[Script Info]
Title: 
[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:00.00,0:00:03.28,Default,,0000,0000,0000,,Let's say you're me and you're in math class and you're supposed to be learning about factoring.
Dialogue: 0,0:00:03.28,0:00:07.14,Default,,0000,0000,0000,,Trouble is, your teacher is too busy trying to convince you that factoring is a useful skill
Dialogue: 0,0:00:07.14,0:00:10.58,Default,,0000,0000,0000,,for the average person to know with real-world applications ranging from passing your state exams
Dialogue: 0,0:00:10.58,0:00:12.03,Default,,0000,0000,0000,,all the way to getting a higher SAT score
Dialogue: 0,0:00:12.03,0:00:14.38,Default,,0000,0000,0000,,and unfortunately does not have the time to show you
Dialogue: 0,0:00:14.38,0:00:16.39,Default,,0000,0000,0000,,why factoring is actually interesting.
Dialogue: 0,0:00:16.39,0:00:19.36,Default,,0000,0000,0000,,It's perfectly reasonable for you to get bored in this situation.
Dialogue: 0,0:00:19.36,0:00:21.93,Default,,0000,0000,0000,,So like any reasonable person, you start doodling.
Dialogue: 0,0:00:21.93,0:00:24.51,Default,,0000,0000,0000,,Maybe it's because your teacher's sophorific voice reminds you of a lullaby
Dialogue: 0,0:00:24.52,0:00:27.01,Default,,0000,0000,0000,,but you're drawing stars.
Dialogue: 0,0:00:27.01,0:00:29.37,Default,,0000,0000,0000,,And because you're me, you quickly get bored of the usual 5-pointed star
Dialogue: 0,0:00:29.37,0:00:31.70,Default,,0000,0000,0000,,and get to wondering: why five?
Dialogue: 0,0:00:31.70,0:00:33.48,Default,,0000,0000,0000,,So you start exploring.
Dialogue: 0,0:00:33.48,0:00:35.85,Default,,0000,0000,0000,,It seems obvious that a 5-pointed star is the simplest one-
Dialogue: 0,0:00:35.85,0:00:38.25,Default,,0000,0000,0000,,the one that takes the least number of strokes to draw.
Dialogue: 0,0:00:38.25,0:00:41.00,Default,,0000,0000,0000,,Sure you can make a star with 4 points but that's not really a star
Dialogue: 0,0:00:41.00,0:00:42.58,Default,,0000,0000,0000,,the way you're defining stars.
Dialogue: 0,0:00:42.58,0:00:44.97,Default,,0000,0000,0000,,Then there's the 6-pointed star which is also familiar
Dialogue: 0,0:00:44.98,0:00:46.90,Default,,0000,0000,0000,,but totally different from the 5-pointed star because
Dialogue: 0,0:00:46.90,0:00:48.67,Default,,0000,0000,0000,,it takes 2 seperate lines to make.
Dialogue: 0,0:00:48.67,0:00:50.94,Default,,0000,0000,0000,,And then you're thinking about how
Dialogue: 0,0:00:50.94,0:00:52.97,Default,,0000,0000,0000,,much like you can put 2 triangles together to make a 6-pointed star,
Dialogue: 0,0:00:52.97,0:00:55.38,Default,,0000,0000,0000,,you can put two squares together to make an 8-pointed star.
Dialogue: 0,0:00:55.38,0:01:00.01,Default,,0000,0000,0000,,And any even numbered star with "p" points can be made of 2 "p over 2" gons.
Dialogue: 0,0:01:00.01,0:01:03.88,Default,,0000,0000,0000,,It is at this point that you realize if you wanted to avoid thinking about factoring
Dialogue: 0,0:01:03.88,0:01:06.50,Default,,0000,0000,0000,,maybe drawing stars was not the brightest idea.
Dialogue: 0,0:01:06.50,0:01:09.34,Default,,0000,0000,0000,,But wait! 4 would be an even number of points
Dialogue: 0,0:01:09.34,0:01:11.28,Default,,0000,0000,0000,,but that would mean you could make it out of 2 "2-gons"
Dialogue: 0,0:01:11.28,0:01:13.78,Default,,0000,0000,0000,,Maybe you were taught polygons with only two sides can't exist
Dialogue: 0,0:01:13.78,0:01:16.88,Default,,0000,0000,0000,,but for the purposes of drawing stars it works out rather well.
Dialogue: 0,0:01:16.88,0:01:19.20,Default,,0000,0000,0000,,Sure, the 4-pointed star doesn't look too star-like
Dialogue: 0,0:01:19.20,0:01:22.55,Default,,0000,0000,0000,,But then you realize that you can make a 6-pointed star out of 3 of these things
Dialogue: 0,0:01:22.55,0:01:25.38,Default,,0000,0000,0000,,and you've got an asterisk, which is definitely a legitimate star.
Dialogue: 0,0:01:25.38,0:01:28.48,Default,,0000,0000,0000,,In fact, for any star with a number of points that is divisible by 2
Dialogue: 0,0:01:28.48,0:01:30.71,Default,,0000,0000,0000,,you can draw it asterisk style.
Dialogue: 0,0:01:30.71,0:01:32.18,Default,,0000,0000,0000,,But that's not quite what you're looking for
Dialogue: 0,0:01:32.18,0:01:34.34,Default,,0000,0000,0000,,what you want is a doodle game, and here it is:
Dialogue: 0,0:01:34.34,0:01:36.34,Default,,0000,0000,0000,,draw "p" points in a circle, evenly spaced.
Dialogue: 0,0:01:36.34,0:01:38.20,Default,,0000,0000,0000,,Pick a number "q".
Dialogue: 0,0:01:38.20,0:01:41.08,Default,,0000,0000,0000,,Starting at one point, go around the circle and connect to the point q places over.
Dialogue: 0,0:01:41.08,0:01:42.68,Default,,0000,0000,0000,,Repeat.
Dialogue: 0,0:01:42.68,0:01:44.58,Default,,0000,0000,0000,,If you get to the starting place before you've covered all the points
Dialogue: 0,0:01:44.58,0:01:46.05,Default,,0000,0000,0000,,jump to a lonely point and keep going.
Dialogue: 0,0:01:46.05,0:01:47.38,Default,,0000,0000,0000,,That's how you draw stars.
Dialogue: 0,0:01:47.38,0:01:49.84,Default,,0000,0000,0000,,And it's a successfull game in that previously you were considering
Dialogue: 0,0:01:49.84,0:01:51.34,Default,,0000,0000,0000,,running, screaming, from the room
Dialogue: 0,0:01:51.34,0:01:53.38,Default,,0000,0000,0000,,or the window is open so that's an option too.
Dialogue: 0,0:01:53.38,0:01:55.05,Default,,0000,0000,0000,,But now you're not only entertained,
Dialogue: 0,0:01:55.05,0:01:57.74,Default,,0000,0000,0000,,but beginning to become curious about the nature of this game.
Dialogue: 0,0:01:57.74,0:01:59.44,Default,,0000,0000,0000,,The interesting thing is that the more points you have,
Dialogue: 0,0:01:59.44,0:02:01.68,Default,,0000,0000,0000,,the more different ways there is to draw the star.
Dialogue: 0,0:02:01.68,0:02:05.04,Default,,0000,0000,0000,,I happen to like 7-pointed stars because there's two really good ways to draw them.
Dialogue: 0,0:02:05.04,0:02:06.54,Default,,0000,0000,0000,,but they're still simple.
Dialogue: 0,0:02:06.54,0:02:09.81,Default,,0000,0000,0000,,I would like to note here that I have never actually left a math class via the window,
Dialogue: 0,0:02:09.81,0:02:12.01,Default,,0000,0000,0000,,not that I can say the same for other subjects.
Dialogue: 0,0:02:12.01,0:02:14.92,Default,,0000,0000,0000,,8 is interesting too, because not only are there a couple nice ways to draw it,
Dialogue: 0,0:02:14.92,0:02:16.41,Default,,0000,0000,0000,,but one's a composite of two polygons
Dialogue: 0,0:02:16.41,0:02:19.15,Default,,0000,0000,0000,,while another can be drawn without picking up the pencil.
Dialogue: 0,0:02:19.15,0:02:20.57,Default,,0000,0000,0000,,Then there's 9,
Dialogue: 0,0:02:20.57,0:02:22.87,Default,,0000,0000,0000,,which, in addition to a couple of other nice versions, you can make out of 3 triangles.
Dialogue: 0,0:02:22.87,0:02:25.43,Default,,0000,0000,0000,,And, because you're me, and you're a nerd, and you like to amuse yourself,
Dialogue: 0,0:02:25.43,0:02:27.84,Default,,0000,0000,0000,,you decide to call this kind of star a Square Star.
Dialogue: 0,0:02:27.84,0:02:29.84,Default,,0000,0000,0000,,because that's kind of a funny name.
Dialogue: 0,0:02:29.84,0:02:31.44,Default,,0000,0000,0000,,So you start drawing other square stars.
Dialogue: 0,0:02:31.44,0:02:32.33,Default,,0000,0000,0000,,4 4-gons,
Dialogue: 0,0:02:32.33,0:02:33.51,Default,,0000,0000,0000,,2 2-gons,
Dialogue: 0,0:02:33.51,0:02:35.85,Default,,0000,0000,0000,,even the completely degenerate case of 1 1-gon.
Dialogue: 0,0:02:35.85,0:02:38.75,Default,,0000,0000,0000,,Unfortunately 5 pentagons is already difficult to discern,
Dialogue: 0,0:02:38.75,0:02:41.81,Default,,0000,0000,0000,,and beyond that it's very hard to see and appreciate the structure of square stars.
Dialogue: 0,0:02:41.81,0:02:44.18,Default,,0000,0000,0000,,So you get bored and move on to 10 dots and a circle,
Dialogue: 0,0:02:44.18,0:02:47.38,Default,,0000,0000,0000,,which is interesting because this is the first number where you can make a star
Dialogue: 0,0:02:47.38,0:02:48.99,Default,,0000,0000,0000,,as a composite of smaller stars,
Dialogue: 0,0:02:48.99,0:02:50.92,Default,,0000,0000,0000,,that is, 2 boring old 5-pointed stars.
Dialogue: 0,0:02:50.92,0:02:54.26,Default,,0000,0000,0000,,Unless you count asterisk stars, in which case 8 was 2 4s, or 4 2's. or 2 2's and a 4.
Dialogue: 0,0:02:54.26,0:02:57.75,Default,,0000,0000,0000,,But 10 is interesting, because you can make it as a composite in more than one way.
Dialogue: 0,0:02:57.75,0:03:01.51,Default,,0000,0000,0000,,because it's divisible by five which itself can be made in 2 ways.
Dialogue: 0,0:03:01.51,0:03:05.75,Default,,0000,0000,0000,,Then there's 11, which can't be made out of seperate parts at all, because 11 is prime.
Dialogue: 0,0:03:05.75,0:03:09.18,Default,,0000,0000,0000,,Though here you start to wonder how to predict how many times around the circle
Dialogue: 0,0:03:09.18,0:03:10.75,Default,,0000,0000,0000,,it will go before getting back to the start.
Dialogue: 0,0:03:10.75,0:03:14.21,Default,,0000,0000,0000,,But instead of exploring the exciting world of modular arithmetic, you move on to 12
Dialogue: 0,0:03:14.21,0:03:16.17,Default,,0000,0000,0000,,which is a really cool number
Dialogue: 0,0:03:16.17,0:03:17.56,Default,,0000,0000,0000,,because it has a whole bunch of factors.
Dialogue: 0,0:03:17.56,0:03:18.95,Default,,0000,0000,0000,,And then something starts to bother you:
Dialogue: 0,0:03:18.95,0:03:23.20,Default,,0000,0000,0000,,Is a 25 pointed star composite made of 5 5-pointed stars a Square Star?
Dialogue: 0,0:03:23.20,0:03:26.54,Default,,0000,0000,0000,,You've been thinking only of pentagons because the lower numbers didn't have this question.
Dialogue: 0,0:03:26.54,0:03:28.27,Default,,0000,0000,0000,,How could you have missed that?
Dialogue: 0,0:03:28.27,0:03:29.94,Default,,0000,0000,0000,,Maybe your teacher said something interesting about prime numbers
Dialogue: 0,0:03:29.94,0:03:31.83,Default,,0000,0000,0000,,and you accidentally lost focus for a moment.
Dialogue: 0,0:03:31.83,0:03:32.33,Default,,0000,0000,0000,,And, oh no.
Dialogue: 0,0:03:32.83,0:03:33.88,Default,,0000,0000,0000,,It gets even worse.
Dialogue: 0,0:03:33.88,0:03:36.62,Default,,0000,0000,0000,,6 squared would be a 36 pointed star, made of 6 hexagons.
Dialogue: 0,0:03:36.62,0:03:39.54,Default,,0000,0000,0000,,but if you allow use of 6 pointed stars, then it's the same as
Dialogue: 0,0:03:39.54,0:03:41.04,Default,,0000,0000,0000,,a composite of 12 triangles.
Dialogue: 0,0:03:41.04,0:03:44.05,Default,,0000,0000,0000,,And that doesn't seem in keeping with the spirit of square stars.
Dialogue: 0,0:03:44.05,0:03:46.18,Default,,0000,0000,0000,,You'll have to define square stars more strictly.
Dialogue: 0,0:03:46.18,0:03:49.81,Default,,0000,0000,0000,,But you do like the idea that there's three ways to make the 7th square star.
Dialogue: 0,0:03:49.81,0:03:53.20,Default,,0000,0000,0000,,Anyway, the whole theory of what kind of stars can be made with what numbers
Dialogue: 0,0:03:53.20,0:03:54.04,Default,,0000,0000,0000,,is quite interesting
Dialogue: 0,0:03:54.04,0:03:56.87,Default,,0000,0000,0000,,and I encourage you to explore this during your math class.