Hi! Welcome to Math Antics. We’ve learned a lot about Geometry so far, but there’s one really important geometric shape that we still need to cover, and that shape is a circle. Since the invention of the wheel, circles have been extremely important to all humanity. Grog make wheel. Thanks Grog! In fact, you probably see circles

almost everywhere you turn… But mathematically, what is a circle? Well in Geometry, a circle is defined as: the set of all points that are equidistant (or the same distance) from another single point. And the best way to understand what that means is to see it in action. So… here’s a single point to start with. Now let’s start drawing points

that are equidistant from it. This point is a foot away to the right. Now let’s make another point a foot away but in another direction. Let’s say up here. Now let’s make another one, also a foot away, but in another direction. Right here. Now let’s make another, right here and another, and another, and another, and another… Wheew… I’m getting tired! But do you see what’s happening? The more equidistant points we add, the more the pattern looks like a circle. That’s why a circle is defined as the set of points that are equidistant from a center point. But of course, we usually don’t see it as a set of points because there are infinitely many of them, so they form a continuous circle. Okay, now let’s learn about the

parts that make up a circle. First of all we have

the original point that we started with. That’s called the center, or the origin of the circle. Next, we have the distance that we used to draw all of the equidistant point that form the circle. That distance is called the radius. The radius is important because it’s the distance from the center of a circle to ANY other point on the perimeter of that circle. And even though a circle only has one radius dimension, you can draw as many radius lines as you want to. Usually you’ll only see one radius line drawn since it’s the same length no matter where you draw it. Another important circle dimension is called the diameter. The diameter is the distance across a circle. If you start at one point on the circle and then draw a line straight through the center to the other side, that distance is the diameter. As you can see, the diameter is really just the same as two radius lines drawn in exactly opposite directions. So, for any circle, the diameter is always exactly

twice as long as the radius. All of the equidistant points we drew combine to form the perimeter of the circle. Remember that perimeter is just

the distance all the way around a shape. But because a circle is a special shape,

the perimeter of a circle gets a special name. It’s called the circumference. The circumference is the distance

all the way around a circle. We’re going to learn how to calculate the circumference of any circle in the next video. We’ll also learn how to calculate the area of any circle. But before we can learn those things,

we first need to learn about Pi. Grog make Pie! Sorry Grog, not that kind of pie. In math, the word Pi (which is spelled ‘P’ ‘i’)

refers to a very special number. In fact, it’s so special that it gets its own symbol. This greek letter here is the symbol for the number Pi. But…

if Pi is just a number, why don’t we write it like that? Why do we use a special symbol for it? That’s a good question. And I’ll get to that in just a minute. But first, let’s learn what Pi really is by seeing how it relates to a circle. It turns out that Pi is a really a Ratio! Now if you’re not sure what a ratio is, you can watch our video about them. But basically, a ratio is just a relationship between two numbers that is written like a fraction. Pi is the ratio of two different distances on a circle. It’s the ratio of the distance around a circle to the distance across a circle. And what do we call those two distances? Yep, the circumference and the diameter. So Pi is the relationship of the circumference to the diameter. And as you’ll see in a minute, because Pi is a ratio, it’s the same number for any circle,

no matter how big or small. Okay, but what number is it? What’s the value of Pi? Well, to figure that out, have a look at these two circles, one big and one small. We’re going to imagine that our circles’ diameters are flexible, like a piece of string, and that we can wrap them around the outside edges (circumferences) of the circles. So for each circle, if we start at the top and wrap the diameter around the circumference, we see that 1 diameter is not enough to go all the way around. So, let’s get another diameter and keep going where the first diameter stopped. Hmmm… two diameters still isn’t enough to go all the way around. It looks like we’re going to need to get a third diameter and keep going. Awwww! So close!! Three diameters is almost enough but it looks like we’re going to need just a little bit more to form a full circumference. That little bit more turns out to be about 0.14 diameters. That means that it takes 3.14 diameters to equal one circumference for any circle, big or small. So the value of Pi is always 3.14. Well okay… Pi is a little more complicated than that. 3.14 is really just Pi rounded off to two decimal places. And we actually have to round Pi off because it’s a type of number that’s called ‘irrational’. An irrational number has decimal digits

that never end and never repeat. Grog confused. Yes, ‘irrational’ numbers are confusing, but seeing some more of Pi’s decimal digits

will help you understand what I mean. To be more precise, Pi is 3.141592653589793238… and the decimal digits keep on going forever

without repeating!! Pretty amazing, huh? But the good news is that saying Pi is 3.14 is usually close enough for most math problems, so that’s all you really need to memorize. And that’s why we use a symbol for Pi in equations. We could write Pi with just two decimal places. Or we could write it with 5 decimal places

to be more accurate. Or, we could write it with hundreds of decimal places

to be super accurate. Or, we could just use the symbol to represent the true value, which is infinitely accurate. Okay, so in this video, we’ve learned what a circle is, and we’ve learned about the important parts of a circle: the center, the radius,

the diameter and the circumference. We’ve also learned about

a very special number called Pi. Pi is the ratio of a circle’s circumference to its diameter, and its value is about 3.14

no matter what size the circle is. In our next video about circles, we’re going to learn how we can use the number PI to find

the circumference and the area of any circle. And even though there is not much math you can actually practice in this section, don’t worry… there will be lots of practice problems in the next section to make up for it! Thanks for watching Math Antics

and I’ll see ya next time. Mmmm, Grog good at math! Learn more at www.mathantics.com

I'm practicing for the 11plus but my mum is scaring me which doesn't help me but this helps .

Best video ever supervisor teacher

I've always hated math still hate it but you make it so much easier to learn and your very entertaining

Cant even pronounce pi correctly

THANK YOU

You explain concepts so well that taking notes is unnecessary. Thanks for sharing your gift of teaching with the world!

if my teachers were like this i would become Einstein

math made me mad!!!

Who else here has a Asian teacher and can’t understand half the words there saying so u just come here

"Another circle to mention is Diameter" –

mathantics2014Complex subjects become easy if they are taught well. You teach well.

I’m in Australia (we use metric)

You have not explained why the circumference is pi times the diameter. What I mean to say is why isn't circumference some rational number times diameter rather it is irrational number times the diameter. I hope you understood the question.

well done sir, brilliantly explained

I honestly think his educational videos should be seen by everyone

I learned about PI in 4th grade but never understood the meaning of “the relationship between the circumference and the diameter” part. I never understood why PI was infinite. I just knew how to put it into a problem and solve in. That picture he showed of the diameter wrapping around the circle was so simple but sooooo incredibly brilliant. I don’t understand why nobody shows this example more often. I’m in 9th grade now and I finally know what it means. 🤯

I love this guy …. I love him so much 💕💕

this is awesome!!!!!!!!!!!!!

I ever read that in Wikipedia

I also

thanks

a very precise way of explanation i am satisfied with pi now

who else is watching this in 2019 ?

Wish I had this video in high school.

Dude, why r adults watching this crap

i should have skipped school, i could save so much time and do something better for my life and get knowledge from youtube. Sadly there was no YT by the time of my school haha! Great video and thanks for clarifications i was looking for years! Oh and one more thing, screw you all math teachers from my past!

Is this math or you are joking ?

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1:58 it's a radius

Me:oh so that's the hand of my clock

Awesome explanation. In math class they just throw pi out there in the equation without explaining why it's there. Great video!

3:22 grog make pie lol xd

People who disliked this video hates math ahahha

Who had meet match antics in 2019 hit me a like and watching this for exams hit the like button right here if u did👇👇👇💓💓👇👇💕

I did pi on my calulater and it say 3.141592654…

PLZ Make a video on what is sine

Let Me Give You Guys A Nice Tip For Studying…SPECIALLY MATHS

Wear Headphones 🎧

They will help you stay concentrated😇

If you want,you can watch a subject video while studying or you can enjoy some nice tunes 😉.

TRY IT,AND IF IT HELPS PLEASE REPLY!

thanks!

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In next video could you put pitcher plant pie chart

I’ve been wanting to know the point of pi (bad pun) but thanks a lot for teaching me how

y y y y yy yy y y

yyyyyyyyyyyyyyyyyyyyy 3:21

Hola

Best dude ever

When i was in 4th grade i didnt get this and all my staar tests failed so that means i am a complete retard

(y)

Please teach my teacher how to teach…

Do you like your teacher or mathantics more?

Pi equals 3 point 141592653589793238462643383279502884197169399375 what I remember lol

Ｇｒｏｇ ｍａｋｅ ｗｈｅｅｌ 0:24

I asked myself all the time in the school, why PI is 3.14…

My teachers never explained it to me and now i know it. Nobody is bad at math, we all had just the worst teachers ever in our life!

Teacher:

trying to explain how to do long divisionMe: wtf r u talking about

Math antics:

explains piMe: becomes a pi genius

Anyone else watching this for Math class?

Why is math so easy now that I watch his vids

Who watches him at school

But if PI never repeats, then how about the first 6 decimal digits with the next 6 decimal digits? Aren't they identical? Please reply.

Another thing that could help is that PI is closest in value to the fraction 22/7

Thanks for the videos, refreshing and learning methods i did not learn in school.

What is pi

Baby don't hurt me

Dont hurt me

No more

I want this guy be my school teacher maths.My friend will be exiteddddd😂😂😂😂😂😂😂😆😆😆😆😆😆👏👏👏👏

Why isn’t this guy my math teacher? Literally, math would be seven minutes then some work and bam done

By the best math teacher I've ever seen. This guy just made up for all the waste of time with math teachers here in Germany. My respect – awesome method

This dude is smarter then my math teacher

Hi im john … My prof says that pi = 3.1416? This is the same to 3.14?

who is thinking that he is da best at math like

2.02 what is radius again

2:02 dont undrestand

Did you hold the place value

You rock.

Pi is the left over of the circle

Thank you because I can do it school work because of this

The dislikes are from math teachers

perfect explanation we never had in school.. thank you.

22/7 ? I only know Egyptian math sir!

no cap

This is honestly great. It's been so long since I've taken math classes that I need to brush up before my college math classes, this has been so helpful. I've even learned things that were never explained like this before. Bloody brilliant.