The Best Explanation of Pi
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- Опубликовано: 20 сен 2024
- mathematicsonl...
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A simple way to understand pi. The number π is a mathematical constant, approximately equal to 3.14159. It is defined in Euclidean geometry[a] as the ratio of a circle's circumference to its diameter, and also has various equivalent definitions.
Finally! Someone explaining this in 60 seconds, without some self-indulgent rant that lasts for 30 minutes and only confuses the viewer. Thank you!
They realized that all circles are similar in shape and thus the circumference must grow in proportion to the diameter. In other words, the circumference to diameter ratio is a constant. So after some careful measurements, they found pi to a reasonable accuracy.
រឯថង
@@SaDa-jk7xq I like your funny words magic man
Thank you.
Inaccurate is reasonable? And we wonder why we don't have a complete model of the universe.
We can't even figure out circles but I guess everyone seems satisfied with being a little off. What does it matter if we are 10^-100 off?.... right?
Or perhaps using the relationship between a straight line and a curved line is like comparing apples to oranges.
There has to be a better way. A circle is completely enclosed. It's finite but pi is not.
Our language of mathematics is fundamentally flawed. We need a new language that goes beyond calculus. One that is more truly accurate. And doesn't have ANY error.
@@duckyoutube6318or maybe we just cant understand irrational numbers fully?
I truly underestimated a 1 minute video wow. This just made my understanding of mathematics so much clearer. Thank you
holy shiet 1 minute video worth more than 12 years of school 😭🙏
This video is amazing. I used it to teach a class and they better understood the lesson after I showed this video. Thanks
maybe they didn't understand you because of your english
English is not seince
Math sucks pick a better subject to teach!
@@domgena uh no actually math is the only important subject that exists in every country so duh 🤦♂️
@@NovaStrike118 there's nothing wrong with the sentence...
I was today years old when I finally understood what pi represents. Thanks!
The crust is flakey, warm fruit or savory meat filling, and cherry is the best.... with creama.
Best explaination of pie.
Great explanation.
Another way to demonstrate this is to take a CD/DVD/ or any circular disc, cut a piece of string/wire (preferably a kind of string that cannot be stretched too much), that can be wrapped around the circumference of the disc with exact length, and cut another piece of string/wire that is equal to the diameter of the disc.
Assume that the disc's diameter is equal to 1, and compare the lengths of the 2 strings. The circumference string should be PI times longer than that of the diameter string.
that is stupid
Thank you Ima try that to get more clarity
WAAAAAY easier to undurstand and WAAAAAY shorter than the Wikipedia explanation. Great job!
In my career of pipe welding/fitting...I put to memory...Pi X Diameter = Circumference. Use this for making laterals. Like a 12" on a 12"branch. I like the "long" method. Making a template out of .025" paper board. (like the paperboard cereal boxes are made from). I make the branch...Using Pi X Diameter to get the "stretch out" of the pipe (for the branch). There are several steps after this. Don't feel like writing them all out. Tape up the stretched out part so it is round, then mark the hole where the branch will go. Cut out the hole for the branch, grind it, then tack up the branch in place.
Last, weld it out so there are no leaks.
You explained what pi is but what I'm curious is how it is calculated. If I didn't know what pi was and I had a circle with a known diameter, how would I figure out the ratio between that and the circumference?
xxuncexx Archimedes made a brilliant way of calculating pi. He didn't measure it at all, he calculated it, and you can use his method to get as many decimals as you want. I think that it was genius, make sure you take a look at it! 😊
Yes he did. You can imply a calculation from the explanation.
Circumference = Pi . Diameter (there in his example D =1)
Therefore:
Pi = Circumference / Diameter
You can also calculate PI if you measure the are of the circle.
Area = Pi . Radius^2
Pi = Area / Radius is ^2
Also, if you differentiate the A = Pi.R^2 formula, you get 2.Pi.R ... where 2R = D which is the circumference.
Also, if you integrate the c = Pi.D formula (2.Pi.R) , you get 2.Pi.R ^2 / 2 or Pi.R^2, which is the area.
@@paulg687 I think ops point is that in the case of Pi = Circumference / Diameter or Pi = Area / Radius is ^2 both circumference and area are difficult to find without the use of Pi in the first place.
If you don't know either Pi, the area of a given circle, or the Circumference of a given circle flipping these equations around doesn't help.
@@cavycorp9136 if you measure the circumference and the diameter and find their ratio you’ll get a number. Try this for ANY circle, this will be the same. It’s therefore a constant. More importantly though , it’s a natural number for the circle since it can be done for all circles. That’s all there is to it. You can then deduce a formula which includes this constant. Btw, you shouldn’t get hung up about the Greek symbol itself. Just use 3.14 if it looks strange to use. PI, or any Greek letters, are used like this to represent a long number. Easier to write. So you wrote pi instead of 3.141592657….
It’s also the same deal with the ‘e’ in continuous compounding. People shy off when they see it. That too is just a number of 2.7183. This one is the natural number for continuous compounding. You can use the number instead of ‘e’.
If you know basics of trignometry, you can study finding of pie from archimedes method, if you know binomial expansion and calculus, you can study method of newton.Till now, several ways of finding pie are devised
PI IS IRRATIONAL THEN HOW CAN THIS BE IN THE FORM P/Q
Clear and precise. I think once I have got my daughter to physically do this, she will never have a problem working out the other formula to do with a circle.
But why can't it be exact instead of just 3.14, but 3.14159 . . . . ad infinitum? Because we're comparing a straight line (diameter) to a curved surface?
@@Unfamous_Buddha Yes its strange to me that the numbers go on forever. Why is pi irrational? Is the circumference irrational too?
thank you so much for this very simple explination. i've learnt pre algebra, geometry, trigonometry, and i even memorized the unit circle in a day, heck, i even memorized 50 digits of pi! yet i never trully understood WHY is pi, until now, thank you so much
so, pi is a natural number we didnt invented it we discovered it, right? correct me if i m wrong
vaibhav patil discovered
+JoePro Cast yeah i agree
+vaibhav patil ..... PI was invented with a very big Circle to make the equation an everlasting oo infinity. There is an actual equation for PI. LOL
+vaibhav patil
We invented the method of mathematics that allows us to discover Pi
Mathematics is a human invention, and it is not absolute knowledge: there is no such a thing as existing formal concepts of mathematics as phenomena, such as the sun, a dog, a human or an ant. Concepts do not exist, they just subsist in their thinking ontological frame of principles and intuition.
My old Amiga has code to draw circles in pixels only requires 3.1 or 3.14 ,as the algorithm draws circles in quarters, so three quarters of the circle were extrapolated from the quarter circle calculation. The other three quarters are plotted by flipping the coordinate values.
Amiga never gets old! 🙂
Thanks! I would’ve died as an engineer without knowing this!
I thought this was going to be a heavy history into the mathematics of the ancient Greeks and other awesome stuff I didn’t know. This is the exact thing I told my kids 2 years ago.
I feel pi is the constant increase in separation of a circle when it’s offset so the lines don’t meet so it’s a spiral starting at a center point. Because it’s three portions of different size triangles to needed to measure the increase in separation of the spiral from one line to the next.
Also I believe pi is means to signify forward progression in the the development of our subconscious which in turn molds our personality, our heart, so we eventually use the parts of our brain that are trigger by impulse , emotion and intellectual thought so in time through repetition become a single intellectual engrained heartfelt response , 3 to 1. Pi in nature is good luck. I feel it’s God reminding to stay righteous and upright no matter the size of the storm. God is always there present whether you believe or not. God is life and the interactions of life and love is the appreciation of life and the interactions of life. God is the epitome of good. God is an all encompassing spirit and not a sinner.
i think some old-school Greek philosopher just took a wooden wheel and wrapped a thread around it. then he just alined the thread with the diameter of the wheel and tried his best to sub-divide and sub-divide the thread as much as possible to get an accurate Pi ratio. After someone did such experiment it boiled down to getting a better wheel and thinner and thinner thread and making more and more equidistant sub-divisions on the wheel's diameter and on the thread it-self to get a better result
Stop with that nonsense. Who are these Greeks? Read unbiased ancient history There were no Greeks.
i'm obsessed for an answer that you've just provided.
Thank you ! So clear ! Very interesting and …mysterious..
why was i expecting something totally out of the ordinary
Does that mean you can’t accurately measure the circumference of a circle since Pi is a repeating fraction?
it is irrational not repeating. And, in reality, you can't measure ANYTHING with zero uncertainty.
Well done.
0:00 actually an amazing explanation! 0:02
this is not a way to calculate pi, it's a way to proof that pi is a constant number.
I think that the way to calculate pi is to divide a circle into small lines (who's points are acalculated with sinuses and cosinuses) and add the length of all these little lines together. the precision of pi depends on the number of lines you divide the circle into.
I know that this comment is 12yo, but actually, this video doesn't prove that this is constant, it just provides visual intuition what pi is in relation to diameter.
Calculating the numerical value of pi can be done through many (infinite!) ways, and most of them are using very complicated power series that don't make much sense intuitively!
Proof it dumbo
Calculating an irrational number as a fraction (pro tip: just dont)
Yeah, irrational numbers are simply not meant to be converted into fractions because they cannot be.
@@pratijitpodder4345 But they can be approximated to any degree of precision by a fraction (i.e., rational number).
Fred
@NickMinaj69 Yes there is an infinite number of digits in pi, but that doesn't mean the value of pi increases every time you add a digit. Pi will never be larger than 3.1416 no matter how many digits you calculate the accuracy of pi.
thats all we know but where does this relation come from. we cannot accurately measure the circumference or the diameter upto 100s of decimal places but we know the value of pi upto n decimal places
That was a piece of pi.
Cheers, man.
Thanks a lot dude! Trust me, this teaches me more than school. *π* is really interesting when you learn more of its purpose.
Thank a ton sir 🙏🏻
Your so short video has cleared me all doubts
I have watched 8 videos but couldn’t solute what pie is actually
Thanks god bless you 🙏🏻
“In school we learned that pi equals the circumference over the diameter.”
Wow, maybe public school really DID make my mathematics education suffer.
How do you explain the irrational nature of pi, though? In the video, you straighten the circumference into a line. I'd expect it to be a fixed length.
But if we physically cannot make a perfect Circle how do we measure the circumference??
thanks, i’m learning what pi is at school tomorrow, now people with think i’m super smart
Archimedes calculated pi long time ago as 3.14 & maybe infinity , and he was a smart cookie . We can appreciate much from ancient Greek culture . Wonder which genius stumbled on the wheel & said Eureka. And I wonder if pi is sort of like the undefined big 0 since it 's division is infinite ?? Or is it ?
Chinese man also Lui
Each digit is an order 1/10 the size of the previous digit. Since pi is irrational, there are an infinite number of digits. This means that, since each digit is 1/10 the size of the one before it, the series of digits actually approaches 0 in value. Once you start adding 0, the value doesn't change, so pi is finite. It's called a "convergent infinite series" if you want to look up more about it.
Aren’t you just saying that if you sum it the value of each digit in pi it tends towards a total of… pi? 🤔
I wish I thought high school by you. STAY BLESSED!!!!
Why does it turn out to be pi every time you divide circumference by diameter?
@mathematicsonline It will never be larger than 3.1416 because the number is actually 3.14159 and so on
@NickMinaj69
Say achilles is having a race with a snail, but because the snails slower its given 1m head start.
They both start at the same time. By the time achilles has ran 1m the snail has moved a little bit further from where achilles now is. By the time achilles gets to where the snail was whilst achilles was at 1m, the snail has moved a little bit further. And again, by the time achilles gets to where the snail was then, the snail moves a little further. Does that mean achilles cant win?
I liked this. I subscribed. This is an accurate description of pi. Thank you.
Thank you for the simplest explanation yet! This always confused the crap outa me in school
The ratio of the length of a circles diameter to its circumference. (The ratio of the length of the line you can draw from the side through the center and to the other side and the length of the outside or perimeter of the circle)
Wow how perfectly you cleared something that is been haunting me for 20 years...
My mind started with "why a circle?"
why not
You cant draw a perfect circle. You ever see that SpongeBob episode where SpongeBob draws a perfect circle free hand? Call me squidward
You get the constant pi because the circumference is pi times the diameter, so dividing the circumference by the diameter is doing nothing but undoing the math to figure out the circumference.
Since the value of pi has so far proven to be “infinite” and the circumference of a circle is finite, how can the discrepancy be explained?
Holy crap, I was just about to make the same comment! You can take a string of arbitrary , finite length and form a 2D circle with it.
Where u get it the circumference is finite???
This music was pretty scary, but it helped a lot
Thanks. I study engineering so my doubts are beyond that. I know you can approximate the area of the circle by any regular poligon (one on the inside and one on the outside), weight the average and of course as the number of edges tends to infinity the area will tend to the true area of the circle. But my question, really, is something completely different. What was the big use of pi back in the days and why are people today still calculating millions of digits of it? What's the use?
We concern us with pie to understand how to calculate things like a dam for water, etc. That you may know. The goal to achieve accuracy for pie, in my opinion, has more to do with achieving mathematical prove and certainty and to find completeness. Any other possibility must either be prove as complete, or dismiss as not satisfying such prove, or exclude any other prove that may or may not have relevance to the completeness of what needs to be proven. For every digit added to pie, our desire to achieve completeness by prove is satisfied and our suspicion that the prove for completeness does indeed exist is solidify for the benefit of future generations. Mathematicians needs prove, so does Scientists and Biologists for their respective field of study. Unknowns must either be prove or disprove. Careful elimination is needed, and mistakes can have disastrous consequences. Why does a gap exist when a diameter is fitted around the circumference, leaving us with 3.14...(excluding other possibilities) The circumference is complete, but the diameter causes a calculated shortcoming. Should it be like this or shouldn't it? No matter what logical explanation is giving, it appears from prove that the gap is infinite, and that the prove that the gap can be complete is elusive in its make up, hence the prove for the next digit(s)Until then, the next digits will remain like this, dot,dot, dot....
@frankwewers58dot dot19
I can also get pie by driving to Marie Calendars lol
All jokes aside, it was the easiest explanation for pi. I plan to use this video with my future students =)
Finally the clearest example of them all
Oh so π is ACTUALLY SOMETHING that has to do with the circles and isn't some random number someone pulled out of their ass. Honestly I'm disappointed I didn't know this sooner. I'm 21 btw. Thank you.
Idk what your age have to do with anything
Wonderful illustration! thank you!
why are they of unequal parts. like if the diameter is 1 cm then circumference is 3 + 0.1 + 0.04 + 0.001... cm we are adding small quantities of length upto infinitly and still it is a finite length? is the circumference of a circle non existent in reality? even if so why are the next smaller parts unequally divided rather than equally divided or why there is no pattern of decreasing order rather it is random in decreasing order of length. what is this? please explain.
I'm sorry, but there seems to be a misunderstanding in your question. A circle does not have a finite number associated with it in the same way that a numerical value or quantity is associated with a finite number.
A circle is a geometric shape defined by a set of points equidistant from a fixed point called the center. It is a two-dimensional object with no edges or corners. The properties of a circle, such as its circumference, area, radius, and diameter, can be expressed as numerical values, but the circle itself is not inherently associated with a finite number.
For example, the circumference and area of a circle can be calculated using numerical formulas, but the circle itself is not a numerical value. Its properties depend on the measurements (such as radius or diameter) assigned to it.
wow this made me realize, what if pi represents the number of dimensions that exist? we happen to know 3 but what if the fourth is not really a fourth, a whole number… but yet just dimension 0.141? and because it’s not complete we can not understand it as a whole…
A circle must have a diameter to exist. For each perfect circle to be perfect the diameter of that circle must be constant. So the diameter defines and dictates the circumference. Thus we know C if we know D. In this sense D creates C and we call their ratio Pi.
yes (quote) Pi was discovered by the Greeks by a process called exhaustion. They observed that any polygon could be divided into triangles whose areas could be combined to get the area of the shape, so they tried the same thing with circles. They then factored in the radius of the circle, and they found pi. These triangles can theoretically get infinitely smaller, which is why pi is an irrational number.(unquote)
I didn't understand... how did they get the top no by measuring the circumference of the circle.
But how can a length be irrational like here a circle with 1 unit diameter is said to have a circumfrence of pi which is irrational. Also pi can be written in the form of p/q where q not= 0, Then pi must be rational. I dont understand the idea of lengths being irrational.
A circle is a polygon with an infinite number of sides. I think that is where the answer lies.
@voidphoenix9024 Not every number of the form p/q is rational. p and q are supposed to be integers (we can have q to be only a positive integer since we can obtain negative sign from p)
Really didn't understand it in my math books. Thank god there's RUclips..
Pi is only guaranteed to be constant in flat 2-D space. If you have a 2-D space that's not flat, pi may take on different values. Possibly even exactly 3.
For wise people like you I have choosen to live 🙏❤️ thank you very much
Pie is the ratio of pre-divorce wealth to post-divorce wealth (adjusted for legal fees, of course) minus hangover.
based on that definition, does that mean that pi is a constant that is applied to perfect circles, AND PERFECT CIRCLES ONLY?
But how did they find the formula of a circumference without pi (2piR)
But how do you calculate the circumference without pi?
Because for example you said the diameter is 8 and then you said from nowhere that the circumference is 25.13274123... And then the ratio gave pi, but how did you know that the circumference was 25.13274123...?
Basically its a ratio between the Circumference of a circle and its Diameter.
@MrMegoPego It really depends on how curved you make the edges. If you want to measure the area of a square using pi, you would first have to find the area of the circle, and then you would have to account for the area lost when curving the edges.
But, if your just asking "If we curved the edges of a square so it was no longer a polygon, could we calculate the area with pi?" the answer would be no.
Something isn't a circle because it has no angles, a circle has the same diameter everywhere
That's when you use the Pythagorean theorem to find the radius of the curved edge right?
I don't know. What is Panacea I? Towers?
Circles will always be a joke without towers. The person supposedly doing it and creating it was hit and Canada beaten to a pulp.
You might be able to see some of him in it, but it is a vague and under inspiring when contrasting with the actual reason for its accidental creation.
I have also a question , to calculate Pi we need the Circumference and Diameter Of our Cercle ... then Pi = Circumference / Diameter , my question is : How to Calculate the Circumference without using PI ?
I assume it would have originally been derived by physically measuring circular objects, such as putting thread around a wheel.
I was bit confuse and sorry for that, if 3.14... is the circumference of a circle then what its diameter? Is it 1?
Explanained in simple language.
Thanks
excellent work to promote mathematics. hope we get more in future. Abdul Rehman Khan
okey but how is it possible that we don't know the exact number? or like how come it's so long...like how do we measure/calculate all those numbers??
Such a simple explanation that took thousands of years to find the proof of pi's being irrational....
This was so clear and amazing! Thank you! I needed this info. I totally get it!
Are teachers using diameters for circumference now?
We were taught to use the radius squared.
(before you say "that IS the diameter", remember the formula for a sphere deals with the radius cubed, and no one wants to have to remember different variables for similar formulas... or have to do extra math (i e: the diameter divided by two, in parenthesis, cubed)).
1.4 seconds in my brain jus exploded
Thank you for this video. Excellent explanation. Subscribed.
In the video it looked like he added the diameter which was 1 to the circumference to get pi, but your supposed to divide it.
E (1/10)^n. Hmm. The geometric series wow haha. You're the only person who actually explained it correctly to me. I completely understand now. 5 months of mystery solved xD!
initially how did we measure the circumference without knowing what PI is ?
Just knowing lol 😅 how u know right and wrong ??
Nice! Now I got to understand it better! Thanks for sharing!
@mathematicsonline This is true, but that would mean that there is an upper limit to this growth at 3.1416.. however, wouldn't a circle's circumferance be continually increasing untill it "reached" some point N where, beyond which, Epsilon
value of pi is not a fix value it is 3.141592....., nd 3.1415 > 3.141 that means we can never calculate the exact length of circumference what ever we measure it's going to be less even if it's is in a very minute scale even billionth time smaller than radius of electron .
3+10/70>π>3+10/71, proved by Αρχιμήδης!
So its basically 3,141592654?
1:01 Is Pi also the constant for circles that don’t exist?
This is not the best explanation of pi, simply a consequence of pi being the ratio of the circumference to the diameter. The best way to describe it is as a constant of proportionality. It's the linear relationship between a circles circumference and its diameter. Increase the diameter by 1, and the circumference increases by 3.14159. This video is dedicated mostly to the consequence of that on the unit circle.
So if I made a circle with diameter 1 foot right, would the circumference be pi? But isn't it finite?
by what has said, is that pi is negative ... to 3.1416 and not 1415. not be larger than 1416 means it can be 1416 but pi is 141592653....... the value will be higher if you add numbers to the early numbers. for example 3.141592 + 0.001 = 3.141692
How would that help anything? You'd just get a square with a perimeter equal to the circle's circumference.
How do you precisely measure the circumference!? As it stand it can't be done.
I'm sorry, but there seems to be a misunderstanding in your question. A circle does not have a finite number associated with it in the same way that a numerical value or quantity is associated with a finite number.
A circle is a geometric shape defined by a set of points equidistant from a fixed point called the center. It is a two-dimensional object with no edges or corners. The properties of a circle, such as its circumference, area, radius, and diameter, can be expressed as numerical values, but the circle itself is not inherently associated with a finite number.
For example, the circumference and area of a circle can be calculated using numerical formulas, but the circle itself is not a numerical value. Its properties depend on the measurements (such as radius or diameter) assigned to it.
This video was very helpful. Thanks.
@NJHpro you could say that its irrational, but that doesnt mean it isnt possible. just give the sollution as a multiple of Pi. for example a circle with a radius of 5 would have a circumference of 10*Pi. its irrational but using the short form of pi you can easily right it down. you hand over the problem of defining pi to your teacher or whoever has to correct that shit.
Someone introduced a circle into explaining calculus and introduced pi as if that's an established fact. But I then watched this video and for the first time today I understood something.
I have a HUGE quesiton. If Pi is irrational... does that mean that the circumferance of a circle is always growing.. in the sense that pi never ends and is always is always bigger than you can calculate because you can always add one more digit?