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Mathematics Goes to the Movies
by Burkard Polster and Marty Ross
Principle Singleton (Keene Curtis) is fighting with Mr. Freeman (Tom Reda), the Head of mathematics at Stonewood High School.
PRINCIPLE: I guess Stonewood could use a new head of the mathematics department. Good bye Mr. Freeman, You’re fired.
Mr. FREEMAN: Screw you, Singleton!
Kevin “Blade” Laird (J. Eddie Peck) is teaching a math class at Stonewood.
BLADE: Complementary … angles. They’re like partners … in a dance. If you know one … the other one follows. But, without both, you have nothing. Together, you have what? Egghead (Eric Taslitz) raises his hand. Egghead.
EGGHEAD: A right angle.
BLADE: Right. The most useful angle in trigonometry. Does everyone understand? Some bored yeahs from the class. Good. Glad you’re so excited about it. Now remembering that, we get the key equation, the basis of all measurements, all navigation. Without the use of a right angle, Columbus would have never discovered America and the astronauts would have never landed on the moon. O.K.? How about the difference between an adjacent and a non-adjacent complementary angle? Sandy Thomas (Melora Hardin) raises her hand. Yes, Sandy.
SANDY: Um, I was just wondering how you’d feel about a teacher posing for a calendar. I mean, if it was for a good cause.
BLADE: Sandy, posing for calendars has no relevance to what we’re doing in class today. So please pay attention.
SANDY (looking him over): I am.
REMARKS: “Adjacent and non-adjacent complementary angles” is meaningless.
Sandy and Murial (Debra Spagnoli) are at the dance club No Man’s Land, and they see Blade dancing.
SANDY: Oh my God! That’s Mr. Laird!
MIRIA (lustily): You know him?
SANDY: He’s my math teacher!
Blade is in the poolroom at No Man’s Land, in front of a room of kids at the dance floor.
BLADE: Well. Let’s do it! Blade walks to the blackboard, starts to write, and we cut to Blade writing on the blackboard at Stonewood High. The square of cosine theta plus, the square of sin theta, equals 1. This establishes the relationships, and here the theta symbol stands for the angle.
Good. Cause remembering that, we get the key equation. It’s simple. And what do we know about the symbol theta? Theta is a Greek letter. It’s a variable, whose domain is a set of all angles. Sandy drifts off, and fantasises about dancing with Blade. Her dreaming is interrupted by Blade’s talking. … we should be able to derive a proof, the absolute proof, of The Law of Sines. Sandy? Back to Sandy in class. Sandy.
SANDY: Yes, Kevin? Giggle from the class. I’m sorry. What is it, Mr. Laird?
BLADE: Can you give us the proof of the Law of Sines?
BLADE: What’s with you today, Sandy? The Proof of The Law of Sines, please. Sandy looks around, puzzled. The bell rings. Saved by the bell.
Blade is in Principle Singleton’s office.
SINGLETON: Well, I’ll make this short. I’m sure you’ve heard we need a new head for the math department.
BLADE: Mr. Freeman’s job.
SINGLETON: Mr. Freeman has abdicated his position.
Sandy is dressing in sexy clothes to attract Blade at No Man’s Land, with her friend Lesley (Rita Bland) watching.
LESLEY: Sandy! Tall, dark and handsome is one thing. Tall, dark handsome and your math teacher is another.
Blade is reluctantly dancing with Sandy at No Man’s Land.
SANDY: Come on! Math class is over. Then comes biology. And if you’re lucky … anatomy.
Blade is about to teach a class at “Galaxy High”, the poolroom at No Man’s Land.
BLADE: Anyway, where did we leave off last time?
BOOKWORM (Elsie Sniffen): Uh, rectangular coordinate systems. Ramone (Shabba-Doo) is trying to play pool.
RAMONE: Hey. Keep it down! I’m trying to play some pool here, man.
BLADE: Is that so? Blade and the students walk over to the pool table. Looks to me like you’re gonna lose your shot. Ramone shoots and misses.
BLADE: It’s too bad you don’t know the rectangular coordinate system.
RAMONE: Oh, yeah? So, you think with your degree you can make this shot, man?
BLADE: Piece a cake. If you know the rectangular coordinate system.
RAMONE: O.K. Let’s see you make it.
BLADE: Gotta set it up first. See first, I need to decide which ball that I want to hit.
RAMONE: What is this? The eight ball, right here.
BLADE: Right here, man (he points to one side of the eight-ball) or (pointing to the other side) right here? It’s not good enough. You need to define it in relation to something. (To the students) To what does it relate? One of the students, Richocet (Jimmy Locust) replies.
RICOCHET: it’s the c-c-cueball.
BLADE (to Ramone): Start with the cueball?
RAMONE: I believe so.
BLADE: You’re sure about that?
RAMONE: Yeah. Blade picks up the cue.
BLADE: How long is this stick, Ramone? Ramone looks down at his crotch.
RAMONE: This stick? Sixteen inches!
BLADE: Sixty inches. The cueball is halfway up the stick, which means? Another student, Pink Toes (Leticia Vasquez), replies.
PINK TOES: Thirty inches.
RAMONE: Come on! Take the shot!
BLADE: Hey, chill out, man. I’m dealing with a system here.
RAMONE: Yeah? He holds up a banknote. Well deal with this. I’ll bet you can’t make the shot.
BLADE (to the students): Cover it. Drop your money in. The students cover the bet. Slogan, pick up my stakes there and hold ‘em for me, … while I try to decide what direction the stick is. Blade lays the cue on the table. Let’s make this the zero degree direction right here.
RAMONE: O.K. But let’s make this a three-cushion shot.
BLADE: O.K. Cover it. Blade taps a diamond marker on the table. Vertex number one, vertex number two and vertex number three. Uncle Big (Dennis Burkley), the manager of the club, enters the room. Wait a minute, wait a minute. I need to decide which angle that I need to use.
UNCLE BIG: What the hell are you doin’? You know I don’t allow gambling in here.
BLADE: Gambling. This is education (he holds up a protractor) … on how to use a protractor, to measure angles … by degrees. He lays down the protractor on the pool table.
Thirty-seven degrees. Could be tough. Forty-four degrees. Hmm.
UNCLE BIG: This is too damn good to pass up. I got me a hundred dollar bill here says you ain’t gonna make it.
BLADE: Grab it quick, Book, before he backs out. Blade lines up and makes the shot. The rectangular coordinate system. He throws the protactor over a cue held by Ramone, and takes the money from booker. Thank-you all. Class dismissed. Ramone stares at the protractor. One of the bettors goes up to Double J.
BETTOR: Damn! That dude walked off with all our cash!
UNCLE BIG: Blade. He throws the eight-ball to Blade. Gameball.
REMARKS: The planning of a pool shot is indeed based around rectangular coordinates, and knowing the angles. However, apart from a fleeting reference to the points system of calculating shots, there’s not much content in Blade’s description.
Blade is in bed with his wife, Linda (Kristina Starman).
LINDA: You got something you want to take care of with me?
BLADE: Have I ever shown you my rectangular coordinate system?
WIFE: I love it when you talk dirty to me.
51:35 Laird is sneaking copies of the magazine “Mathematics Unlimited” into the school library, presumably after using them at Galaxy High.
Superintendent Leland (Basil Hoffman) is visiting Blade’s classroom, and is looking over a student’s shoulder at a computer screen.
LELAND: This is interesting. Where did you get this program?
STUDENT: Mr. Laird designed it, sir.
Blade is teaching his class.
BLADE: Class, why are we studying double angle identities? Well, imagine, we finally get the big one. Stonewood High is hit. Result?
LESLEY: A crack opens down the middle of the classroom.
BLADE: Make it Rodeo Drive. And Sandy is trapped at Gucci’s, which is now on fire.
SANDY: Why me?
BLADE: Don’t worry. Dean’s on the way to the rescue, and all he has is a protractor. What are you gonna do, Dean?
DEAN (Ricky Paull Goldin): Uh, I’ll build a bridge.
BLADE: Good. How long does the bridge have to be?
DEAN: I don’t know.
BLADE: Use your protractor. And what else?
DEAN: Um. Telephone pole?
BLADE: Excellent, Dean. Now what is the angle of the pole to the street?
DEAN: The … angle? Oh, the angle of the pole to the street. Oh, uh … (Dean’s friends whisper the answer) ninety degrees.
BLADE: Exactly, Dean. Very good. The bell rings for the end of class. Tomorrow we explore how to derive an unknown solution from a known angle. Class dismissed.
REMARKS: Blade’s problem gives no real motivation for learning double angle identities, though he does indicate a valid, simple and well-known method for calculating distances.
Suppose L is the length of the bridge, H is the height of the telephone pole, and A is the angle from the horizontal to the telephone pole. Then knowing A and H we can obviously calculate L. 54:10
Sandy is flirting with Blade. We see a standard problem in Euclidean geometry problems on the blackboard in the background. Given the one angle JKE, and assuming the lines KM and EF are paralle, the problem seems to be to calculate the (complementary) angle JKE angle.
Blade is teaching the Galaxy High students.
BLADE: Right triangle. What is it? Double J (Richard Giorla) sits, puzzled. What do you think, Double J?
DOUBLE J: Don’t you think this is a waste, Man?
BLADE: It’s only a waste if you don’t try. If you don’t, it’s gonna be the same old moppin’ floors.
RICOCHET: You’ll burning yourself on the f-f-french fry machine for the next f-fifty years.
STUDENT: That’s right.
BLADE: Look, if you screw up, you just got back to the basics. Yo, Pass, dribble, shoot! Right triangle, what is it?
STUDENT: Any triangle with a right angle.
BLADE: Which is?
STUDENT: Ninety degrees, Homey.
BLADE: Right! Which means?
STUDENT: The other two angles add up to ninety degrees.
The class is interrupted by Sandy, and then continues.
BLADE: So where were we?
STUDENT: The other two angles add up to ninety degrees.
BLADE: Right. Which we means what?
STUDENTS: Acute angles.
BLADE: Acute angles. Right triangles. Sine, cosine, what are all of these?
BLADE: To do what?
STUDENTS: Build a bridge!
RICOCHET: G-go to the m-moon!
Blade has lost his position at Stonewood High, and has been replaced by Mr. Collins (Michael Gates). The definitions of the trigonometric functions can been seen on the blackboard.
MR. COLLINS: I guess we’ll just pick it up at the sines and the cosines. Turn to page fifty-two, please.
The students from Galaxy High have come to defend Blade to the Principle and Superintendent.
SINGLETON: Well, Laird is a math teacher. Why not let him prove himself in his own field?
LELAND: Great! And the wonderful thing is, Singleton, you’ll be proving that Mr. Laird’s methods don’t work. Because if they do, he has his job back.
Stonewood High and Galaxy High are engaged in a math competition.
SINGLETON: First question. You plotted the position of a star in relation to the background stars six months ago and again last night.
The angle of shift in the star’s position is eight tenths of a second. How would you determine the distance of this star from the Earth? A Galaxy High student raises his hand. Galaxy High. Go ahead.
STUDENT: With a big tape measure. (Laughter). O.K. O.K. But if I couldn’t find no tape measure, I guess I’d have to use the trigonometric parallax. See, I’d start with a right triangle formed by the Sun, the stars and the position of the Earth last night. That makes my angle of interest .4 seconds, and the far side is the distance from the Earth to the Sun in one astronomical unit. The near side, with the length we don’t know, is the distance from our solar system to the star. Now you measure the ratio far side over near side for a right triangle when the angle of interest is .4 seconds. Uh, somethin’ like that.
SINGLETON: … Correct.
REMARKS: The proposed solution is not precisely correct, though it is close enough in practice. The star, the Earth and the Sun will not in general form a right triangle, and the angle of interest, A, will not in general be .4 degrees. Of course, because of the Earth’s elliptical orbit, the Sun will be at a focal point of the orbit rather than the centre. However, because the star is so far away in comparison to the Sun-Earth distance, treating the triangle as a right triangle is a quick and accurate method for estimating the distance to the star.
At the competition.
SINGLETON: Describe the Cartesian coordinate system. Rod, a Stonewood High student, raises his hand. Go ahead, Rod.
ROD: It’s a system where points on a plane are identified by pairs of numbers that represent distances from two perpendicular lines.
SINGLETON: Point, Stonewood High.
At the competition.
SINGLETON: If point number one on a map of Stonewood is Fieldstone Avenue and Taft Boulevard, and point number two is Beverley Drive and Choat Boulevard, and point number three forms an equilateral triangle, where is that third point?
BLADE: How do you expect these kids to know Beverley Hills geography?
REMARKS: Blade’s question misses the point in two ways. First, the question is essentially non-mathematical, no matter whether the students know the geography or not. Secondly, there are obviously two correct answers, so the question is ill-formed.
At the competition.
SINGLETON: The next question is, the abscissa of a point in the plane is the distance of the point from the X axis. The ordinate is the distance of the point from the Y axis. Given an equation , what are the coordinates of the solution?
PINK TOES: You got the question wrong.
SINGLETON: Young lady, if you can’t answer the question, leave the microphone.
PINK TOES; No, see you reversed them. The abscissa is the vertical line from the point in the plane from the Y axis. Well anyway it don’t matter. The answer is the abscissa of the point is –3 and the ordinate is 6.
LELAND: Singleton. She’s right.
SINGLETON: Correct. Point to Galaxy High.
REMARKS: Both Singleton and Pink Toes get the definitions wrong. The abscissa of a point P(x,y) is x, i.e. the distance from the point to the Y axis, and the ordinate of P is y. The question also makes no sense, since the equation has an infinite line of solutions. In fact, (-3,6) is on this line, so perhaps the problem was intended to be one of finding the intersection of two lines.
At the competition.
SINGLETON: Last question. Describe for the rectangular coordinate system. Long silence as Ramone stands, clueless. Blade, in the audience, shows the eight ball to Ramone, who raises his hand.
SINGLETON: Galaxy High? A rectangular coordinated system. (Laughter) Well whatever you call it. See you wanna hit the eight ball, right?
RAMONE: You wanna figure out where the eight ball is on the pool table.
SINGLETON: I fail to see what this has to do with the question.
LELAND (to Ramone): Go on, Son.
RAMONE: The exact position of the eight ball can be spotted if you measure how far it is from the cueball. Which you can do with the cue stick. But I don’t have one, so … you have to figure the direction straight to the right of the cueball. And that you call the zero direction, the zero degree direction. And you measure the angle between the zero degree direction and the line from the cueball to the eight ball … That’s it!
SINGLETON: What’s it?
RAMONE: The rectangular coordinate system!
SINGLETON: I’m afraid I cannot consider this a correct answer.
LELAND: Singleton … you’d better consider that a correct answer.
SINGLETON: … The winner is … Galaxy High.
REMARKS: The rectangular coordinate system is another name for the Cartesian coordinate system, so this question has already been asked above.
During the credits we see Ricochet, having become a math teacher himself.
REMARKS: In general plot, Lambada is a clumsy version of Stand and Deliver. The mathematics in the movie is very clumsy. Given that some of the mathematics is quite detailed and correct, and given that the mistakes and consistencies are so glaring, the errors have presumably arisen from post-production editing. Even when the individual mathematical scenes makes sense, there is not much consistency in what the students are studying, and the level of the material presented.