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• 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.

• 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.

• Hmmmtwo 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 okayPi 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!

Hi! Welcome to Math Antics.

B2 中高級 美國腔

# Math Antics - 圓，什麼是PI？ (Math Antics - Circles, What Is PI?)

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Yassion Liu 發佈於 2021 年 01 月 14 日