[Script Info]
Title: 
[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:00.00,0:00:00.82,Default,,0000,0000,0000,,
Dialogue: 0,0:00:00.82,0:00:03.01,Default,,0000,0000,0000,,If someone walks up to you\Non the street and says,
Dialogue: 0,0:00:03.01,0:00:05.26,Default,,0000,0000,0000,,all right, I have a\Nchallenge for you.
Dialogue: 0,0:00:05.26,0:00:11.99,Default,,0000,0000,0000,,I want to construct a triangle\Nthat has sides of length 2.
Dialogue: 0,0:00:11.99,0:00:15.92,Default,,0000,0000,0000,,So sides of length-- let me\Nwrite this a little bit neater.
Dialogue: 0,0:00:15.92,0:00:21.05,Default,,0000,0000,0000,,Sides of length 2, 2, and 5.
Dialogue: 0,0:00:21.05,0:00:23.19,Default,,0000,0000,0000,,Can you do this?
Dialogue: 0,0:00:23.19,0:00:25.05,Default,,0000,0000,0000,,Well, let's try to do it.
Dialogue: 0,0:00:25.05,0:00:29.08,Default,,0000,0000,0000,,And we'll start with the longest\Nside, the side of length 5.
Dialogue: 0,0:00:29.08,0:00:32.20,Default,,0000,0000,0000,,So the side of length 5.
Dialogue: 0,0:00:32.20,0:00:34.25,Default,,0000,0000,0000,,That's that side\Nright over there.
Dialogue: 0,0:00:34.25,0:00:37.07,Default,,0000,0000,0000,,And now, let's try to draw\Nthe sides of length 2.
Dialogue: 0,0:00:37.07,0:00:38.57,Default,,0000,0000,0000,,Every side on a\Ntriangle, obviously,
Dialogue: 0,0:00:38.57,0:00:39.86,Default,,0000,0000,0000,,connects with every other side.
Dialogue: 0,0:00:39.86,0:00:42.26,Default,,0000,0000,0000,,So that's one side of length 2.
Dialogue: 0,0:00:42.26,0:00:44.94,Default,,0000,0000,0000,,And then this is another\Nside of lengths 2.
Dialogue: 0,0:00:44.94,0:00:46.12,Default,,0000,0000,0000,,Another side of length 2.
Dialogue: 0,0:00:46.12,0:00:48.50,Default,,0000,0000,0000,,And you might say, fine, these\Naren't touching right now,
Dialogue: 0,0:00:48.50,0:00:49.43,Default,,0000,0000,0000,,these two points.
Dialogue: 0,0:00:49.43,0:00:51.56,Default,,0000,0000,0000,,In order to make a triangle,\Nwe have to touch them.
Dialogue: 0,0:00:51.56,0:00:53.28,Default,,0000,0000,0000,,So let me move them\Ncloser to each other.
Dialogue: 0,0:00:53.28,0:00:55.32,Default,,0000,0000,0000,,But we have to remember, we\Nhave to keep these side lengths
Dialogue: 0,0:00:55.32,0:00:56.11,Default,,0000,0000,0000,,the same.
Dialogue: 0,0:00:56.11,0:00:58.57,Default,,0000,0000,0000,,And we have to keep touching\Nthe side of length 5
Dialogue: 0,0:00:58.57,0:00:59.72,Default,,0000,0000,0000,,at its endpoint.
Dialogue: 0,0:00:59.72,0:01:01.51,Default,,0000,0000,0000,,So we could try to move them in.
Dialogue: 0,0:01:01.51,0:01:04.77,Default,,0000,0000,0000,,We could try to move them in,\Nbut what's going to happen?
Dialogue: 0,0:01:04.77,0:01:07.07,Default,,0000,0000,0000,,Well, you could rotate\Nthem all the way down
Dialogue: 0,0:01:07.07,0:01:10.98,Default,,0000,0000,0000,,and they're still not going\Nto touch because 2 plus 2
Dialogue: 0,0:01:10.98,0:01:12.26,Default,,0000,0000,0000,,is still not equal to 5.
Dialogue: 0,0:01:12.26,0:01:13.80,Default,,0000,0000,0000,,They rotate all the\Nway down, they're
Dialogue: 0,0:01:13.80,0:01:15.64,Default,,0000,0000,0000,,still going to be 1 apart.
Dialogue: 0,0:01:15.64,0:01:18.61,Default,,0000,0000,0000,,So you cannot construct\Nthis triangle.
Dialogue: 0,0:01:18.61,0:01:20.44,Default,,0000,0000,0000,,You cannot construct\Nthis triangle.
Dialogue: 0,0:01:20.44,0:01:24.95,Default,,0000,0000,0000,,And I think you're noticing\Na property of triangles.
Dialogue: 0,0:01:24.95,0:01:28.76,Default,,0000,0000,0000,,The longest side cannot\Nbe longer than the sum
Dialogue: 0,0:01:28.76,0:01:30.59,Default,,0000,0000,0000,,of the other two sides.
Dialogue: 0,0:01:30.59,0:01:33.16,Default,,0000,0000,0000,,Here, the sum of the\Nother two sides is 4.
Dialogue: 0,0:01:33.16,0:01:34.28,Default,,0000,0000,0000,,2 plus 2 is 4.
Dialogue: 0,0:01:34.28,0:01:36.03,Default,,0000,0000,0000,,And the other side is longer.
Dialogue: 0,0:01:36.03,0:01:37.74,Default,,0000,0000,0000,,And even if the other\Nside was exactly
Dialogue: 0,0:01:37.74,0:01:39.45,Default,,0000,0000,0000,,equal to the sum of\Nthe other two sides,
Dialogue: 0,0:01:39.45,0:01:41.44,Default,,0000,0000,0000,,you're going to have\Na degenerate triangle.
Dialogue: 0,0:01:41.44,0:01:42.50,Default,,0000,0000,0000,,Let me draw that.
Dialogue: 0,0:01:42.50,0:01:47.14,Default,,0000,0000,0000,,So this would be side,\Nsay, 2, 2, and 4.
Dialogue: 0,0:01:47.14,0:01:49.61,Default,,0000,0000,0000,,So let's draw the\Nside of length 4.
Dialogue: 0,0:01:49.61,0:01:52.13,Default,,0000,0000,0000,,Side of length 4.
Dialogue: 0,0:01:52.13,0:01:53.71,Default,,0000,0000,0000,,Side of length 4.
Dialogue: 0,0:01:53.71,0:01:57.42,Default,,0000,0000,0000,,Let me draw it a\Nlittle bit shorter.
Dialogue: 0,0:01:57.42,0:01:59.96,Default,,0000,0000,0000,,So that's your side of length 4.
Dialogue: 0,0:01:59.96,0:02:03.18,Default,,0000,0000,0000,,And then, in order to make the\Ntwo sides of length 2 touch,
Dialogue: 0,0:02:03.18,0:02:06.23,Default,,0000,0000,0000,,in order to make them touch,\Nyou have to rotate them
Dialogue: 0,0:02:06.23,0:02:09.05,Default,,0000,0000,0000,,all the way inward You\Nhave to rotate them
Dialogue: 0,0:02:09.05,0:02:12.65,Default,,0000,0000,0000,,all the way inward so that\Nboth this angle and this angle
Dialogue: 0,0:02:12.65,0:02:15.01,Default,,0000,0000,0000,,essentially have to\Nbecome 0 degrees.
Dialogue: 0,0:02:15.01,0:02:17.26,Default,,0000,0000,0000,,And so your resulting triangle,\Nif you rotate this one
Dialogue: 0,0:02:17.26,0:02:18.88,Default,,0000,0000,0000,,all the way in and you\Nrotate this all the way in,
Dialogue: 0,0:02:18.88,0:02:20.59,Default,,0000,0000,0000,,the points will actually touch.
Dialogue: 0,0:02:20.59,0:02:22.84,Default,,0000,0000,0000,,But this triangle will\Nhave no area anymore.
Dialogue: 0,0:02:22.84,0:02:26.19,Default,,0000,0000,0000,,This will become a\Ndegenerate triangle.
Dialogue: 0,0:02:26.19,0:02:28.79,Default,,0000,0000,0000,,And it really looks more\Nlike a line segment.
Dialogue: 0,0:02:28.79,0:02:29.87,Default,,0000,0000,0000,,So let me write that down.
Dialogue: 0,0:02:29.87,0:02:32.42,Default,,0000,0000,0000,,This is a degenerate.
Dialogue: 0,0:02:32.42,0:02:35.44,Default,,0000,0000,0000,,In order for you to draw\Na non-degenerate triangle,
Dialogue: 0,0:02:35.44,0:02:37.47,Default,,0000,0000,0000,,the sum of the\Nother two sides have
Dialogue: 0,0:02:37.47,0:02:40.60,Default,,0000,0000,0000,,to be longer than\Nthe longest side.
Dialogue: 0,0:02:40.60,0:02:44.16,Default,,0000,0000,0000,,So for example, you could\Ndefinitely draw a triangle
Dialogue: 0,0:02:44.16,0:02:47.79,Default,,0000,0000,0000,,with sides of\Nlength 3, 3, and 5.
Dialogue: 0,0:02:47.79,0:02:52.44,Default,,0000,0000,0000,,So if that's the side of\Nlength 5, and then this--
Dialogue: 0,0:02:52.44,0:02:53.98,Default,,0000,0000,0000,,if you were to rotate\Nall the way in,
Dialogue: 0,0:02:53.98,0:03:00.07,Default,,0000,0000,0000,,those two points would-- let me\Ndraw this a little bit neater.
Dialogue: 0,0:03:00.07,0:03:02.90,Default,,0000,0000,0000,,
Dialogue: 0,0:03:02.90,0:03:04.79,Default,,0000,0000,0000,,So let's say that's\Nwhere they connect.
Dialogue: 0,0:03:04.79,0:03:06.21,Default,,0000,0000,0000,,And we know that\Nwe could do that,
Dialogue: 0,0:03:06.21,0:03:08.03,Default,,0000,0000,0000,,because if you think about it,\Nif you were to keep rotating
Dialogue: 0,0:03:08.03,0:03:10.68,Default,,0000,0000,0000,,these, they're going to pass\Neach other at some point.
Dialogue: 0,0:03:10.68,0:03:12.44,Default,,0000,0000,0000,,They're going to\Nhave to overlap.
Dialogue: 0,0:03:12.44,0:03:14.23,Default,,0000,0000,0000,,If you tried to make\Na degenerate triangle,
Dialogue: 0,0:03:14.23,0:03:15.40,Default,,0000,0000,0000,,these points wouldn't touch.
Dialogue: 0,0:03:15.40,0:03:18.20,Default,,0000,0000,0000,,They'd actually overlap by\None unit right over here.
Dialogue: 0,0:03:18.20,0:03:20.69,Default,,0000,0000,0000,,So you could rotate them\Nout and actually form
Dialogue: 0,0:03:20.69,0:03:22.73,Default,,0000,0000,0000,,a non-degenerate triangle.
Dialogue: 0,0:03:22.73,0:03:24.36,Default,,0000,0000,0000,,So this one, you\Nabsolutely could.
Dialogue: 0,0:03:24.36,0:03:26.28,Default,,0000,0000,0000,,And then there's another\Ninteresting question,
Dialogue: 0,0:03:26.28,0:03:28.44,Default,,0000,0000,0000,,is this the only triangle\Nthat you could construct
Dialogue: 0,0:03:28.44,0:03:31.56,Default,,0000,0000,0000,,that has sides of\Nlength 3, 3, and 5?
Dialogue: 0,0:03:31.56,0:03:33.81,Default,,0000,0000,0000,,Well, you can't\Nchange this length.
Dialogue: 0,0:03:33.81,0:03:36.21,Default,,0000,0000,0000,,So you can't change that\Npoint and that point.
Dialogue: 0,0:03:36.21,0:03:38.27,Default,,0000,0000,0000,,And then, you can't\Nchange these two lengths.
Dialogue: 0,0:03:38.27,0:03:39.64,Default,,0000,0000,0000,,So the only place\Nwhere they will
Dialogue: 0,0:03:39.64,0:03:42.58,Default,,0000,0000,0000,,be able to touch each other is\Ngoing to be right over there.
Dialogue: 0,0:03:42.58,0:03:45.11,Default,,0000,0000,0000,,So this right over here\Nis the only triangle
Dialogue: 0,0:03:45.11,0:03:46.52,Default,,0000,0000,0000,,that meets those constraints.
Dialogue: 0,0:03:46.52,0:03:48.10,Default,,0000,0000,0000,,You could rotate it\Nand whatever else.
Dialogue: 0,0:03:48.10,0:03:50.93,Default,,0000,0000,0000,,But if you rotate this, it's\Nstill the same triangle.
Dialogue: 0,0:03:50.93,0:03:53.48,Default,,0000,0000,0000,,This is the only triangle\Nthat has sides of length 3, 3,
Dialogue: 0,0:03:53.48,0:03:54.23,Default,,0000,0000,0000,,and 5.
Dialogue: 0,0:03:54.23,0:03:55.72,Default,,0000,0000,0000,,You can't change\Nany of the angles
Dialogue: 0,0:03:55.72,0:03:58.18,Default,,0000,0000,0000,,somehow to get a\Ndifferent triangle.
Dialogue: 0,0:03:58.18,0:03:58.68,Default,,0000,0000,0000,,