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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