[Script Info]
Title: 
[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:00.78,0:00:04.88,Default,,0000,0000,0000,,The circle is arguably the most\Nfundamental shape in our
Dialogue: 0,0:00:04.88,0:00:08.49,Default,,0000,0000,0000,,universe, whether you look at\Nthe shapes of orbits of
Dialogue: 0,0:00:08.49,0:00:11.14,Default,,0000,0000,0000,,planets, whether you look at\Nwheels, whether you look at
Dialogue: 0,0:00:11.14,0:00:12.84,Default,,0000,0000,0000,,things on kind of a\Nmolecular level.
Dialogue: 0,0:00:12.84,0:00:15.86,Default,,0000,0000,0000,,The circle just keeps\Nshowing up over and
Dialogue: 0,0:00:15.86,0:00:17.35,Default,,0000,0000,0000,,over and over again.
Dialogue: 0,0:00:17.35,0:00:21.11,Default,,0000,0000,0000,,So it's probably worthwhile for\Nus to understand some of the
Dialogue: 0,0:00:21.11,0:00:23.33,Default,,0000,0000,0000,,properties of the circle.
Dialogue: 0,0:00:23.33,0:00:26.20,Default,,0000,0000,0000,,So the first thing when people\Nkind of discovered the circle,
Dialogue: 0,0:00:26.20,0:00:28.96,Default,,0000,0000,0000,,and you just have a look at the\Nmoon to see a circle, but the
Dialogue: 0,0:00:28.96,0:00:31.57,Default,,0000,0000,0000,,first time they said well, what\Nare the properties
Dialogue: 0,0:00:31.57,0:00:32.91,Default,,0000,0000,0000,,of any circle?
Dialogue: 0,0:00:32.91,0:00:36.15,Default,,0000,0000,0000,,So the first one they might\Nwant to say is well, a circle
Dialogue: 0,0:00:36.15,0:00:38.69,Default,,0000,0000,0000,,is all of the points that are\Nequal distant from the
Dialogue: 0,0:00:38.69,0:00:40.44,Default,,0000,0000,0000,,center of the circle.
Dialogue: 0,0:00:40.44,0:00:43.71,Default,,0000,0000,0000,,All of these points along the\Nedge are equal distant from
Dialogue: 0,0:00:43.71,0:00:45.21,Default,,0000,0000,0000,,that center right there.
Dialogue: 0,0:00:45.21,0:00:47.62,Default,,0000,0000,0000,,So one of the first things\Nsomeone might want to ask is
Dialogue: 0,0:00:47.62,0:00:50.28,Default,,0000,0000,0000,,what is that distance, that\Nequal distance that everything
Dialogue: 0,0:00:50.28,0:00:51.77,Default,,0000,0000,0000,,is from the center?
Dialogue: 0,0:00:51.77,0:00:52.95,Default,,0000,0000,0000,,Right there.
Dialogue: 0,0:00:52.95,0:00:58.11,Default,,0000,0000,0000,,We call that the\Nradius of the circle.
Dialogue: 0,0:00:58.11,0:01:00.35,Default,,0000,0000,0000,,It's just the distance from\Nthe center out to the edge.
Dialogue: 0,0:01:00.35,0:01:02.82,Default,,0000,0000,0000,,If that radius is 3\Ncentimeters, then this radius
Dialogue: 0,0:01:02.82,0:01:04.49,Default,,0000,0000,0000,,is going to be 3 centimeters.
Dialogue: 0,0:01:04.49,0:01:07.17,Default,,0000,0000,0000,,And this radius is going\Nto be 3 centimeters.
Dialogue: 0,0:01:07.17,0:01:08.27,Default,,0000,0000,0000,,It's never going to change.
Dialogue: 0,0:01:08.27,0:01:11.69,Default,,0000,0000,0000,,By definition, a circle is all\Nof the points that are equal
Dialogue: 0,0:01:11.69,0:01:13.40,Default,,0000,0000,0000,,distant from the center point.
Dialogue: 0,0:01:13.40,0:01:17.05,Default,,0000,0000,0000,,And that distance\Nis the radius.
Dialogue: 0,0:01:17.05,0:01:19.88,Default,,0000,0000,0000,,Now the next most interesting\Nthing about that, people might
Dialogue: 0,0:01:19.88,0:01:22.04,Default,,0000,0000,0000,,say well, how fat\Nis the circle?
Dialogue: 0,0:01:22.04,0:01:26.36,Default,,0000,0000,0000,,How wide is it along\Nits widest point?
Dialogue: 0,0:01:26.36,0:01:28.71,Default,,0000,0000,0000,,Or if you just want to cut it\Nalong its widest point, what
Dialogue: 0,0:01:28.71,0:01:30.39,Default,,0000,0000,0000,,is that distance right there?
Dialogue: 0,0:01:30.39,0:01:32.34,Default,,0000,0000,0000,,And it doesn't have to be just\Nright there, I could have just
Dialogue: 0,0:01:32.34,0:01:35.49,Default,,0000,0000,0000,,as easily cut it along its\Nwidest point right there.
Dialogue: 0,0:01:35.49,0:01:38.52,Default,,0000,0000,0000,,I just wouldn't be cutting it\Nlike some place like that
Dialogue: 0,0:01:38.52,0:01:40.12,Default,,0000,0000,0000,,because that wouldn't be\Nalong its widest point.
Dialogue: 0,0:01:40.12,0:01:41.81,Default,,0000,0000,0000,,There's multiple places\Nwhere I could cut it
Dialogue: 0,0:01:41.81,0:01:43.48,Default,,0000,0000,0000,,along its widest point.
Dialogue: 0,0:01:43.48,0:01:46.73,Default,,0000,0000,0000,,Well, we just saw the radius\Nand we see that widest point
Dialogue: 0,0:01:46.73,0:01:49.58,Default,,0000,0000,0000,,goes through the center\Nand just keeps going.
Dialogue: 0,0:01:49.58,0:01:52.92,Default,,0000,0000,0000,,So it's essentially two radii.
Dialogue: 0,0:01:52.92,0:01:55.64,Default,,0000,0000,0000,,You got one radius there\Nand then you have another
Dialogue: 0,0:01:55.64,0:01:57.24,Default,,0000,0000,0000,,radius over there.
Dialogue: 0,0:01:57.24,0:02:01.38,Default,,0000,0000,0000,,We call this distance along\Nthe widest point of the
Dialogue: 0,0:02:01.38,0:02:03.03,Default,,0000,0000,0000,,circle, the diameter.
Dialogue: 0,0:02:03.03,0:02:06.39,Default,,0000,0000,0000,,So that is the diameter\Nof the circle.
Dialogue: 0,0:02:06.39,0:02:09.26,Default,,0000,0000,0000,,It has a very easy\Nrelationship with the radius.
Dialogue: 0,0:02:09.26,0:02:16.16,Default,,0000,0000,0000,,The diameter is equal to\Ntwo times the radius.
Dialogue: 0,0:02:19.06,0:02:21.79,Default,,0000,0000,0000,,Now, the next most interesting\Nthing that you might be
Dialogue: 0,0:02:21.79,0:02:24.56,Default,,0000,0000,0000,,wondering about a circle is how\Nfar is it around the circle?
Dialogue: 0,0:02:24.56,0:02:27.34,Default,,0000,0000,0000,,So if you were to get your tape\Nmeasure out and you were to
Dialogue: 0,0:02:27.34,0:02:35.91,Default,,0000,0000,0000,,measure around the circle like\Nthat, what's that distance?
Dialogue: 0,0:02:35.91,0:02:44.71,Default,,0000,0000,0000,,We call that word the\Ncircumference of the circle.
Dialogue: 0,0:02:44.71,0:02:47.44,Default,,0000,0000,0000,,Now, we know how the diameter\Nand the radius relates, but how
Dialogue: 0,0:02:47.44,0:02:49.79,Default,,0000,0000,0000,,does the circumference relate\Nto, say, the diameter.
Dialogue: 0,0:02:49.79,0:02:51.55,Default,,0000,0000,0000,,And if you're not really used\Nto the diameter, it's very
Dialogue: 0,0:02:51.55,0:02:54.29,Default,,0000,0000,0000,,easy to figure out how it\Nrelates to the radius.
Dialogue: 0,0:02:54.29,0:02:57.13,Default,,0000,0000,0000,,Well, many thousands of years\Nago, people took their tape
Dialogue: 0,0:02:57.13,0:02:58.89,Default,,0000,0000,0000,,measures out and they keep\Nmeasuring circumferences
Dialogue: 0,0:02:58.89,0:03:00.43,Default,,0000,0000,0000,,and radiuses.
Dialogue: 0,0:03:00.43,0:03:03.28,Default,,0000,0000,0000,,And let's say when their tape\Nmeasures weren't so good,
Dialogue: 0,0:03:03.28,0:03:05.01,Default,,0000,0000,0000,,let's say they measured the\Ncircumference of the circle
Dialogue: 0,0:03:05.01,0:03:07.96,Default,,0000,0000,0000,,and they would get well, it\Nlooks like it's about 3.
Dialogue: 0,0:03:07.96,0:03:11.60,Default,,0000,0000,0000,,And then they measure the\Nradius of the circle right here
Dialogue: 0,0:03:11.60,0:03:14.28,Default,,0000,0000,0000,,or the diameter of that circle,\Nand they'd say oh, the diameter
Dialogue: 0,0:03:14.28,0:03:16.29,Default,,0000,0000,0000,,looks like it's about 1.
Dialogue: 0,0:03:16.29,0:03:17.74,Default,,0000,0000,0000,,So they would say -- let\Nme write this down.
Dialogue: 0,0:03:17.74,0:03:21.75,Default,,0000,0000,0000,,So we're worried about\Nthe ratio -- let me
Dialogue: 0,0:03:21.75,0:03:22.66,Default,,0000,0000,0000,,write it like this.
Dialogue: 0,0:03:22.66,0:03:33.96,Default,,0000,0000,0000,,The ratio of the circumference\Nto the diameter.
Dialogue: 0,0:03:37.56,0:03:40.90,Default,,0000,0000,0000,,So let's say that somebody had\Nsome circle over here -- let's
Dialogue: 0,0:03:40.90,0:03:43.17,Default,,0000,0000,0000,,say they had this circle, and\Nthe first time with not that
Dialogue: 0,0:03:43.17,0:03:45.88,Default,,0000,0000,0000,,good of a tape measure, they\Nmeasured around the circle
Dialogue: 0,0:03:45.88,0:03:49.34,Default,,0000,0000,0000,,and they said hey, it's\Nroughly equal to 3 meters
Dialogue: 0,0:03:49.34,0:03:50.49,Default,,0000,0000,0000,,when I go around it.
Dialogue: 0,0:03:50.49,0:03:52.80,Default,,0000,0000,0000,,And when I measure the\Ndiameter of the circle,
Dialogue: 0,0:03:52.80,0:03:55.05,Default,,0000,0000,0000,,it's roughly equal to 1.
Dialogue: 0,0:03:55.05,0:03:56.00,Default,,0000,0000,0000,,OK, that's interesting.
Dialogue: 0,0:03:56.00,0:03:57.52,Default,,0000,0000,0000,,Maybe the ratio of\Nthe circumference of
Dialogue: 0,0:03:57.52,0:03:58.50,Default,,0000,0000,0000,,the diameter's 3.
Dialogue: 0,0:03:58.50,0:04:00.82,Default,,0000,0000,0000,,So maybe the circumference\Nis always three
Dialogue: 0,0:04:00.82,0:04:02.02,Default,,0000,0000,0000,,times the diameter.
Dialogue: 0,0:04:02.02,0:04:03.61,Default,,0000,0000,0000,,Well that was just for this\Ncircle, but let's say they
Dialogue: 0,0:04:03.61,0:04:05.72,Default,,0000,0000,0000,,measured some other\Ncircle here.
Dialogue: 0,0:04:05.72,0:04:07.87,Default,,0000,0000,0000,,It's like this -- I\Ndrew it smaller.
Dialogue: 0,0:04:07.87,0:04:11.20,Default,,0000,0000,0000,,Let's say that on this circle\Nthey measured around it and
Dialogue: 0,0:04:11.20,0:04:14.96,Default,,0000,0000,0000,,they found out that the\Ncircumference is 6 centimeters,
Dialogue: 0,0:04:14.96,0:04:18.21,Default,,0000,0000,0000,,roughly -- we have a bad\Ntape measure right then.
Dialogue: 0,0:04:18.21,0:04:21.71,Default,,0000,0000,0000,,Then they find out\Nthat the diameter is
Dialogue: 0,0:04:21.71,0:04:23.52,Default,,0000,0000,0000,,roughly 2 centimeters.
Dialogue: 0,0:04:23.52,0:04:25.49,Default,,0000,0000,0000,,And once again, the ratio of\Nthe circumference of the
Dialogue: 0,0:04:25.49,0:04:30.23,Default,,0000,0000,0000,,diameter was roughly 3.
Dialogue: 0,0:04:30.23,0:04:32.14,Default,,0000,0000,0000,,OK, this is a neat\Nproperty of circles.
Dialogue: 0,0:04:32.14,0:04:35.43,Default,,0000,0000,0000,,Maybe the ratio of the\Ncircumference to the diameters
Dialogue: 0,0:04:35.43,0:04:38.08,Default,,0000,0000,0000,,always fixed for any circle.
Dialogue: 0,0:04:38.08,0:04:40.26,Default,,0000,0000,0000,,So they said let me\Nstudy this further.
Dialogue: 0,0:04:40.26,0:04:42.51,Default,,0000,0000,0000,,So they got better\Ntape measures.
Dialogue: 0,0:04:42.51,0:04:45.09,Default,,0000,0000,0000,,When they got better tape\Nmeasures, they measured hey,
Dialogue: 0,0:04:45.09,0:04:47.63,Default,,0000,0000,0000,,my diameter's definitely 1.
Dialogue: 0,0:04:47.63,0:04:49.43,Default,,0000,0000,0000,,They say my diameter's\Ndefinitely 1, but when I
Dialogue: 0,0:04:49.43,0:04:51.81,Default,,0000,0000,0000,,measure my circumference\Na little bit, I realize
Dialogue: 0,0:04:51.81,0:04:53.04,Default,,0000,0000,0000,,it's closer to 3.1.
Dialogue: 0,0:04:56.00,0:04:57.29,Default,,0000,0000,0000,,And the same thing\Nwith this over here.
Dialogue: 0,0:04:57.29,0:04:59.37,Default,,0000,0000,0000,,They notice that this\Nratio is closer to 3.1.
Dialogue: 0,0:04:59.37,0:05:01.83,Default,,0000,0000,0000,,Then they kept measuring it\Nbetter and better and better,
Dialogue: 0,0:05:01.83,0:05:05.20,Default,,0000,0000,0000,,and then they realized that\Nthey were getting this number,
Dialogue: 0,0:05:05.20,0:05:07.30,Default,,0000,0000,0000,,they just kept measuring it\Nbetter and better and they were
Dialogue: 0,0:05:07.30,0:05:10.85,Default,,0000,0000,0000,,getting this number 3.14159.
Dialogue: 0,0:05:10.85,0:05:12.55,Default,,0000,0000,0000,,And they just kept adding\Ndigits and it would
Dialogue: 0,0:05:12.55,0:05:13.62,Default,,0000,0000,0000,,never repeat.
Dialogue: 0,0:05:13.62,0:05:16.64,Default,,0000,0000,0000,,It was a strange fascinating\Nmetaphysical number
Dialogue: 0,0:05:16.64,0:05:18.30,Default,,0000,0000,0000,,that kept showing up.
Dialogue: 0,0:05:18.30,0:05:20.94,Default,,0000,0000,0000,,So since this number was so\Nfundamental to our universe,
Dialogue: 0,0:05:20.94,0:05:23.50,Default,,0000,0000,0000,,because the circle is so\Nfundamental to our universe,
Dialogue: 0,0:05:23.50,0:05:26.68,Default,,0000,0000,0000,,and it just showed up\Nfor every circle.
Dialogue: 0,0:05:26.68,0:05:28.86,Default,,0000,0000,0000,,The ratio of the circumference\Nof the diameter was this
Dialogue: 0,0:05:28.86,0:05:32.39,Default,,0000,0000,0000,,kind of magical number,\Nthey gave it a name.
Dialogue: 0,0:05:32.39,0:05:37.58,Default,,0000,0000,0000,,They called it pi, or you could\Njust give it the Latin or the
Dialogue: 0,0:05:37.58,0:05:41.88,Default,,0000,0000,0000,,Greek letter pi --\Njust like that.
Dialogue: 0,0:05:41.88,0:05:45.09,Default,,0000,0000,0000,,That represents this number\Nwhich is arguably the most
Dialogue: 0,0:05:45.09,0:05:46.79,Default,,0000,0000,0000,,fascinating number\Nin our universe.
Dialogue: 0,0:05:46.79,0:05:50.43,Default,,0000,0000,0000,,It first shows up as the ratio\Nof the circumference to the
Dialogue: 0,0:05:50.43,0:05:54.07,Default,,0000,0000,0000,,diameter, but you're going to\Nlearn as you go through your
Dialogue: 0,0:05:54.07,0:05:57.16,Default,,0000,0000,0000,,mathematical journey, that\Nit shows up everywhere.
Dialogue: 0,0:05:57.16,0:05:59.50,Default,,0000,0000,0000,,It's one of these fundamental\Nthings about the universe that
Dialogue: 0,0:05:59.50,0:06:03.06,Default,,0000,0000,0000,,just makes you think that\Nthere's some order to it.
Dialogue: 0,0:06:03.06,0:06:07.75,Default,,0000,0000,0000,,But anyway, how can we\Nuse this in I guess
Dialogue: 0,0:06:07.75,0:06:09.33,Default,,0000,0000,0000,,our basic mathematics?
Dialogue: 0,0:06:09.33,0:06:12.49,Default,,0000,0000,0000,,So we know, or I'm telling you,\Nthat the ratio of the
Dialogue: 0,0:06:12.49,0:06:19.42,Default,,0000,0000,0000,,circumference to the diameter\N-- when I say the ratio,
Dialogue: 0,0:06:19.42,0:06:21.39,Default,,0000,0000,0000,,literally I'm just saying if\Nyou divide the circumference by
Dialogue: 0,0:06:21.39,0:06:28.40,Default,,0000,0000,0000,,the diameter, you're\Ngoing to get pi.
Dialogue: 0,0:06:28.40,0:06:29.50,Default,,0000,0000,0000,,Pi is just this number.
Dialogue: 0,0:06:29.50,0:06:33.57,Default,,0000,0000,0000,,I could write 3.14159 and just\Nkeep going on and on and on,
Dialogue: 0,0:06:33.57,0:06:35.95,Default,,0000,0000,0000,,but that would be a waste of\Nspace and it would just be hard
Dialogue: 0,0:06:35.95,0:06:38.57,Default,,0000,0000,0000,,to deal with, so people just\Nwrite this Greek
Dialogue: 0,0:06:38.57,0:06:40.33,Default,,0000,0000,0000,,letter pi there.
Dialogue: 0,0:06:40.33,0:06:41.85,Default,,0000,0000,0000,,So, how can we relate this?
Dialogue: 0,0:06:41.85,0:06:44.92,Default,,0000,0000,0000,,We can multiply both sides of\Nthis by the diameter and we
Dialogue: 0,0:06:44.92,0:06:48.64,Default,,0000,0000,0000,,could say that the\Ncircumference is equal to pi
Dialogue: 0,0:06:48.64,0:06:50.82,Default,,0000,0000,0000,,times the diameter.
Dialogue: 0,0:06:50.82,0:06:55.57,Default,,0000,0000,0000,,Or since the diameter is equal\Nto 2 times the radius, we could
Dialogue: 0,0:06:55.57,0:06:59.42,Default,,0000,0000,0000,,say that the circumference is\Nequal to pi times 2
Dialogue: 0,0:06:59.42,0:07:00.36,Default,,0000,0000,0000,,times the radius.
Dialogue: 0,0:07:00.36,0:07:03.45,Default,,0000,0000,0000,,Or the form that you're\Nmost likely to see it,
Dialogue: 0,0:07:03.45,0:07:07.36,Default,,0000,0000,0000,,it's equal to 2 pi r.
Dialogue: 0,0:07:07.36,0:07:11.22,Default,,0000,0000,0000,,So let's see if we can apply\Nthat to some problems.
Dialogue: 0,0:07:11.22,0:07:17.24,Default,,0000,0000,0000,,So let's say I have a circle\Njust like that, and I were to
Dialogue: 0,0:07:17.24,0:07:22.60,Default,,0000,0000,0000,,tell you it has a radius --\Nit's radius right there is 3.
Dialogue: 0,0:07:22.60,0:07:28.82,Default,,0000,0000,0000,,So, 3 -- let me write this down\N-- so the radius is equal to 3.
Dialogue: 0,0:07:28.82,0:07:32.31,Default,,0000,0000,0000,,Maybe it's 3 meters --\Nput some units in there.
Dialogue: 0,0:07:32.31,0:07:34.66,Default,,0000,0000,0000,,What is the circumference\Nof the circle?
Dialogue: 0,0:07:34.66,0:07:38.18,Default,,0000,0000,0000,,The circumference is equal to\N2 times pi times the radius.
Dialogue: 0,0:07:38.18,0:07:42.09,Default,,0000,0000,0000,,So it's going to be equal to 2\Ntimes pi times the radius,
Dialogue: 0,0:07:42.09,0:07:47.28,Default,,0000,0000,0000,,times 3 meters, which is\Nequal to 6 meters times
Dialogue: 0,0:07:47.28,0:07:49.52,Default,,0000,0000,0000,,pi or 6 pi meters.
Dialogue: 0,0:07:49.52,0:07:52.43,Default,,0000,0000,0000,,6 pi meters.
Dialogue: 0,0:07:52.43,0:07:53.74,Default,,0000,0000,0000,,Now I could multiply this out.
Dialogue: 0,0:07:53.74,0:07:55.90,Default,,0000,0000,0000,,Remember pi is just a number.
Dialogue: 0,0:07:55.90,0:07:59.68,Default,,0000,0000,0000,,Pi is 3.14159 going\Non and on and on.
Dialogue: 0,0:07:59.68,0:08:03.46,Default,,0000,0000,0000,,So if I multiply 6 times that,\Nmaybe I'll get 18 point
Dialogue: 0,0:08:03.46,0:08:05.60,Default,,0000,0000,0000,,something something something.
Dialogue: 0,0:08:05.60,0:08:07.85,Default,,0000,0000,0000,,If you have your calculator you\Nmight want to do it, but for
Dialogue: 0,0:08:07.85,0:08:10.49,Default,,0000,0000,0000,,simplicity people just tend to\Nleave our numbers
Dialogue: 0,0:08:10.49,0:08:12.12,Default,,0000,0000,0000,,in terms of pi.
Dialogue: 0,0:08:12.12,0:08:14.02,Default,,0000,0000,0000,,Now I don't know what this is\Nif you multiply 6 times
Dialogue: 0,0:08:14.02,0:08:18.51,Default,,0000,0000,0000,,3.14159, I don't know if you\Nget something close to 19 or
Dialogue: 0,0:08:18.51,0:08:20.91,Default,,0000,0000,0000,,18, maybe it's approximately\N18 point something
Dialogue: 0,0:08:20.91,0:08:21.72,Default,,0000,0000,0000,,something something.
Dialogue: 0,0:08:21.72,0:08:23.45,Default,,0000,0000,0000,,I don't have my calculator\Nin front of me.
Dialogue: 0,0:08:23.45,0:08:25.30,Default,,0000,0000,0000,,But instead of writing\Nthat number, you just
Dialogue: 0,0:08:25.30,0:08:27.06,Default,,0000,0000,0000,,write 6 pi there.
Dialogue: 0,0:08:27.06,0:08:29.77,Default,,0000,0000,0000,,Actually, I think it\Nwouldn't quite cross the
Dialogue: 0,0:08:29.77,0:08:31.43,Default,,0000,0000,0000,,threshold to 19 yet.
Dialogue: 0,0:08:31.43,0:08:33.77,Default,,0000,0000,0000,,Now, let's ask\Nanother question.
Dialogue: 0,0:08:33.77,0:08:35.27,Default,,0000,0000,0000,,What is the diameter\Nof the circle?
Dialogue: 0,0:08:38.58,0:08:42.69,Default,,0000,0000,0000,,Well if this radius is 3, the\Ndiameter is just twice that.
Dialogue: 0,0:08:42.69,0:08:45.73,Default,,0000,0000,0000,,So it's just going to be 3\Ntimes 2 or 3 plus 3, which
Dialogue: 0,0:08:45.73,0:08:47.17,Default,,0000,0000,0000,,is equal to 6 meters.
Dialogue: 0,0:08:47.17,0:08:50.75,Default,,0000,0000,0000,,So the circumference is 6 pi\Nmeters, the diameter is 6
Dialogue: 0,0:08:50.75,0:08:53.62,Default,,0000,0000,0000,,meters, the radius is 3 meters.
Dialogue: 0,0:08:53.62,0:08:55.11,Default,,0000,0000,0000,,Now let's go the other way.
Dialogue: 0,0:08:55.11,0:08:57.31,Default,,0000,0000,0000,,Let's say I have\Nanother circle.
Dialogue: 0,0:08:57.31,0:09:01.22,Default,,0000,0000,0000,,Let's say I have\Nanother circle here.
Dialogue: 0,0:09:01.22,0:09:04.62,Default,,0000,0000,0000,,And I were to tell you that\Nits circumference is equal
Dialogue: 0,0:09:04.62,0:09:08.56,Default,,0000,0000,0000,,to 10 meters -- that's the\Ncircumference of the circle.
Dialogue: 0,0:09:08.56,0:09:10.99,Default,,0000,0000,0000,,If you were to put a tape\Nmeasure to go around it and
Dialogue: 0,0:09:10.99,0:09:18.37,Default,,0000,0000,0000,,someone were to ask you what is\Nthe diameter of the circle?
Dialogue: 0,0:09:18.37,0:09:22.81,Default,,0000,0000,0000,,Well, we know that the diameter\Ntimes pi, we know that pi times
Dialogue: 0,0:09:22.81,0:09:26.83,Default,,0000,0000,0000,,the diameter is equal to\Nthe circumference; is
Dialogue: 0,0:09:26.83,0:09:28.70,Default,,0000,0000,0000,,equal to 10 meters.
Dialogue: 0,0:09:28.70,0:09:31.02,Default,,0000,0000,0000,,So to solve for this we would\Njust divide both sides
Dialogue: 0,0:09:31.02,0:09:32.52,Default,,0000,0000,0000,,of this equation by pi.
Dialogue: 0,0:09:32.52,0:09:35.86,Default,,0000,0000,0000,,The diameter would equal\N10 meters over pi or
Dialogue: 0,0:09:35.86,0:09:38.71,Default,,0000,0000,0000,,10 over pi meters.
Dialogue: 0,0:09:38.71,0:09:40.02,Default,,0000,0000,0000,,And that is just a number.
Dialogue: 0,0:09:40.02,0:09:42.54,Default,,0000,0000,0000,,If you have your calculator,\Nyou could actually divide 10
Dialogue: 0,0:09:42.54,0:09:46.03,Default,,0000,0000,0000,,divided by 3.14159, you're\Ngoing to get 3 point something
Dialogue: 0,0:09:46.03,0:09:47.50,Default,,0000,0000,0000,,something something meters.
Dialogue: 0,0:09:47.50,0:09:48.96,Default,,0000,0000,0000,,I can't do it in my head.
Dialogue: 0,0:09:48.96,0:09:50.07,Default,,0000,0000,0000,,But this is just a number.
Dialogue: 0,0:09:50.07,0:09:53.32,Default,,0000,0000,0000,,But for simplicity we often\Njust leave it that way.
Dialogue: 0,0:09:53.32,0:09:55.27,Default,,0000,0000,0000,,Now what is the radius?
Dialogue: 0,0:09:55.27,0:09:58.59,Default,,0000,0000,0000,,Well, the radius is equal\Nto 1/2 the diameter.
Dialogue: 0,0:09:58.59,0:10:02.87,Default,,0000,0000,0000,,So this whole distance right\Nhere is 10 over pi meters.
Dialogue: 0,0:10:02.87,0:10:06.23,Default,,0000,0000,0000,,If we just 1/2 of that, if\Nwe just want the radius, we
Dialogue: 0,0:10:06.23,0:10:07.58,Default,,0000,0000,0000,,just multiply it times 1/2.
Dialogue: 0,0:10:07.58,0:10:13.16,Default,,0000,0000,0000,,So you have 1/2 times 10 over\Npi, which is equal to 1/2 times
Dialogue: 0,0:10:13.16,0:10:16.77,Default,,0000,0000,0000,,10, or you just divide the\Nnumerator and the
Dialogue: 0,0:10:16.77,0:10:18.14,Default,,0000,0000,0000,,denominator by 2.
Dialogue: 0,0:10:18.14,0:10:21.13,Default,,0000,0000,0000,,You get 5 there, so\Nyou get 5 over pi.
Dialogue: 0,0:10:21.13,0:10:23.89,Default,,0000,0000,0000,,So the radius over\Nhere is 5 over pi.
Dialogue: 0,0:10:23.89,0:10:25.69,Default,,0000,0000,0000,,Nothing super fancy about this.
Dialogue: 0,0:10:25.69,0:10:29.76,Default,,0000,0000,0000,,I think the thing that confuses\Npeople the most is to just
Dialogue: 0,0:10:29.76,0:10:31.82,Default,,0000,0000,0000,,realize that pi is a number.
Dialogue: 0,0:10:31.82,0:10:38.64,Default,,0000,0000,0000,,Pi is just 3.14159 and it just\Nkeeps going on and on and on.
Dialogue: 0,0:10:38.64,0:10:41.95,Default,,0000,0000,0000,,There's actually thousands of\Nbooks written about pi, so
Dialogue: 0,0:10:41.95,0:10:45.10,Default,,0000,0000,0000,,it's not like -- I don't know\Nif there's thousands, I'm
Dialogue: 0,0:10:45.10,0:10:48.34,Default,,0000,0000,0000,,exaggerating, but you could\Nwrite books about this number.
Dialogue: 0,0:10:48.34,0:10:49.34,Default,,0000,0000,0000,,But it's just a number.
Dialogue: 0,0:10:49.34,0:10:52.48,Default,,0000,0000,0000,,It's a very special number, and\Nif you wanted to write it in a
Dialogue: 0,0:10:52.48,0:10:54.39,Default,,0000,0000,0000,,way that you're used to writing\Nnumbers, you could literally
Dialogue: 0,0:10:54.39,0:10:55.68,Default,,0000,0000,0000,,just multiply this out.
Dialogue: 0,0:10:55.68,0:10:58.53,Default,,0000,0000,0000,,But most the time people just\Nrealize they like leaving
Dialogue: 0,0:10:58.53,0:11:00.64,Default,,0000,0000,0000,,things in terms of pi.
Dialogue: 0,0:11:00.64,0:11:01.68,Default,,0000,0000,0000,,Anyway, I'll leave you there.
Dialogue: 0,0:11:01.68,0:11:05.09,Default,,0000,0000,0000,,In the next video we'll figure\Nout the area of a circle.