[Script Info]
Title: 
[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:00.00,0:00:05.79,Default,,0000,0000,0000,,[silence]
Dialogue: 0,0:00:05.79,0:00:06.93,Default,,0000,0000,0000,,So I heard you didn't really
Dialogue: 0,0:00:06.93,0:00:08.69,Default,,0000,0000,0000,,get the transformations,
Dialogue: 0,0:00:08.69,0:00:10.11,Default,,0000,0000,0000,,but I think I can help you
Dialogue: 0,0:00:10.11,0:00:11.74,Default,,0000,0000,0000,,out a little bit.
Dialogue: 0,0:00:11.74,0:00:13.86,Default,,0000,0000,0000,,So, transform just means
Dialogue: 0,0:00:13.86,0:00:14.79,Default,,0000,0000,0000,,change something.
Dialogue: 0,0:00:14.79,0:00:15.98,Default,,0000,0000,0000,,You already know that.
Dialogue: 0,0:00:15.98,0:00:17.38,Default,,0000,0000,0000,,And in geometry,
Dialogue: 0,0:00:17.38,0:00:19.30,Default,,0000,0000,0000,,there are some\Ntypes of transformations
Dialogue: 0,0:00:19.30,0:00:21.80,Default,,0000,0000,0000,,that are helpful to know about.
Dialogue: 0,0:00:21.80,0:00:22.96,Default,,0000,0000,0000,,So, the main thing is
Dialogue: 0,0:00:22.96,0:00:24.95,Default,,0000,0000,0000,,you have a first thing
Dialogue: 0,0:00:24.95,0:00:25.92,Default,,0000,0000,0000,,and then a second thing.
Dialogue: 0,0:00:25.92,0:00:27.59,Default,,0000,0000,0000,,So, one shape changes
Dialogue: 0,0:00:27.59,0:00:29.32,Default,,0000,0000,0000,,into another shape.
Dialogue: 0,0:00:29.32,0:00:31.03,Default,,0000,0000,0000,,And, the first one's called
Dialogue: 0,0:00:31.03,0:00:32.10,Default,,0000,0000,0000,,the pre-image,
Dialogue: 0,0:00:32.10,0:00:33.70,Default,,0000,0000,0000,,and the next one's\Ncalled the image.
Dialogue: 0,0:00:33.70,0:00:35.17,Default,,0000,0000,0000,,So, "pre" just means before.
Dialogue: 0,0:00:35.17,0:00:36.65,Default,,0000,0000,0000,,Just remember that,
Dialogue: 0,0:00:36.65,0:00:39.71,Default,,0000,0000,0000,,like pre-liminary and\Npre-historic
Dialogue: 0,0:00:39.71,0:00:41.55,Default,,0000,0000,0000,,and then the next image.
Dialogue: 0,0:00:41.55,0:00:43.27,Default,,0000,0000,0000,,So, the first kind
Dialogue: 0,0:00:43.27,0:00:44.72,Default,,0000,0000,0000,,is a reflection.
Dialogue: 0,0:00:44.72,0:00:46.81,Default,,0000,0000,0000,,And again, you know what\Nthis means already,
Dialogue: 0,0:00:46.81,0:00:48.48,Default,,0000,0000,0000,,but a reflection in geometry
Dialogue: 0,0:00:48.48,0:00:49.80,Default,,0000,0000,0000,,just means that
Dialogue: 0,0:00:49.80,0:00:51.17,Default,,0000,0000,0000,,you've flipped something
Dialogue: 0,0:00:51.17,0:00:52.66,Default,,0000,0000,0000,,over an axis.
Dialogue: 0,0:00:52.66,0:00:54.39,Default,,0000,0000,0000,,So, you could even look
Dialogue: 0,0:00:54.39,0:00:56.40,Default,,0000,0000,0000,,at your hands.
Dialogue: 0,0:00:56.40,0:00:58.11,Default,,0000,0000,0000,,This hand is a reflection\Nof the other hand.
Dialogue: 0,0:00:58.11,0:01:00.34,Default,,0000,0000,0000,,So, they've just flipped\Nonto each other,
Dialogue: 0,0:01:00.36,0:01:01.87,Default,,0000,0000,0000,,or you could think about a
Dialogue: 0,0:01:01.87,0:01:03.97,Default,,0000,0000,0000,,um, like a landscape scene.
Dialogue: 0,0:01:03.97,0:01:05.76,Default,,0000,0000,0000,,If you look at a lake
Dialogue: 0,0:01:05.76,0:01:07.13,Default,,0000,0000,0000,,that's reflecting,
Dialogue: 0,0:01:07.13,0:01:08.22,Default,,0000,0000,0000,,like the mountains,
Dialogue: 0,0:01:08.22,0:01:09.25,Default,,0000,0000,0000,,then it's just,
Dialogue: 0,0:01:09.25,0:01:11.82,Default,,0000,0000,0000,,the axis is that line
Dialogue: 0,0:01:11.82,0:01:14.37,Default,,0000,0000,0000,,of where the lake starts.
Dialogue: 0,0:01:14.37,0:01:16.85,Default,,0000,0000,0000,,So, that's a good way\Nto remember.
Dialogue: 0,0:01:16.85,0:01:19.38,Default,,0000,0000,0000,,Another kind\Nis called a rotation,
Dialogue: 0,0:01:19.38,0:01:20.86,Default,,0000,0000,0000,,and you know what that is too.
Dialogue: 0,0:01:20.87,0:01:22.29,Default,,0000,0000,0000,,But a rotation just means
Dialogue: 0,0:01:22.29,0:01:23.55,Default,,0000,0000,0000,,you're switching a shape
Dialogue: 0,0:01:23.55,0:01:26.48,Default,,0000,0000,0000,,onto a rotating axis.
Dialogue: 0,0:01:26.48,0:01:28.62,Default,,0000,0000,0000,,So, like this.
Dialogue: 0,0:01:28.62,0:01:30.37,Default,,0000,0000,0000,,And, another way to think
Dialogue: 0,0:01:30.37,0:01:31.83,Default,,0000,0000,0000,,about a rotation
Dialogue: 0,0:01:31.83,0:01:34.26,Default,,0000,0000,0000,,is two reflections.
Dialogue: 0,0:01:34.26,0:01:36.09,Default,,0000,0000,0000,,And, that doesn't need
Dialogue: 0,0:01:36.09,0:01:37.31,Default,,0000,0000,0000,,to be confusing.
Dialogue: 0,0:01:37.31,0:01:38.67,Default,,0000,0000,0000,,All you need to know is that
Dialogue: 0,0:01:38.67,0:01:40.69,Default,,0000,0000,0000,,if you have one thing
Dialogue: 0,0:01:40.69,0:01:42.22,Default,,0000,0000,0000,,reflected onto another
Dialogue: 0,0:01:42.22,0:01:43.86,Default,,0000,0000,0000,,and then it reflects again,
Dialogue: 0,0:01:43.86,0:01:45.75,Default,,0000,0000,0000,,it ends up being a rotation.
Dialogue: 0,0:01:45.75,0:01:47.45,Default,,0000,0000,0000,,So...
Dialogue: 0,0:01:50.64,0:01:53.63,Default,,0000,0000,0000,,That's a good way to\Nremember that too.
Dialogue: 0,0:01:53.63,0:01:55.76,Default,,0000,0000,0000,,And, one more type
Dialogue: 0,0:01:55.76,0:01:58.28,Default,,0000,0000,0000,,is called a translation.
Dialogue: 0,0:01:58.28,0:02:00.84,Default,,0000,0000,0000,,So, this is just like a slide.
Dialogue: 0,0:02:00.84,0:02:02.68,Default,,0000,0000,0000,,So, just like this
Dialogue: 0,0:02:02.68,0:02:03.78,Default,,0000,0000,0000,,moving over here.
Dialogue: 0,0:02:03.78,0:02:05.67,Default,,0000,0000,0000,,That's a translation.
Dialogue: 0,0:02:05.67,0:02:06.60,Default,,0000,0000,0000,,Another way to think
Dialogue: 0,0:02:06.60,0:02:08.86,Default,,0000,0000,0000,,about a translation is again,
Dialogue: 0,0:02:08.86,0:02:11.10,Default,,0000,0000,0000,,two reflections,
Dialogue: 0,0:02:11.10,0:02:12.55,Default,,0000,0000,0000,,but this time the reflections
Dialogue: 0,0:02:12.55,0:02:14.27,Default,,0000,0000,0000,,are in a straight line.
Dialogue: 0,0:02:14.27,0:02:17.80,Default,,0000,0000,0000,,So, if you reflect\Nthis hand...here
Dialogue: 0,0:02:17.80,0:02:19.49,Default,,0000,0000,0000,,and you reflect it\None more time,
Dialogue: 0,0:02:19.49,0:02:20.31,Default,,0000,0000,0000,,then this hand
Dialogue: 0,0:02:20.31,0:02:22.03,Default,,0000,0000,0000,,has reflected over here.
Dialogue: 0,0:02:22.03,0:02:23.04,Default,,0000,0000,0000,,So, sorry
Dialogue: 0,0:02:23.04,0:02:26.13,Default,,0000,0000,0000,,this hand has translated\Nover here.
Dialogue: 0,0:02:26.13,0:02:29.77,Default,,0000,0000,0000,,So, these types, um,
Dialogue: 0,0:02:29.77,0:02:33.26,Default,,0000,0000,0000,,of transformations\Nare called isometric.
Dialogue: 0,0:02:33.26,0:02:36.42,Default,,0000,0000,0000,,A translation, a rotation,\Nand a reflection
Dialogue: 0,0:02:36.42,0:02:39.23,Default,,0000,0000,0000,,are all\Nisometric transformations.
Dialogue: 0,0:02:39.23,0:02:40.92,Default,,0000,0000,0000,,That just means same.
Dialogue: 0,0:02:40.92,0:02:42.97,Default,,0000,0000,0000,,So, when you start out
Dialogue: 0,0:02:42.97,0:02:44.03,Default,,0000,0000,0000,,with a pre-image,
Dialogue: 0,0:02:44.03,0:02:45.71,Default,,0000,0000,0000,,it will always be the same size
Dialogue: 0,0:02:45.71,0:02:48.24,Default,,0000,0000,0000,,and shape as the image.
Dialogue: 0,0:02:48.24,0:02:49.29,Default,,0000,0000,0000,,But, there's one more type
Dialogue: 0,0:02:49.29,0:02:50.48,Default,,0000,0000,0000,,of transformation
Dialogue: 0,0:02:50.48,0:02:52.23,Default,,0000,0000,0000,,that isn't isometric,
Dialogue: 0,0:02:52.23,0:02:54.31,Default,,0000,0000,0000,,and that's called dilation.
Dialogue: 0,0:02:54.31,0:02:55.67,Default,,0000,0000,0000,,And, if you ever go
Dialogue: 0,0:02:55.67,0:02:56.96,Default,,0000,0000,0000,,to the eye doctor,
Dialogue: 0,0:02:56.96,0:02:58.71,Default,,0000,0000,0000,,and they dilate your eyes,
Dialogue: 0,0:02:58.71,0:02:59.90,Default,,0000,0000,0000,,it means they made them
Dialogue: 0,0:02:59.90,0:03:01.21,Default,,0000,0000,0000,,really big so that they could
Dialogue: 0,0:03:01.21,0:03:02.63,Default,,0000,0000,0000,,see inside them.
Dialogue: 0,0:03:02.63,0:03:05.92,Default,,0000,0000,0000,,So, when you dilate a shape,
Dialogue: 0,0:03:05.92,0:03:06.79,Default,,0000,0000,0000,,you make it either
Dialogue: 0,0:03:06.79,0:03:08.55,Default,,0000,0000,0000,,smaller or bigger,
Dialogue: 0,0:03:08.55,0:03:10.31,Default,,0000,0000,0000,,one of those two.
Dialogue: 0,0:03:11.12,0:03:13.25,Default,,0000,0000,0000,,So, one more term
Dialogue: 0,0:03:13.25,0:03:15.63,Default,,0000,0000,0000,,is a glide reflection.
Dialogue: 0,0:03:15.63,0:03:16.83,Default,,0000,0000,0000,,And a glide reflection
Dialogue: 0,0:03:16.83,0:03:18.55,Default,,0000,0000,0000,,is exactly what it sounds like.
Dialogue: 0,0:03:18.55,0:03:20.06,Default,,0000,0000,0000,,It's just one reflection
Dialogue: 0,0:03:20.06,0:03:21.75,Default,,0000,0000,0000,,plus one translation,
Dialogue: 0,0:03:21.75,0:03:23.50,Default,,0000,0000,0000,,and these can be\Nin either order.
Dialogue: 0,0:03:23.50,0:03:25.92,Default,,0000,0000,0000,,You could either\Ntranslate and then reflect
Dialogue: 0,0:03:25.92,0:03:28.54,Default,,0000,0000,0000,,or you could \Nreflect and then translate.
Dialogue: 0,0:03:28.54,0:03:30.34,Default,,0000,0000,0000,,Either way.
Dialogue: 0,0:03:30.34,0:03:31.81,Default,,0000,0000,0000,,[pause]
Dialogue: 0,0:03:31.81,0:03:34.59,Default,,0000,0000,0000,,So, transformations are helpful,
Dialogue: 0,0:03:34.59,0:03:36.34,Default,,0000,0000,0000,,because we can know about
Dialogue: 0,0:03:36.34,0:03:38.71,Default,,0000,0000,0000,,something called a tessellation.
Dialogue: 0,0:03:38.71,0:03:40.22,Default,,0000,0000,0000,,And a tessellation is
Dialogue: 0,0:03:40.22,0:03:42.28,Default,,0000,0000,0000,,just a repeating shape,
Dialogue: 0,0:03:42.28,0:03:44.34,Default,,0000,0000,0000,,but only certain types\Nof shapes can repeat
Dialogue: 0,0:03:44.34,0:03:47.08,Default,,0000,0000,0000,,in patterns that don't overlap.
Dialogue: 0,0:03:47.08,0:03:48.68,Default,,0000,0000,0000,,So, if we had like
Dialogue: 0,0:03:48.68,0:03:50.39,Default,,0000,0000,0000,,a crazy star or something,
Dialogue: 0,0:03:50.39,0:03:51.36,Default,,0000,0000,0000,,it wouldn't tessellate,
Dialogue: 0,0:03:51.36,0:03:53.17,Default,,0000,0000,0000,,because it's a weird shape.
Dialogue: 0,0:03:53.17,0:03:56.24,Default,,0000,0000,0000,,But, if we had just like\Na square or a rectangle,
Dialogue: 0,0:03:56.24,0:03:57.81,Default,,0000,0000,0000,,it'll tessellate perfectly,
Dialogue: 0,0:03:57.81,0:03:59.19,Default,,0000,0000,0000,,because they can overlap
Dialogue: 0,0:03:59.19,0:04:00.52,Default,,0000,0000,0000,,in any sort of pattern.
Dialogue: 0,0:04:00.52,0:04:02.07,Default,,0000,0000,0000,,So like, it's why we can have
Dialogue: 0,0:04:02.07,0:04:03.70,Default,,0000,0000,0000,,a brick wall or something,
Dialogue: 0,0:04:03.70,0:04:04.50,Default,,0000,0000,0000,,you know.
Dialogue: 0,0:04:04.50,0:04:06.14,Default,,0000,0000,0000,,They can...
Dialogue: 0,0:04:06.14,0:04:07.71,Default,,0000,0000,0000,,they perfectly fit\Nnext to each other
Dialogue: 0,0:04:07.71,0:04:09.100,Default,,0000,0000,0000,,and on top of each other.
Dialogue: 0,0:04:09.100,0:04:11.18,Default,,0000,0000,0000,,But, if you need to know
Dialogue: 0,0:04:11.18,0:04:13.43,Default,,0000,0000,0000,,what types of shapes\Ncan tessellate,
Dialogue: 0,0:04:13.43,0:04:16.09,Default,,0000,0000,0000,,we can remember\Nby angle measure.
Dialogue: 0,0:04:16.09,0:04:20.39,Default,,0000,0000,0000,,So, if all the angles of a shape
Dialogue: 0,0:04:20.39,0:04:22.78,Default,,0000,0000,0000,,equal 360 degrees,
Dialogue: 0,0:04:22.78,0:04:24.47,Default,,0000,0000,0000,,then they'll be able\Nto tessellate.
Dialogue: 0,0:04:24.47,0:04:25.64,Default,,0000,0000,0000,,So, sometimes you can look
Dialogue: 0,0:04:25.64,0:04:27.08,Default,,0000,0000,0000,,at a shape and figure it out.
Dialogue: 0,0:04:27.08,0:04:29.07,Default,,0000,0000,0000,,Other times, maybe you can't.
Dialogue: 0,0:04:29.07,0:04:30.45,Default,,0000,0000,0000,,So, if you need to remember
Dialogue: 0,0:04:30.45,0:04:32.42,Default,,0000,0000,0000,,what types of shapes can,
Dialogue: 0,0:04:32.42,0:04:34.19,Default,,0000,0000,0000,,if all the angles that meet up
Dialogue: 0,0:04:34.19,0:04:36.19,Default,,0000,0000,0000,,equal 360,
Dialogue: 0,0:04:36.19,0:04:37.55,Default,,0000,0000,0000,,then you're in business.
Dialogue: 0,0:04:37.55,0:04:38.84,Default,,0000,0000,0000,,You can tessellate.
Dialogue: 0,0:04:38.84,0:04:40.66,Default,,0000,0000,0000,,So, you know rectangles can,
Dialogue: 0,0:04:40.66,0:04:42.26,Default,,0000,0000,0000,,like in this picture.
Dialogue: 0,0:04:42.26,0:04:43.77,Default,,0000,0000,0000,,But then in the next one,
Dialogue: 0,0:04:43.77,0:04:45.14,Default,,0000,0000,0000,,we have two different shapes.
Dialogue: 0,0:04:45.14,0:04:48.66,Default,,0000,0000,0000,,We have squares and triangles,
Dialogue: 0,0:04:48.66,0:04:50.71,Default,,0000,0000,0000,,and you can see that
Dialogue: 0,0:04:50.71,0:04:52.66,Default,,0000,0000,0000,,all these angles together,
Dialogue: 0,0:04:52.66,0:04:56.83,Default,,0000,0000,0000,,the 90 plus 90 plus\N60 plus 60 plus 60
Dialogue: 0,0:04:56.83,0:04:59.65,Default,,0000,0000,0000,,equals 360 degrees.
Dialogue: 0,0:04:59.65,0:05:01.18,Default,,0000,0000,0000,,And, if you just add up
Dialogue: 0,0:05:01.18,0:05:02.63,Default,,0000,0000,0000,,all the angles that touch
Dialogue: 0,0:05:02.63,0:05:04.34,Default,,0000,0000,0000,,and they equal 360,
Dialogue: 0,0:05:04.34,0:05:06.36,Default,,0000,0000,0000,,then you can see,
Dialogue: 0,0:05:06.36,0:05:07.15,Default,,0000,0000,0000,,like right here,
Dialogue: 0,0:05:07.15,0:05:09.52,Default,,0000,0000,0000,,that they tessellate perfectly.