[Script Info]
Title: 
[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:00.00,0:00:00.62,Default,,0000,0000,0000,,
Dialogue: 0,0:00:00.62,0:00:03.12,Default,,0000,0000,0000,,So let's say that this is\Nan equilateral triangle.
Dialogue: 0,0:00:03.12,0:00:05.08,Default,,0000,0000,0000,,And what I want to do is\Nmake another shape out
Dialogue: 0,0:00:05.08,0:00:06.20,Default,,0000,0000,0000,,of this equilateral triangle.
Dialogue: 0,0:00:06.20,0:00:07.62,Default,,0000,0000,0000,,And I'm going to\Ndo that by taking
Dialogue: 0,0:00:07.62,0:00:09.37,Default,,0000,0000,0000,,each of the sides\Nof this triangle,
Dialogue: 0,0:00:09.37,0:00:11.85,Default,,0000,0000,0000,,and divide them into\Nthree equal sections.
Dialogue: 0,0:00:11.86,0:00:15.01,Default,,0000,0000,0000,,
Dialogue: 0,0:00:15.01,0:00:18.74,Default,,0000,0000,0000,,So my equilateral triangle\Nwasn't drawn super ideally.
Dialogue: 0,0:00:18.74,0:00:20.11,Default,,0000,0000,0000,,But I think you'll\Nget the point.
Dialogue: 0,0:00:20.11,0:00:21.81,Default,,0000,0000,0000,,And in the middle section\NI want to construct
Dialogue: 0,0:00:21.81,0:00:23.10,Default,,0000,0000,0000,,another equilateral triangle.
Dialogue: 0,0:00:23.10,0:00:29.51,Default,,0000,0000,0000,,
Dialogue: 0,0:00:29.51,0:00:32.68,Default,,0000,0000,0000,,So it's going to look\Nsomething like this.
Dialogue: 0,0:00:32.68,0:00:35.09,Default,,0000,0000,0000,,And then right\Nover here I'm going
Dialogue: 0,0:00:35.09,0:00:37.74,Default,,0000,0000,0000,,to put another\Nequilateral triangle.
Dialogue: 0,0:00:37.74,0:00:40.27,Default,,0000,0000,0000,,And so now I went from\Nthat equilateral triangle
Dialogue: 0,0:00:40.27,0:00:43.25,Default,,0000,0000,0000,,to something that's looking\Nlike a star, or a Star of David.
Dialogue: 0,0:00:43.25,0:00:44.67,Default,,0000,0000,0000,,And then I'm going\Nto do it again.
Dialogue: 0,0:00:44.67,0:00:46.70,Default,,0000,0000,0000,,So each of the sides\Nnow I'm going to divide
Dialogue: 0,0:00:46.70,0:00:48.41,Default,,0000,0000,0000,,into three equal sides.
Dialogue: 0,0:00:48.41,0:00:50.00,Default,,0000,0000,0000,,And in that middle\Nsegment I'm going
Dialogue: 0,0:00:50.00,0:00:51.30,Default,,0000,0000,0000,,to put an equilateral triangle.
Dialogue: 0,0:00:51.30,0:00:54.13,Default,,0000,0000,0000,,
Dialogue: 0,0:00:54.13,0:00:56.37,Default,,0000,0000,0000,,So in the middle\Nsegment I'm going
Dialogue: 0,0:00:56.37,0:00:59.35,Default,,0000,0000,0000,,to put an equilateral triangle.
Dialogue: 0,0:00:59.35,0:01:01.95,Default,,0000,0000,0000,,So I'm going to do it for\Nevery one of the sides.
Dialogue: 0,0:01:01.95,0:01:05.60,Default,,0000,0000,0000,,So let me do it right there.
Dialogue: 0,0:01:05.60,0:01:06.76,Default,,0000,0000,0000,,And then right there.
Dialogue: 0,0:01:06.76,0:01:10.03,Default,,0000,0000,0000,,I think you get the idea,\Nbut I want to make it clear.
Dialogue: 0,0:01:10.03,0:01:15.26,Default,,0000,0000,0000,,So let me just, so then like\Nthat, and then like that,
Dialogue: 0,0:01:15.26,0:01:20.06,Default,,0000,0000,0000,,like that, and then almost\Ndone for this iteration.
Dialogue: 0,0:01:20.06,0:01:21.84,Default,,0000,0000,0000,,This pass.
Dialogue: 0,0:01:21.84,0:01:23.26,Default,,0000,0000,0000,,And it'll look like that.
Dialogue: 0,0:01:23.26,0:01:24.33,Default,,0000,0000,0000,,Then I could do it again.
Dialogue: 0,0:01:24.33,0:01:26.66,Default,,0000,0000,0000,,Each of the segments I can\Ndivide into three equal sides
Dialogue: 0,0:01:26.66,0:01:28.26,Default,,0000,0000,0000,,and draw another\Nequilateral triangle.
Dialogue: 0,0:01:28.26,0:01:31.44,Default,,0000,0000,0000,,So I could just there,\Nthere, there, there.
Dialogue: 0,0:01:31.44,0:01:33.26,Default,,0000,0000,0000,,I think you see\Nwhere this is going.
Dialogue: 0,0:01:33.26,0:01:37.53,Default,,0000,0000,0000,,And I could keep going\Non forever and forever.
Dialogue: 0,0:01:37.53,0:01:38.95,Default,,0000,0000,0000,,So what I want to\Ndo in this video
Dialogue: 0,0:01:38.95,0:01:40.93,Default,,0000,0000,0000,,is think about\Nwhat's going on here.
Dialogue: 0,0:01:40.93,0:01:43.00,Default,,0000,0000,0000,,And what I'm actually\Ndrawing, if we just
Dialogue: 0,0:01:43.00,0:01:45.00,Default,,0000,0000,0000,,keep on doing this\Nforever and forever,
Dialogue: 0,0:01:45.00,0:01:47.99,Default,,0000,0000,0000,,every side, every iteration,\Nwe look at each side,
Dialogue: 0,0:01:47.99,0:01:49.52,Default,,0000,0000,0000,,we divide into\Nthree equal sides.
Dialogue: 0,0:01:49.52,0:01:52.18,Default,,0000,0000,0000,,And then the next iteration,\Nor three equal segments,
Dialogue: 0,0:01:52.18,0:01:53.76,Default,,0000,0000,0000,,the next iteration,\Nthe middle segment
Dialogue: 0,0:01:53.76,0:01:55.80,Default,,0000,0000,0000,,we turn to another\Nequilateral triangle.
Dialogue: 0,0:01:55.80,0:01:57.59,Default,,0000,0000,0000,,This shape that we're\Ndescribing right here
Dialogue: 0,0:01:57.59,0:01:59.95,Default,,0000,0000,0000,,is called a Koch snowflake.
Dialogue: 0,0:01:59.95,0:02:03.30,Default,,0000,0000,0000,,And I'm sure I'm\Nmispronouncing the Koch part.
Dialogue: 0,0:02:03.30,0:02:05.48,Default,,0000,0000,0000,,A Koch snowflake,\Nand it was first
Dialogue: 0,0:02:05.48,0:02:08.23,Default,,0000,0000,0000,,described by this gentleman\Nright over here, who
Dialogue: 0,0:02:08.23,0:02:11.27,Default,,0000,0000,0000,,is a Swedish mathematician,\NNiels Fabian Helge von
Dialogue: 0,0:02:11.27,0:02:14.61,Default,,0000,0000,0000,,Koch, who I'm sure\NI'm mispronouncing it.
Dialogue: 0,0:02:14.61,0:02:17.74,Default,,0000,0000,0000,,And this was one of the\Nearliest described fractals.
Dialogue: 0,0:02:17.74,0:02:19.69,Default,,0000,0000,0000,,So this is a fractal.
Dialogue: 0,0:02:19.69,0:02:22.12,Default,,0000,0000,0000,,And the reason why it\Nis considered a fractal
Dialogue: 0,0:02:22.12,0:02:24.89,Default,,0000,0000,0000,,is that it looks the same,\Nor it looks very similar,
Dialogue: 0,0:02:24.89,0:02:26.63,Default,,0000,0000,0000,,on any scale you look at it.
Dialogue: 0,0:02:26.63,0:02:29.59,Default,,0000,0000,0000,,So when you look at it at this\Nscale, so if you look at this,
Dialogue: 0,0:02:29.59,0:02:31.09,Default,,0000,0000,0000,,it like you see a\Nbunch of triangles
Dialogue: 0,0:02:31.09,0:02:32.32,Default,,0000,0000,0000,,with some bumps on it.
Dialogue: 0,0:02:32.32,0:02:35.13,Default,,0000,0000,0000,,But then if you were to\Nzoom in right over there,
Dialogue: 0,0:02:35.13,0:02:38.19,Default,,0000,0000,0000,,then you would still see\Nthat same type of pattern.
Dialogue: 0,0:02:38.19,0:02:39.93,Default,,0000,0000,0000,,And then if you were\Nto zoom in again,
Dialogue: 0,0:02:39.93,0:02:41.30,Default,,0000,0000,0000,,you would see it\Nagain and again.
Dialogue: 0,0:02:41.30,0:02:43.32,Default,,0000,0000,0000,,So a fractal is anything\Nthat at on any scale,
Dialogue: 0,0:02:43.32,0:02:46.77,Default,,0000,0000,0000,,on any level of zoom, it kind\Nof looks roughly the same.
Dialogue: 0,0:02:46.77,0:02:48.27,Default,,0000,0000,0000,,So that's why it's\Ncalled a fractal.
Dialogue: 0,0:02:48.27,0:02:49.79,Default,,0000,0000,0000,,Now what's particularly\Ninteresting,
Dialogue: 0,0:02:49.79,0:02:53.70,Default,,0000,0000,0000,,and why I'm putting it at this\Npoint in the geometry playlist,
Dialogue: 0,0:02:53.70,0:02:56.42,Default,,0000,0000,0000,,is that this actually has\Nan infinite perimeter.
Dialogue: 0,0:02:56.42,0:02:58.50,Default,,0000,0000,0000,,If you were to keep doing\Nit, if you were actually
Dialogue: 0,0:02:58.50,0:03:00.69,Default,,0000,0000,0000,,to make the Koch\Nsnowflake, where
Dialogue: 0,0:03:00.69,0:03:04.13,Default,,0000,0000,0000,,you keep an infinite number\Nof times on every smaller
Dialogue: 0,0:03:04.13,0:03:05.84,Default,,0000,0000,0000,,little triangle\Nhere, you keep adding
Dialogue: 0,0:03:05.84,0:03:09.75,Default,,0000,0000,0000,,another equilateral\Ntriangle on its side.
Dialogue: 0,0:03:09.75,0:03:11.67,Default,,0000,0000,0000,,And to show that it has\Nan infinite perimeter,
Dialogue: 0,0:03:11.67,0:03:13.89,Default,,0000,0000,0000,,let's just consider\None side over here.
Dialogue: 0,0:03:13.89,0:03:15.96,Default,,0000,0000,0000,,So let's say that\Nthis side, so let's
Dialogue: 0,0:03:15.96,0:03:18.02,Default,,0000,0000,0000,,say we're starting\Nright when we started
Dialogue: 0,0:03:18.02,0:03:19.94,Default,,0000,0000,0000,,with that original\Ntriangle, that's that side.
Dialogue: 0,0:03:19.94,0:03:21.56,Default,,0000,0000,0000,,Let's say it has length s.
Dialogue: 0,0:03:21.56,0:03:23.56,Default,,0000,0000,0000,,And then we divide it\Ninto three equal segments.
Dialogue: 0,0:03:23.56,0:03:26.17,Default,,0000,0000,0000,,
Dialogue: 0,0:03:26.17,0:03:29.91,Default,,0000,0000,0000,,So those are going to\Nbe s/3, s/3-- actually,
Dialogue: 0,0:03:29.91,0:03:31.67,Default,,0000,0000,0000,,let me write it this way.
Dialogue: 0,0:03:31.67,0:03:36.17,Default,,0000,0000,0000,,s/3, s/3, and s/3.
Dialogue: 0,0:03:36.17,0:03:38.73,Default,,0000,0000,0000,,And in the middle segment, you\Nmake an equilateral triangle.
Dialogue: 0,0:03:38.73,0:03:41.84,Default,,0000,0000,0000,,
Dialogue: 0,0:03:41.84,0:03:44.46,Default,,0000,0000,0000,,So each of these sides\Nare going to be s/3.
Dialogue: 0,0:03:44.46,0:03:47.29,Default,,0000,0000,0000,,s/3, s/3.
Dialogue: 0,0:03:47.29,0:03:51.47,Default,,0000,0000,0000,,And now the length of this new\Npart-- I can't call it a line
Dialogue: 0,0:03:51.47,0:03:53.18,Default,,0000,0000,0000,,anymore, because it\Nhas this bump in it--
Dialogue: 0,0:03:53.18,0:03:57.58,Default,,0000,0000,0000,,the length of this part right\Nover here, this side, now
Dialogue: 0,0:03:57.58,0:04:01.51,Default,,0000,0000,0000,,doesn't have just a length\Nof s, it is now s/3 times 4.
Dialogue: 0,0:04:01.51,0:04:03.16,Default,,0000,0000,0000,,Before it was s/3 times 3.
Dialogue: 0,0:04:03.16,0:04:07.73,Default,,0000,0000,0000,,Now you have 1, 2, 3, 4\Nsegments that are s/3.
Dialogue: 0,0:04:07.73,0:04:10.40,Default,,0000,0000,0000,,So now, after one\Ntime, after one pace,
Dialogue: 0,0:04:10.40,0:04:15.16,Default,,0000,0000,0000,,after one time of doing\Nthis adding triangles,
Dialogue: 0,0:04:15.16,0:04:17.48,Default,,0000,0000,0000,,our new side, after\Nwe add that bump,
Dialogue: 0,0:04:17.48,0:04:20.76,Default,,0000,0000,0000,,is going to be four times s/3.
Dialogue: 0,0:04:20.76,0:04:23.73,Default,,0000,0000,0000,,Or it equals 4/3 s.
Dialogue: 0,0:04:23.73,0:04:28.67,Default,,0000,0000,0000,,So if our original\Nperimeter when it was just
Dialogue: 0,0:04:28.67,0:04:31.10,Default,,0000,0000,0000,,a triangle is p sub 0.
Dialogue: 0,0:04:31.10,0:04:33.93,Default,,0000,0000,0000,,After one pass, after\Nwe add one set of bumps,
Dialogue: 0,0:04:33.93,0:04:39.84,Default,,0000,0000,0000,,then our perimeter is going to\Nbe 4/3 times the original one.
Dialogue: 0,0:04:39.84,0:04:42.63,Default,,0000,0000,0000,,Because each of the sides are\Ngoing to be 4/3 bigger now.
Dialogue: 0,0:04:42.63,0:04:44.61,Default,,0000,0000,0000,,So this was made\Nup of three sides.
Dialogue: 0,0:04:44.61,0:04:46.87,Default,,0000,0000,0000,,Now each of those sides\Nare going to be 4/3 bigger.
Dialogue: 0,0:04:46.87,0:04:49.40,Default,,0000,0000,0000,,So the new perimeter's\Ngoing to be 4/3 times that.
Dialogue: 0,0:04:49.40,0:04:51.68,Default,,0000,0000,0000,,And then when we take\Na second pass on it,
Dialogue: 0,0:04:51.68,0:04:54.74,Default,,0000,0000,0000,,it's going to be 4/3\Ntimes this first pass.
Dialogue: 0,0:04:54.74,0:04:57.65,Default,,0000,0000,0000,,So every pass you take,\Nit's getting 4/3 bigger.
Dialogue: 0,0:04:57.65,0:05:00.38,Default,,0000,0000,0000,,Or it's getting, I guess,\Na 1/3 bigger on every,
Dialogue: 0,0:05:00.38,0:05:03.44,Default,,0000,0000,0000,,it's getting 4/3\Nthe previous pass.
Dialogue: 0,0:05:03.44,0:05:05.52,Default,,0000,0000,0000,,And so if you do that an\Ninfinite number of times,
Dialogue: 0,0:05:05.52,0:05:09.22,Default,,0000,0000,0000,,if you multiply any\Nnumber by 4/3 an
Dialogue: 0,0:05:09.22,0:05:11.18,Default,,0000,0000,0000,,infinite number of\Ntimes, you're going
Dialogue: 0,0:05:11.18,0:05:13.82,Default,,0000,0000,0000,,to get an infinite number\Nof infinite length.
Dialogue: 0,0:05:13.82,0:05:16.27,Default,,0000,0000,0000,,So P infinity.
Dialogue: 0,0:05:16.27,0:05:18.69,Default,,0000,0000,0000,,The perimeter, if you do this\Nan infinite number of times,
Dialogue: 0,0:05:18.69,0:05:20.37,Default,,0000,0000,0000,,is infinite.
Dialogue: 0,0:05:20.37,0:05:21.92,Default,,0000,0000,0000,,Now that by itself\Nis kind of cool,
Dialogue: 0,0:05:21.92,0:05:24.46,Default,,0000,0000,0000,,just to think about something\Nthat has an infinite perimeter.
Dialogue: 0,0:05:24.46,0:05:28.19,Default,,0000,0000,0000,,But what's even neater is that\Nit actually has a finite area.
Dialogue: 0,0:05:28.19,0:05:29.90,Default,,0000,0000,0000,,And when I say a finite\Narea, it actually
Dialogue: 0,0:05:29.90,0:05:32.16,Default,,0000,0000,0000,,covers a bounded\Namount of space.
Dialogue: 0,0:05:32.16,0:05:34.08,Default,,0000,0000,0000,,And I could actually\Ndraw a shape around this,
Dialogue: 0,0:05:34.08,0:05:36.12,Default,,0000,0000,0000,,and this thing will\Nnever expand beyond that.
Dialogue: 0,0:05:36.12,0:05:37.62,Default,,0000,0000,0000,,And to think about\Nit, I'm not going
Dialogue: 0,0:05:37.62,0:05:39.24,Default,,0000,0000,0000,,to do a really\Nformal proof, just
Dialogue: 0,0:05:39.24,0:05:42.52,Default,,0000,0000,0000,,think about it, what happens\Non any one of these sides.
Dialogue: 0,0:05:42.52,0:05:44.63,Default,,0000,0000,0000,,So on that first pass we\Nhave that this triangle
Dialogue: 0,0:05:44.63,0:05:46.01,Default,,0000,0000,0000,,gets popped out.
Dialogue: 0,0:05:46.01,0:05:49.34,Default,,0000,0000,0000,,And then, if you think about it,\Nif you just draw what happens,
Dialogue: 0,0:05:49.34,0:05:51.68,Default,,0000,0000,0000,,the next iteration you draw\Nthese two triangles right
Dialogue: 0,0:05:51.68,0:05:52.18,Default,,0000,0000,0000,,over there.
Dialogue: 0,0:05:52.18,0:05:54.27,Default,,0000,0000,0000,,And these two characters\Nright over there.
Dialogue: 0,0:05:54.27,0:05:56.33,Default,,0000,0000,0000,,And then you put some\Ntriangles over here,
Dialogue: 0,0:05:56.33,0:05:58.52,Default,,0000,0000,0000,,and here, and here,\Nand here, and here.
Dialogue: 0,0:05:58.52,0:05:59.70,Default,,0000,0000,0000,,So on and so forth.
Dialogue: 0,0:05:59.70,0:06:01.96,Default,,0000,0000,0000,,But notice, you can keep\Nadding more and more.
Dialogue: 0,0:06:01.96,0:06:04.63,Default,,0000,0000,0000,,You can add essentially an\Ninfinite number of these bumps,
Dialogue: 0,0:06:04.63,0:06:07.38,Default,,0000,0000,0000,,but you're never going to\Ngo past this original point.
Dialogue: 0,0:06:07.38,0:06:10.49,Default,,0000,0000,0000,,And the same thing is going\Nto be true on this side
Dialogue: 0,0:06:10.49,0:06:11.54,Default,,0000,0000,0000,,right over here.
Dialogue: 0,0:06:11.54,0:06:14.24,Default,,0000,0000,0000,,It's also going to be true\Nof this side over here.
Dialogue: 0,0:06:14.24,0:06:16.92,Default,,0000,0000,0000,,Also going to be true\Nat this side over here.
Dialogue: 0,0:06:16.92,0:06:19.68,Default,,0000,0000,0000,,Also going to be true\Nthis side over there.
Dialogue: 0,0:06:19.68,0:06:22.13,Default,,0000,0000,0000,,And then also going to be\Ntrue that side over there.
Dialogue: 0,0:06:22.13,0:06:24.75,Default,,0000,0000,0000,,So even if you do this an\Ninfinite number of times,
Dialogue: 0,0:06:24.75,0:06:27.45,Default,,0000,0000,0000,,this shape, this Koch\Nsnowflake will never
Dialogue: 0,0:06:27.45,0:06:30.43,Default,,0000,0000,0000,,have a larger area than\Nthis bounding hexagon.
Dialogue: 0,0:06:30.43,0:06:33.19,Default,,0000,0000,0000,,Or which will never have a\Nlarger area than a shape that
Dialogue: 0,0:06:33.19,0:06:34.34,Default,,0000,0000,0000,,looks something like that.
Dialogue: 0,0:06:34.34,0:06:35.92,Default,,0000,0000,0000,,I'm just kind of\Ndrawing an arbitrary,
Dialogue: 0,0:06:35.92,0:06:38.07,Default,,0000,0000,0000,,well I want to make it\Noutside of the hexagon,
Dialogue: 0,0:06:38.07,0:06:40.85,Default,,0000,0000,0000,,I could put a circle\Noutside of it.
Dialogue: 0,0:06:40.85,0:06:44.69,Default,,0000,0000,0000,,So this thing I drew in blue, or\Nthis hexagon I drew in magenta,
Dialogue: 0,0:06:44.69,0:06:47.05,Default,,0000,0000,0000,,those clearly have a fixed area.
Dialogue: 0,0:06:47.05,0:06:49.29,Default,,0000,0000,0000,,And this Koch snowflake\Nwill always be bounded.
Dialogue: 0,0:06:49.29,0:06:52.07,Default,,0000,0000,0000,,Even though you can add these\Nbumps an infinite number
Dialogue: 0,0:06:52.07,0:06:53.05,Default,,0000,0000,0000,,of times.
Dialogue: 0,0:06:53.05,0:06:55.06,Default,,0000,0000,0000,,So a bunch of really\Ncool things here.
Dialogue: 0,0:06:55.06,0:06:55.89,Default,,0000,0000,0000,,One, it's a fractal.
Dialogue: 0,0:06:55.89,0:06:58.88,Default,,0000,0000,0000,,You can keep zooming in\Nand it'll look the same.
Dialogue: 0,0:06:58.88,0:07:01.75,Default,,0000,0000,0000,,The other thing, infinite,\Ninfinite perimeter,
Dialogue: 0,0:07:01.75,0:07:04.79,Default,,0000,0000,0000,,and finite, finite area.
Dialogue: 0,0:07:04.79,0:07:06.12,Default,,0000,0000,0000,,Now you might say, wait Sal, OK.
Dialogue: 0,0:07:06.12,0:07:07.59,Default,,0000,0000,0000,,This is a very abstract thing.
Dialogue: 0,0:07:07.59,0:07:10.51,Default,,0000,0000,0000,,Things like this don't actually\Nexist in the real world.
Dialogue: 0,0:07:10.51,0:07:12.85,Default,,0000,0000,0000,,And there's a fun\Nthought experiment
Dialogue: 0,0:07:12.85,0:07:14.88,Default,,0000,0000,0000,,that people talk about\Nin the fractal world,
Dialogue: 0,0:07:14.88,0:07:17.54,Default,,0000,0000,0000,,and that's finding the\Nperimeter of England.
Dialogue: 0,0:07:17.54,0:07:19.39,Default,,0000,0000,0000,,Or you can actually\Ndo it with any island.
Dialogue: 0,0:07:19.39,0:07:21.02,Default,,0000,0000,0000,,And so England looks\Nsomething like--
Dialogue: 0,0:07:21.02,0:07:22.75,Default,,0000,0000,0000,,and I'm not an\Nexpert on, let's say
Dialogue: 0,0:07:22.75,0:07:24.60,Default,,0000,0000,0000,,it looks something\Nlike that-- so at first
Dialogue: 0,0:07:24.60,0:07:26.10,Default,,0000,0000,0000,,you might approximate\Nthe perimeter.
Dialogue: 0,0:07:26.10,0:07:28.33,Default,,0000,0000,0000,,And you might measure\Nthis distance,
Dialogue: 0,0:07:28.33,0:07:32.24,Default,,0000,0000,0000,,you might measure this\Ndistance, plus this distance,
Dialogue: 0,0:07:32.24,0:07:34.97,Default,,0000,0000,0000,,plus this distance, plus that\Ndistance, plus that distance,
Dialogue: 0,0:07:34.97,0:07:36.05,Default,,0000,0000,0000,,plus that distance.
Dialogue: 0,0:07:36.05,0:07:38.05,Default,,0000,0000,0000,,And you're like look, it\Nhas a finite perimeter.
Dialogue: 0,0:07:38.05,0:07:39.66,Default,,0000,0000,0000,,It clearly has a finite area.
Dialogue: 0,0:07:39.66,0:07:42.07,Default,,0000,0000,0000,,But you're like, look, that\Nhas a finite perimeter.
Dialogue: 0,0:07:42.07,0:07:43.61,Default,,0000,0000,0000,,But you're like, no,\Nwait that's not as good.
Dialogue: 0,0:07:43.61,0:07:45.61,Default,,0000,0000,0000,,You have to approximate it a\Nlittle bit better than that.
Dialogue: 0,0:07:45.61,0:07:47.07,Default,,0000,0000,0000,,Instead of doing\Nit that rough, you
Dialogue: 0,0:07:47.07,0:07:48.76,Default,,0000,0000,0000,,need to make a bunch\Nof smaller lines.
Dialogue: 0,0:07:48.76,0:07:50.47,Default,,0000,0000,0000,,You need to make a\Nbunch of smaller lines
Dialogue: 0,0:07:50.47,0:07:52.40,Default,,0000,0000,0000,,so you can hug the coast\Na little bit better.
Dialogue: 0,0:07:52.40,0:07:55.65,Default,,0000,0000,0000,,And you're like, OK, that's\Na much better approximation.
Dialogue: 0,0:07:55.65,0:07:57.73,Default,,0000,0000,0000,,But then, let's say you're\Nat some piece of coast,
Dialogue: 0,0:07:57.73,0:08:02.62,Default,,0000,0000,0000,,if we zoom in enough,\Nthe actual coast line
Dialogue: 0,0:08:02.62,0:08:04.49,Default,,0000,0000,0000,,is going to look\Nsomething like this.
Dialogue: 0,0:08:04.49,0:08:05.95,Default,,0000,0000,0000,,The actual coast\Nline will have all
Dialogue: 0,0:08:05.95,0:08:08.24,Default,,0000,0000,0000,,of these little divots in it.
Dialogue: 0,0:08:08.24,0:08:10.96,Default,,0000,0000,0000,,And essentially, when you did\Nthat first, when did this pass,
Dialogue: 0,0:08:10.96,0:08:13.29,Default,,0000,0000,0000,,you were just measuring that.
Dialogue: 0,0:08:13.29,0:08:15.75,Default,,0000,0000,0000,,And you're like, that's not\Nthe perimeter of the coastline.
Dialogue: 0,0:08:15.75,0:08:17.79,Default,,0000,0000,0000,,You're going to have to\Ndo many, many more sides.
Dialogue: 0,0:08:17.79,0:08:22.30,Default,,0000,0000,0000,,You're going to do something\Nlike this, to actually get
Dialogue: 0,0:08:22.30,0:08:25.75,Default,,0000,0000,0000,,the perimeter of the coast line.
Dialogue: 0,0:08:25.75,0:08:27.33,Default,,0000,0000,0000,,And you're just like,\Nhey, now that is
Dialogue: 0,0:08:27.33,0:08:29.18,Default,,0000,0000,0000,,a good approximation\Nfor the perimeter.
Dialogue: 0,0:08:29.18,0:08:31.72,Default,,0000,0000,0000,,But if you were to zoom in on\Nthat part of the coastline even
Dialogue: 0,0:08:31.72,0:08:34.54,Default,,0000,0000,0000,,more, it'll actually turn out\Nthat it won't look exactly
Dialogue: 0,0:08:34.54,0:08:35.43,Default,,0000,0000,0000,,like that.
Dialogue: 0,0:08:35.43,0:08:37.23,Default,,0000,0000,0000,,It'll actually come\Nin and out like this.
Dialogue: 0,0:08:37.23,0:08:39.23,Default,,0000,0000,0000,,Maybe it'll look\Nsomething like that.
Dialogue: 0,0:08:39.23,0:08:41.69,Default,,0000,0000,0000,,So instead of having these\Nrough lines that just measure it
Dialogue: 0,0:08:41.69,0:08:43.60,Default,,0000,0000,0000,,like that, you're going\Nto say, oh wait, no, I
Dialogue: 0,0:08:43.60,0:08:46.28,Default,,0000,0000,0000,,need to go a little bit closer\Nand hug it even tighter.
Dialogue: 0,0:08:46.28,0:08:48.39,Default,,0000,0000,0000,,And you can really keep\Non doing that until you
Dialogue: 0,0:08:48.39,0:08:50.56,Default,,0000,0000,0000,,get to the actual atomic level.
Dialogue: 0,0:08:50.56,0:08:55.30,Default,,0000,0000,0000,,So the actual coastline of\Nan island, or a continent,
Dialogue: 0,0:08:55.30,0:08:58.64,Default,,0000,0000,0000,,or anything, is actually\Nsomewhat kind of fractalish.
Dialogue: 0,0:08:58.64,0:09:00.76,Default,,0000,0000,0000,,And it is, you can\Nkind of think of it
Dialogue: 0,0:09:00.76,0:09:02.48,Default,,0000,0000,0000,,as having an almost\Ninfinite perimeter.
Dialogue: 0,0:09:02.48,0:09:04.06,Default,,0000,0000,0000,,Obviously at some\Npoint you're getting
Dialogue: 0,0:09:04.06,0:09:06.64,Default,,0000,0000,0000,,to kind of the atomic level,\Nso it won't quite be the same.
Dialogue: 0,0:09:06.64,0:09:08.45,Default,,0000,0000,0000,,But it's kind of\Nthe same phenomenon.
Dialogue: 0,0:09:08.45,0:09:11.42,Default,,0000,0000,0000,,It's an interesting thing\Nto actually think about.