Math Antics - Circles, What Is PI? - Free Educational videos for Students in K-12 | Lumos Learning

Math Antics - Circles, What Is PI? - Free Educational videos for Students in k-12


Math Antics - Circles, What Is PI? - By Mathantics



Transcript
00:03 Uh huh . Hi , welcome to Math Antics .
00:08 We've learned a lot about geometry so far , but
00:10 there's one really important geometric shape that we still need
00:13 to cover . And that shape is a circle .
00:16 Since the invention of the will circles have been extremely
00:20 important to all humanity . Grog make Well . Thanks
00:26 Greg . In fact , you probably see circles almost
00:30 everywhere you turn . But mathematically what is a circle
00:35 ? Well , in geometry , a circle is defined
00:38 as the set of all points that are equal distant
00:41 or the same distance from another single point . And
00:44 the best way to understand what that means is to
00:46 see it in action . So here's a single point
00:50 to start with . And now let's start drawing points
00:53 that are equally distant from it . This point is
00:56 a foot away to the right now let's make another
00:58 point of foot away . But in another direction ,
01:00 let's say up here , now let's make another one
01:03 . Also a foot away , but in another direction
01:06 right here . Now let's make another right here and
01:09 another . You I'm getting tired . But do you
01:18 see what's happening ? The more equidistant points we add
01:22 , the more the pattern looks like a circle and
01:25 that's why a circle is defined as a set of
01:27 points that are equidistant from a center point . But
01:31 of course we usually don't see it as a set
01:33 of points because there's infinitely many of them . So
01:36 they form a continuous circle . Okay , now let's
01:40 learn about the parts that make up a circle .
01:42 First of all , we have the original point that
01:44 we started with that's called the center or the origin
01:47 of the circle . Next we have the distance that
01:51 we use to draw all of the equidistant points that
01:53 form a circle . That distance is called the radius
01:57 . The radius is important because it's the distance from
02:00 the center of a circle to any other point on
02:03 the perimeter of that circle . And even though a
02:06 circle only has one radius dimension , you can draw
02:09 as many radius lines as you want to . Usually
02:12 you'll only see one radius line drawn since it's the
02:15 same length no matter where you draw it . Another
02:19 important circle dimension is called the diameter . The diameter
02:23 is the distance across the circle . If you start
02:26 at one point on the circle and then draw a
02:28 line straight through the center to the other side ,
02:31 that distance is the diameter . As you can see
02:35 , the diameter is really just the same as two
02:38 radius lines drawn in exactly opposite directions . So for
02:42 any circle , the diameter is always exactly twice as
02:45 long as the radius . All of the equidistant points
02:49 we drew combined to form the perimeter of the circle
02:52 . Remember that perimeter is just the distance all the
02:55 way around the shape , but because the circle is
02:57 a special shape , the perimeter of a circle gets
03:00 a special name , it's called the circumference . The
03:03 circumference is the distance all the way around a circle
03:07 . We're going to learn how to calculate the circumference
03:10 of any circle in the next video , we'll also
03:13 learn how to calculate the area of any circle .
03:16 But before we can learn those things , we first
03:19 need to learn about pie grog , mate . Pie
03:24 , wow , sorry grog ! Not that kind of
03:27 pie in math . The word pie , which is
03:30 spelled P I refers to a very special number .
03:34 In fact it's so special that it gets its own
03:36 symbol . This greek letter here is the symbol for
03:40 the number pi . But if pi is just a
03:42 number , why don't we write it like that ?
03:44 Why do we need to use a special symbol for
03:46 it ? That's a good question . and I'll get
03:49 to that in just a minute . But first let's
03:52 learn what pie really is by seeing how it relates
03:54 to a circle . It turns out that pie is
03:58 really a ratio . Now if you're not sure what
04:00 a ratio is you can watch our video about them
04:03 . But basically a ratio is just a relationship between
04:06 two numbers that's written like a fraction high is the
04:10 ratio of two different distances on a circle . It's
04:13 the ratio of the distance around a circle to the
04:16 distance across the circle . And what do we call
04:19 those two distances , yep , the circumference and the
04:22 diameter . So pi is the relationship of the circumference
04:27 to the diameter . And as you'll see in a
04:29 minute because pie is a ratio , it's the same
04:32 number for any circle no matter how big or small
04:36 . Okay but what number is it ? What's the
04:38 value of pi Well , to figure that out .
04:42 Have a look at these two circles . One big
04:44 and one small . We're going to imagine that our
04:47 circles diameters are flexible like a piece of string that
04:51 we can wrap them around the outside edges . Circumference
04:54 is of the circles . So for each circle if
04:57 we start at the top and wrap the diameter around
05:00 the circumference we see that one diameter is not enough
05:03 to go all the way around . So let's get
05:05 another diameter and keep going where the first diameter stopped
05:08 mm . Two diameters still isn't enough to go all
05:11 the way around . It looks like we're gonna need
05:13 to get a third diameter and keep going Oh so
05:17 close three oz is almost enough but it looks like
05:21 we're gonna need just a little bit more to form
05:24 a full circumference . That little bit more turns out
05:27 to be about 0.14 oz . That means that it
05:31 takes 3.14 oz to equal one circumference for any circle
05:37 big or small . So the value of Pi is
05:40 always 3.14 . Well okay , Pie is a little
05:44 more complicated than that . 3.14 is really just pie
05:48 rounded off to two decimal places . And we actually
05:51 have to round pie off because it's a type of
05:54 number that's called irrational . An irrational number has decimal
05:58 digits that never end and never repeat . Drug confused
06:07 . Yes , irrational numbers are confusing But seeing some
06:11 more of pies , decimal digits will help you understand
06:14 what I mean . To be more precise , pi
06:17 is 3.141592653589793238 . And the decimal digits just keep on
06:28 going forever without repeating . Pretty amazing . Huh ?
06:33 But the good news is that saying Pi is 3.14
06:37 is usually close enough for most math problems . So
06:40 that's all you really need to memorize . And that's
06:43 why we use a symbol for pi and equations .
06:46 We could write Pie with just two decimal places or
06:49 we could write it with five decimal places to be
06:51 more accurate . Or we could write it with hundreds
06:54 of decimal places to be super accurate . Or we
06:58 could just use the symbol to represent the true value
07:01 which is infinitely accurate . Okay , so in this
07:05 video we learned what a circle is and we've learned
07:08 about the important parts of the circle , the center
07:11 , the radius , the diameter and the circumference .
07:14 We've also learned about a very special number called Pie
07:19 . Hi is the ratio of a circle's circumference to
07:22 its diameter and its value is about 3.14 . No
07:26 matter what size the circle is . In our next
07:29 video about circles , we're going to learn how we
07:32 can use the number pi to find the circumference and
07:34 the area of any circle . And even though there's
07:38 not much Matthew can actually practice in this section ,
07:40 don't worry . There'll be lots of practice problems in
07:43 the next section to make up for it . Thanks
07:45 for watching Math Antics and I'll see you next time
07:48 . Mm grow good at Math . Mm . Mhm
07:54 . Learn more at Math Antics dot com .
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