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 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?
When I went to school it was explained in a manner that it could be understood, But not more then that, I still have a great question about π and that is, how is Pi calculated, where do all those number behind the comma (or decimal point in US) come from? It can not be that the π with so many decimals can be measured. What is the proper way to calculate and not measure?
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 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 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 😂
Sorry to rain on your parade, but the ancient Egyptians and Babylonians had already established the Radius ( or Diameter) relationship to the Circumferance. Well before any Greek. Archimedes just worked with Knowledge already spread through out the Mediterannean ( Syracuse was in Sicily, mid-Mediterranean, a melting pot of Knowledge from all over the then known World.
Check on computer it goes upto 24 decimals. I was working on a 3.5 meters project and it gave me wrong dimensions so I checked on computer and it showed upto 24 decimals and it worked fine . Check on computers
I barely could watch this. Why do we need to draw shadows and the like, it stretches out a video and makes me nervous. I am not a math person. I think you may have helped a lot of people.
SOORY BUT NO Pi IS NOT 3.14. It is approximately 3.14. Might seem nit picky but when you’re doing calculations involving large values, 3.14 can be the difference between life and death LITERALLY
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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_
This is absolute rubbish. Archimedes calculated the value of pi based on the area of the circle, not its circumference. He drew regular polygons, whose areas he knew how to calculate, inside and outside of a circle. He could then calculate a value for pi between two values. By increasing the number of sides on the polygons, he eventually got a value between 3 1/7 and 3 10/71. The decimal point wasn't invented for hundreds of years after his death.
I admit that I don’t know what really happened but both could be correct. He could have first calculated pi using the wheel and circumference of the circle. He could have later discovered the relationship to the area using the polygon method. They are two different calculations.
@fatroberto3012 I agree...this DOES NOT explain Pi, just explain how Pi is used in calculation and graphically shows relation of diameter and circumference...
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.
Archimedes??? How Eurocentric can you get! That Johnnie-come-lately was preceded by up to 1500 years of Babylonians, Egyptians, Chinese, and Indians of the use, and increasing precision, of Pi.
I very much appreciate the eplanation, but why did you make us suffer through watching you cut cardboard? Did you not have any wet paint to show us drying?
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.
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*
Mr. Rayner: You did a great job on the arts and crafts. It would make for a neat after-school project. But you only guessed the .14 part of pi. Maybe guesstimate is a better word. You took the idea that we already know that pi is 3.14, and you drew a model that showed where the .14 would fall. But never do you say how the exact .14 is calculated. If I were guessing like you did, and I used you "halves" method to go from 3.5 to 3.25, I would have put pi at 3.125.after all, any dullard of a mathematician in Archimedes' day could have told you that pi was between 3.125 and 3.25. Because of this, you have done Archimedes a huge disservice. After all, he did not draw out a wheel and a road and measure it. He used the method of exhaustion to predict the upper and lower limits of pi by finding the areas of polygons inscribed and circumscribed about a circle. He continued dividing these polygons until he had polygons inside and outside the circle with 96 sides. He thus set the limits of pi as 3.140845 < π < 3.1428571. I like fun and games as much as the next guy. But you did say that Archimedes was a genius for his discovery and then took the conversation to the level of a third grader. Not cool.
It's not a proof or a guess - its a visual explanation of why, for those that don't get maths but do get visual representations - as you will see from the comments. Mathematicians wish to find fault - non mathematicians go - "Oh I see! Now I understand!"
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. ;)
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
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.
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.
You wrote "34m" when you meant 34mm. You'll edificate peeps wrongly, and get Spinal Tap sized stone henges (or worse, the other way round and 1000 times too big)! - OK, corrected yourself at 8:25, but be careful!
I always thought it was a big mistake making the formula 2πr They should have either made the formula πd (where d=the diameter) or make the formula πr (where π is twice as big as it's currently accepted value) It's a simple relationship and adding that 2x was an unneccessary complication that was just redundant.
Impressive graphic skill, but you didn't explain discovery at all. Somebody noticed relation between road length and turns? Maybe, but why was he interested in turns? And circumference can be easily measured with rope. Blacksmith/wheel makers may be interested, when making metal rim - but this happen much later. Also barrel makers. Maybe jewelery/ring makers.
??? This is not enough ,and its not the easiest way. Easiest way,measure the circumference of wheels with a measuring tape..or string.. to know the formula,measure many wheels of different size, and find circumference/diameter is always 3.1459....
An easy way to calculate the first six digits of pi: 1. Take the first three odd numbers: 135. 2. Double each digit: 113355. 3. Divide the last three digits by the first three digits to five decimal places: 355/113. Answer: 3.14159 If anyone knows of numbers that will produce more correct significant decimal places, I’d love to know them.
PI = (approx) 22/7 because if you take the area of any circle and divide it by the square of the radius of that circle, the result is (approx) 22/7 which was defined as pi. Some will take the circumference and divide it by the diameter. And it makes no difference if it's Apple, Lemon, or Chocolate, you get the same pi either way..
I'm afraid I am fed up with the eurocentric misinformation in every walk of life... His might be the first surviving explanation of pi but I'm pretty certain the plenty of civilisations were aware of pi and many other mathematical constants and equations. It'sike the crap we're taught in school about Columbus discovering America despite never actually landing there. What about the civilisations that pre-existed there for thousands of years..
A long time ago I took a roll of duct tape and measured the circumference of it, which was 12 inches. Then I measured the diameter, which was three and thirteen sixteenths (3.8125). Then I divided the circumference by the diameter and got 3.1475. Close enough?
Nobody ever told you that pi was the ratio of a circle's circumference to its diameter?? I find that hard to believe! Actually I remember in grade 8 our teacher had us get into groups of 2 or 3 and cut out circles of diff dia's and measure the circumferences and find the C/R ratio...similar to the video. But even lacking that, yes your teacher at some point said Pi is a ratio,,,c'mon! :)
He could have improved his accuracy by bringing the circle around 10 times. Now, I want to know if this is the way he did it or if this is a guess. The other point is that it would have been known long before he came along, the ancient Babylonians, Egyptians, and Jews knew of Pi earlier.
Now explain why e raised to the power i x pi = -1 This simple explanation is a bit too simple (but works for practical purposes, I guess)). Pi is a converging series with infinite terms and very complicated. i btw is the square root of -1 (what we electronics engineers call j)
The explanation of the value of Pi is OK, but that title on the book... mmmm. There is no historical evidence that Archimedes created the supposed mirror tu burn the Roman warships, and so, kids that read this book would be fixing inaccurate ideas
Good explanation but... the symbol m is for meter! Milimeter is mm! The first m represents mili and the second m represents meter. That's why Km is kilometer, mg is miligram and Kg is kilogram (usually only called kilo).
Archimedes was the bomb. A super genius inventor during an age of great thinkers. If one of the Greek city-states went to war with another, but then they found out Archimedes happened to be in the city, they would retreat. Because they didn't want to screw around with whatever insane invention Archimedes came up with this week.
It's easier to use the diameter. 2 * pi * r is the same as pi * d because 2r=d. Easier to measure diameter on a cardboard model too 😄 I think this formula is also mis-taught in schools by describing it as "2 pi r" instead of "2 r pi" or "pi 2 r" which would help learners to understand that it's really the relationship between the diameter and the circumference. The 2 is just in there so you can use the radius instead because in school we're always taught to work with radii. Maybe young children should be taught this as "to our pie" 😂
To really help understanding it can be pointed out that the 2 in the formula is just to double the radius and make a diameter. It’s not obvious. I’m a teacher and didn’t realise it till adult hood. Wished it had been explained. Start with C= Pi x D
The video and subtext already starts with a falsehood: no, pi is ___NOT___ equal to 3.14. Next falsehood already in the next sentence: Most teachers _do_ explain why pi is _approximately_ 3.14 (the explanation os included in all school books I know!). And what you show in the video was _not_ what Archimedes actually did do!!!
@@shooraynerdrawingOne only needs to know the barest minimum of the history of mathematics in order to know what Archimedes actually did do. Apparently you did not bother to do even a minimum of research.
This video is designed to explain pi to all those people who went through school being taught that pi is an arbitrary number to be learned by rote, while never being given any visual or real-world sense of what on earth it was all about. You, I presume are a mathematically-minded person, or you would not be commenting as you do. As such, pi probably made instinctive sense to you in terms of geometrical relationships. For the rest of us, it was a mystery we were supposed to understand through some mystical form of osmosis. Mathematicians make terrible teachers for non-mathematicians because they assume everyone else sees the world in the same, clear, digital way that they do. Oh! And you have no way of knowing that Archimedes didn't work the basics out with a wheel, like this, and then apply a bit of Euclid to it... unless you were there?
@@shooraynerdrawingActually, I'm a math _teacher_, and most of my students like my teaching (according to anonymous surveys I often do with them). And no, pi did _not_ make sense to me on my own - I simply had a usual teacher who explained it to me. It's a complete mystery to me why you think that most teachers do _not_ explain the concepts contained in your video; as I wrote already in my first comment, that stuff is in every schoolbook I know about. Perhaps _you_ had a bad teacher who did not explain it (or explained it badly) and for some strange reason you think now that _all_ maths teachers are bad?! "And you have no way of knowing that Archimedes didn't work the basics out with a wheel, like this, and then apply a bit of Euclid to it" Oh, now you are shifting the burden of proof? This becomes more and more ridiculous. _You_ made claims for which you gave no evidence at all!
Measuring the circumference wasn't the important point. The point is that the ratio of radius to circumference is always pi and is not related to the size of the radius.
I think what if the story is, someone try to use a wheel with diameter is 1 2 3 4 6 and then measure the circumference. all of those ended up not a whole number. then they stop, take a break and eat some pie. After that they try again with diameter is 7 and this time the circumference is 22 and it's a whole number. So, I call it a pi. Yes I made this up.
To complete your nice prove, and given that your audience are elementary school students, you should repeat the example with another circle of different radius so that students understand that π is independent of the circle you select
But who was the first person to discover that this circumference/diameter ratio is a ratio with infinite value? Where was this discovered and how exactly was this "measurement" found? Can anyone help me find this information?
and then they found better ways to approximate and even a formula for the exact value. in fact, there's more than one method to get the exact value but the best is to press the π button.
-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!
But WHAT is π ??? We know the area of a circle Ac = π . r² So if the radius of your circle is 1 (inch, meter, mile) then the area of the circle Ac = π . 1² = π (inch², meter², mile²). So now we know π is the area of a circle with radius = 1 For example: a circle with radius = 1 meter then the area of the circle will be Ac = π m² ~ 3.14 m²
The only math quibble I have with this is that pi is "about" 3.14. Pi has a defined value that we can't write out with perfect precision other than just "pi". But for ink and cardboard 3.14 is a close enough. approximation for sure. Really, other than that, this is a very good presentation!
