always thought everyone understood pi as being the ratio between the circumference and diameter of a circle, but this video brought back a memory.
When I first saw someone write C=2πr, I was so confused why they used a more complicated and abstract formula. C=πd is so much simpler and tells you explicitly what you showed in this video.
It makes sense if you learned C=2πr, you wouldn't get the same intuitive understanding of what pi is. By the way, I would recommend you measure the diameter instead of the radius, because measuring the diameter gets you a smaller relative error of the measurement.
maybe as it is helpful with the area of a circle being π r2
I had the exact same comment just said a different way before I saw yours 😂
Think of it this way: if I asked you to sketch the circumference of a circle, π would get you only halfway there. You need 2π radians for a complete circle. Now that you have your 2π radians, what's the circumference? Well, that's easy, 2πr. Sure, 2πr and dπ will get you the same circumference, but that's an answer to a single question. The deeper you go into math and physics, the more important the radius becomes. But besides all of that, what would be a more intuitive way of finding the circumference, going all the way around the circle and multiplying by the radius, or stopping halfway and multiplying by the diameter?
because if you use a compass to draw the circle it's easy to use the same compass to accurately measure the radius. ask a carpenter.
@@captain34ca So, are you suggesting that 1st graders should be issued a sharp pointy tool?
We did this in school. We were told to make cardboard discs and to use a piece of string to measure the circumference. Then measure the diameter and divide the first number by the second. No matter what the size of the disc was, the result was always close to 3.1.
This is a really nice explanation of what Pi is / where it comes from. It is NOT a demonstration of how Archimedes determined a more precise value than "a little more than 3". Pi is only approximately 3.14, and Archimedes didn't have access to numbers written in decimal form anyway - they hadn't been invented yet. He was able to work out (using a very brilliant geometric method) that the number of diameters it takes to equal the circumference has to be between 3 10/70 and 3 10/71. That was enough precision for him, and it gives us 3 1/7 (22/7) which is about 3.148. Would love to see you make a video showing that method!
Thanks - It's really for the visually minded and mathematically challenged. For some people the maths only makes sense when there is a practical demonstration behind it. 😃
Yes, I read that he used hexagons inside and outside a circle and doubled them until he got to 96 sides. Then he found out the perimeter that way into the fractions you described.
@@shooraynerdrawing I enjoyed your explanation. I always thought of pi as "just a number," but now I "see" that it's 3.141592... DIAMETERS of a circle!
Nice video. If you do this again, right around the six minute mark of the video, when you were getting three and a half and a then three and a quarter, measure the line with your ruler... to that mark... and divide that by the diameter of your circle. Use that as your decimal. You wrote down 3.14 out of nowhere because that was what we were told pi was in school. The straight line distance divided by the diameter of your wheel is the way to go, if you don't know about 3.14 ahead of time.
22/7 (3.1428) was Archimedes upper boundary for PI not PI itself. Archimedes said PI lies between 3.1408 and 3.1428 which is approximately 3.141. Of course he stated it in fractions not decimals. 223/71 < π < 22/7 or 3.1408 < π < 3.1428 So pi must be ~ 3.141_
I thought it was a complex question and in fact I found a beautifully simple answer in this video. Thank you. Consequently I've now subscribed.
Most math is beautifully simple. This is why I love it.
I have never seen Pi explained like this, like ever. Even though I knew what PI was, this was a really clever explanation.
veritasium have some videos about old geometry men, these guys was insane.
Great explanation and demonstration! I could wish you had pointed out that pi is *approximately* 3.14. It isn't 3.14.
Not really. It is C/D. It is not any numeral. If someone insists it is, ask them what that number is. Either fraction or decimal.
I was taught that pi was a fraction being 22/7.
@markphillips3341 Years ago, a dear friend, who had been to different schools than I had, insisted it was exactly 22/7. We looked at what the calculator showed when we hit the pi key versus 22 divided by 7. It's different at the 1000ths place: 22/7 is 3.142857 (right-of-decimal digits repeat) rather than 3.14159265... So 22/7 is slightly too large. I'm not sure my friend was convinced; irrational numbers can be a hard concept to wrap one's head around.
I thought this also.
@@johncraig2623 - Right. Someone who does not know that pi is irrational should not be writing about it.
Archimedes didn't do any of this. This was known *long* before him. Whoever first noticed that the ratio of the circumference of a circle to its diameter was the same no matter how big the circle is lost to pre-history. Understanding why this was so came from the Greeks, but also well before Archimedes - though they didn't have a rigorous concept of arclength, so couldn't fully prove it (that only came in the Renaissance). What Archimedes did was show that the *area* of circle is half the product of its circumference and radius (thus deriving the pi r squared formula). He used an approach of refining approximations that must later would develop into calculus. He then also used similar methods to find formulas for the surface area and volume of a sphere, which was his proudest accomplishment.
I think he introduced the "exhausting method", an immature way of integration
Probably was discovered by those who made cart wheels. It could have been used to figure out how long of boards they needed.
he know but as a scientist he need to test it out for himself by tgis cardwhiel experience
Does it feel odd to anyone that our final paper math answer for the area has no end when we can see that there is clearly and end to its area..?
@@jonnelson9760 what would that have to do with the circumference? I don't think they cared how far a cart would move in one rotation of the wheel
Super fun to watch. Everybody should be explaining math this way
Gotta respect Archimedes working that out. But you know what, I gotta respect at least as much the people who made nice round wheels out of boards.
I sure would like to try that cereal.
Roll a wheel on something harder than it is for long enough and it will become round. ☸
@@mal2ksc unless it resonates
I can't believe I have not seen this until now. I will definitely do this with my 4th and 5th grade students. Thank you so much.
Although this knowledge was out there, I learned something new at 65 and this is a new learning. wish the teachers - back then, used this theory
The 3.14 constant comes from: whenever you divide the circumference of any circle to its diagonal from the center; no matter how big or small the circle is you always get 3.14
This is the best explanation, and I refuse to learn anything else any other way
Good for you! 😄
It was discovered when e escaped from a pie，and later they found e too.
naturally
I discovered pie when I moved to the USA from India. We didn't have pie in India growing up. Key Lime is my favorite!
I wish there were more teachers like this guy!
Chuck Norris needed a pick up truck, so he invented pi.
I'm dopey and don't get it. 😢
Superb explanation !!!!!! Thats how the math needs be taught !!!!!!❤❤❤❤❤
Glad you think so!
OK. You caught the "mm" ! Very good and it was fun watching. Thanks
This is a very nice explanation. But you seemed to guess where the center of the wheel was when you had a compass available!
The story is a bit more complicated. The Egyptians and the Babylonians understood this ratio too. But it was Archimedes that determined the ratio more precisely. Archimedes did not name it however. According to Petr Beckmann's A History of Pi, the Greek letter π was first used for this purpose by William Jones in 1706, probably as an abbreviation of periphery.
Indeed, associating Pi with mathematics results in a form of Code ... it is not the True symbol for what it claims to represent. For some unknown reason, the true symbol has been lost to modern thought... but it is something that can be 'rediscovered' if someone is so inclined)
Archimedes did not have decimals. He used fractions.
@@Donizen1 He also didn't have a video camera.
I went to school only a little while after Archimedes and we learned about rolling the disk along a line.
Very helpful! That looks like an interesting book!
It is!😆
The budget on this production is astronomically incalculable.
So, by using this formula (l=dxπ), you can calculate the lenght the wheel will cross when you roll it one full circle based on its diametar.
I am 63 years old from Bangalore,India. And I am an Engineer. Till now I thought pi was just a ratio. This is the first time , I saw this kind of explanation.
If my primary school teacher had taught me something like this , I am sure I would have been a better student and an Engineer.
Thanks and God bless you 🙏🙏🙏
That is a very simple explanation which anybody can understand. I like the simple drawing of the wheel too.
🙂👍
This is an awesome illustration of Pi. Thanks!!!!!!
How did that wheel instantly turned into 3D with the addition on Grey sketch 😨😨
Very great explanation sir
Good question!
engineers: pi=3. Take it or leave it
Also "5 eh? So let's call it 2 squared, for really large values of 2. That's close enough for what we're doing". I heard that one pretty much verbatim from a couple crusty old engineers. ;)
Amazing explanation of pi. I've never thought that's how someone would discover it. 👍
The metric system was not around during the time of Archimedes.
What measuring units did he actually use?
What I came for: The history of pi
Why I stay: A quick art attack craft
Archimedes is said to have built odometers for the Roman's. He based it upon the method shown here but he was a little cleverer. He marked of points on a road ar 'diameter intervals into the distance. He started of as You but only stopped when the wheel arrow was on a 'diameter point'. His first fix gave him 7 whole turns for 22 diameters thus giving Pi a ration of 22/7. He foud a better one on a longer road where he got a better fix of 113 whole turns in 355 diameters giving Pi a more accurate ratio of 355/113 .... this is the value he probably used in his odometer designs. Some consider is possible that He designed The AntiKythera Mechanism.
I love these. More please :)
Brilliant explaination
Great explanation! And good cartooning, too! :)
Amazing, this opened my brain, thanks!
Excellent teaching sir...I bet you are a great teacher.
Interesting that you decided to create a road, and then reinvent the wheel. : )
Truly you are one of the best teachers i have ever come across.
Very useful video sir.
I would like to have this book in India .
Pls tell me how may can I purchase it from you ??
Thank you! It should be avaioable ithrough book stores :)
I cannot tell a lie,
Cherry is still my favorite pi.
I have completed my high school. I wish I would have known this when I was in my school and I would rock it before my friends and teachers.
lol
Got it ! Thanks to you ( and Archimedes ). I never knew & now I do.
The explanation and demonstration was outstanding sir.
Thank you so much!
This is the most brilliant explanation of Pi I have ever come across. Well done, good sir! subscribed.
Hello ! Please tell me if the circle was smaller and stopped to say 2 and something ? What happen ?
Great job!
Thanks!
And, except that Archimedes found pi's value was somewhere between 3 1/7 and 3 10/71. He didn't have numerical decimalization available at the time.
Decimals are attributed to Egypt 6 years before his death so he might have been aware of them for 'private' use rather in explanations for the masses.
Fascinating!
Leuk uitgelegd.....aanrader voor scholieren
EXECELLENT! THANK YOU!
This is the first time I ever heard a lesson regarding circumference and diameter of circles
This will help me a LOT in my school project thank you sooooo much mind sir
Most welcome 😊
I just subscribed because of this explanation.
For sure. If my teacher taught me that way, it would be easy to understand.
I swear if someone told me this I would have done pure Maths instead maths literacy in school 😂
Eureka!!!!.... Today everything comes together in my mind!!
Archimedes calculated π by drawing a regular hexagon inside and outside a circle, then successively doubling the number of sides until he reached a 96-sided regular polygon.
A gifted artist you are!
Archimedes didn't have sophisticated tools, all he had was an old wooden cartwheel.
Luckily, we have sophisticated tools like,
*Kellog's Crunchy Nut Cornflakes*
you got it!
The use of the home avalible parts really caught my attention
Awesome!
Thanks!
Thanks this video is very useful
Glad it was helpful!
awesome explanation
Glad you liked it
Very smart, thank you!
perfect.....thank you
Fantastic explanation!!!
Wow great video thanks
Thank you too
Beautiful!!
Thank you! 😊
-Take the first three odd integers: 1,3,5
-Double them thusly: 113355
-Divide the last three by the first three thusly: 355/113
There ya go, Pi accurate to 6 decimal places!
Oh thank you for this information
Doesn’t help nonmathematicians who are visual thinkers! 😃
thanks very for this easy concept.
Glad you liked it!
I think if you explained this to school kids they would enjoy mathematics more. Such a great demonstration
That's why I made the video. Mathematicians wouldn't think to explain this for visual thjinkers!
Hello ! Please tell me if the circle was smaller and stopped to say 2 and something ? What happen ?
I am an engineer so of course I've used pi in my calculations, but this explanation is fascinating! And the fact that pi is also an irrational number impresses me even more! Then there's the calculation of e, imaginary numbers, . . . (sigh).
Im getting really intrigued by the Heisenberg cut at the moment - that’s even more weird than the imaginary numbers LOL
@@shooraynerdrawing So now I'll have to research *that*! 🙂
let's all agree if I had watched this my exam would have been simpler and more fun to memorize.
Wow, great video!
Thanks!
Delightful video
Glad you enjoyed it
I have seen that animation many times on Wikipedia,
but I never thought, it was the origin (not to mention, that Archimedes wasn't the only, but the most accurate Mathematician)
If your maths teacher "haven't told you", then they've done an abysmal job.
Awesome
This is a great illustration to explain pi. I had to school a naysayer, but I did it respectfully per your comment guidelines!
damn the part where he explained how pi came to be blew my mind
( ꈍᴗꈍ)
Makise Kurisu sugoi.
In time, go back
I finally understood what pi is .. incredible and it is soo simple! like all genius things it is simple.
Do you think that anyone would explain in this way in elementary?
Everyone would have understood.
Math teachers think in numbers and don’t understand that others think in images. They don’t get it so carry on the old way
I went to a top 100 high school and I took AP calculus as a junior and I am now 39 and you just explained to me how pie came about
lol you were taught by mathematicians not artists 🤣
Its PI π not pie🥧
@@billshiff2060 cool story bro tell it again
@@thecommonsenseconservative5576 Its a fact not a "story". Something tells me your "top 100" high school had those short busses lol.
@@billshiff2060 your "something" was on those short busses that drove by my high school you dumb pedantic
Very helpful
Love your videos!
Lovely !
Nice video. If you do this again, right around the six minute mark of the video, when you were getting three and a half and a then three and a quarter, measure the line with your ruler... to that mark... and divide that by the diameter of your circle after you measure your wheel. Once you have that answer to the division problem, use that as your decimal. You wrote down 3.14 out of nowhere because that was what we were told pi was in school. The straight line distance divided by the diameter of your wheel is the way to go, if you don't know about 3.14 ahead of time.
A common memory aid is 22/7, which gives 3.1428 - Not accurate past the three digit approximation. However, 355/113 = 3.1415929, which has 7 digits right, and is also an easy-to-remember sequence.
I thought everyone knew that pi was the ratio of diameter to circumferences. You must have skipped the day they introduced pi in school.
I agree. It was explained so many times I have difficulties to believe someone never heard it.
At least, his explanations are very good.
No one ever told me either. Thanks, it's high time teachers knew their job.
I can't believe no one told you this. That's ridiculous. Also good art
6:28 "No one ever told me that, no one. If they did I wouldve understood"
And then there’s my teacher who gave me homework to search how pi how was created?Yaaaaaaaaaaa
THANK YOU!!!!
You're welcome!
I mean THIS IS THE BEST EXPLANATION Thanks man