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Pigeons and You! A Script by Harrison Hunt -------------- [Camera zooms in on a pigeon flying in the sky (the bird pigeon, anyway)] Voiceover: What do you think of when you hear the word "pigeon"? You probably think of the so called "rat bird" that roams and flies about your neighborhood. [Camera follows bird around for a while] Voiceover: Perhaps you think of an old man sitting on a bench. [Camera shows a man sitting on a bench feeding a bunch of birds] [The Man is Mr. Gordon, who will be introduced later in the story] [The camera focuses on the man for a while. He eventually rises his head, and gives a giddy grin] Voiceover: Or, perhaps you think of the animal that decides to make a foul of your automobile. [Camera shows some kid at his car. It appears that he just completed the task of washing his car. He shakes his head in satisfaction. After that, we see bird poop fly from the sky onto the car. The young man gets upset, and throws the sponge in disgust] Voiceover: A small majority would think of this: [Camera shows a clay pigeon] Voiceover: A clay pigeon: the selected target of sharpshooters all over the world. Thousands of these are shot at every year, whether it be in competition, or for recreation. Unfortunately, only a few of these clay pigeons are actually hit, causing the sharpshooter great consternation. [Camera shows a guy at a range. We see him jerk back, indicating he has just fired. Moments later, we see the clay pigeon crash into the ground] [Camera focuses on a little boy standing in the picture] Little Leroy: But what if there was a way to help shooters become more accurate at hitting their targets? Voiceover: Oh, there is a way…and it’s called ‘calculus’. Leroy: Wow! Let’s go learn calculus and hit the range! Voiceover: Not so fast, Leroy! There is something you should know first. And here to tell you it is President George W. Bush, Former Vice President Al Gore, and NRA Representative Charlton Heston. [Camera fades from little boy] [Camera zooms in on the trio, who are sitting at a round table] Charleton Heston: Now, before we let all of you kiddies see this video, there is something you should know. Gun violence is one of the most important issues facing America and schools today. And, although we three disagree on how to stop the problem of gun violence, we all agree that we don’t want you to get the wrong idea from this video. Al Gore: I guess what Mr. Heston is trying to say is that this video tape in no way advocates the use of guns, especially in the school setting. Charlton Heston: And I know that when most of you think of guns, you think of Texas. [Bush starts hollering and hooting] Charlton Heston: Stop that. But the fact is that gun violence takes place elsewhere. From Littleton, to Santee, we all have seen enough. Bush: So, kiddies, since my vocab-oo-lary isn’t as big as Mr. Heston’s or Mr. Gore’s, my message should be pretty easy to understand…Don’t Use Drugs! [Long pause] Heston: George, we are talking about guns here. Bush: Oh, ok…I guess the message here is…Don’t Use Guns! Heston: Very good. And only the second try, too. [Bush giggles like a schoolboy who just got an answer to a hard question correct…Al Gore pats him on the back] Gore: Yeah, the Supreme Court picked the right man to be President! Bush: Was that a face-tious remark? Why don’t you go back to Tennessee, a state I won, and tell them all they voted for an idiot. Gore: George, you just opened a lockbox of pain! [Gore jumps across the table and strangles George to the floor. They grapple. Heston laughs, and says:] Heston: Well, anyway folks, now that you know guns are bad in the class, we can get back to the video. Enjoy! [Heston holds up his arm, which reveals a #1 novelty hand. Bush pries it away, and says as he smacks Gore, who is unflinching:] Bush: Take that! And that! And that! Heston: Hey, Bush…Let my finger go! [He joins fight] [We go to a technical difficulty screen] [We see Leroy] Leroy: Wow…I guess I shouldn’t use guns anymore…instead I will hit only with large foam fingers! Voiceover: Oh, Leroy! Will you ever learn! [Fade to a black screen] --------------------------------- [We see a bunch of students around a table with Mr. Resnick] Tim: Mr. Resnick, we were wondering…there is a rumor going around that myself and the rest of the rifle team have heard about a couple of old mathematics teachers that used to work here. One of them supposedly knew of a way to help people in pigeon shooting. Can you shed some light on this for us? Rest: Yeah! Resnick: I haven’t told this story in years…it is a tale of treason, hatred and mathematics. It…It…I am sorry, kids…I can’t go on. The rate of change of emotions is at a local maximum. Tim: Please. Go on. Resnick: Ok…the derivative of emotions is negative…I think I am ok…just give me t=3 seconds to regain my composure. [kids look at each other] Resnick: Ok…I can go on now…There used to be a teacher here who figured out a way to use calculus to help people do better at skeet shooting…he would go on and on and on, saying that it was brilliant. One day, he decided to show somebody his work. He showed his fellow statistics teacher. The teacher was new, but he figured that he could be trusted. Well, little did he know, the teacher stole the mathematical equations from him before anybody could see it. Needless to say, Wantagh lost to Seaford in the trap shooting finals. Even though the statistics teacher insisted that he did not steal the plans, the school board didn’t believe him, and it was decreed that the two teachers live out eternity in the high school basement for bringing such shame to Wantagh. Some say that you can hear their souls banging on the water heater pipes, struggling to be free. If you find a way to get down there, you may find them…dead or alive. Be careful…it will be dangerous. Tim: Wow…that was a compelling story. [The rest of the team is crying in the background] Berman: I think we know what we have to do…we have to go down there and find these math teachers…school pride is at stake. ------------------------------- Harry: Ok…here is what we are up against. The rifle team finals are this Saturday against Seaford. We have to go down there, find the teachers, and find out the formulas so we can win. Tim: But Mr. Resnick said it would be dangerous. Harry: Well…school pride is on the line here. Danger doesn’t scare me in times like these. Tim: I guess you are right. Lets do it for the sake of beating Seaford! Team: Yeah! Harry: Ok…first thing we have to do is find a way to get down into the basement. For that, we are going to have to ask the oldest teacher in the school…Mr. Gordon. Pomps: Why Mr. Gordon? Harry: He is the oldest member of the faculty. He has been here since they built this school. If anyone knows how to get down to the basement, it is him. Pomps: Lets Go! [camera fades out] -------------------------- [We zoom in and see the team entering Mr. Gordon’s room…there is an old man sitting at his desk, swatting flies] Tim: Mr. Gordon…we have a few questions to ask you. Mr. Gordon: Huh? Tim: [loud] Could we ask you a few questions? Mr. Gordon: Sure… Tim: Do you know of any way to get into the basement? Mr. Gordon: Sure I do. The year was 19-dang-5. I was fresh from the war, and I got a job teaching here. Back in those days, school was no more than sitting and smacking flies and kids all day if they misbehaved. Anywho, this one time I was sitting in my chair, smacking flies, and I noticed that they were dragging the statistics and calculus teachers down the hall. They were screaming and kicking and such, but they were still dragged anyway. So I followed them down the hall, and into the auditorium. They went to the back, and opened up a trap door, stuck them downstairs, and locked the door. Tim: So the doors to the basement are in the back of the auditorium? Mr. Gordon: Should be. Tim: Gee, thanks, Mr. Gordon. Mr. Gordon: Don’t mention it. [He resumes the swatting of flies as the team leaves. He swings and falls right out of his chair. The camera zooms out] -------------- [We zoom in on the team in the back of the auditorium searching the floor] Harry: Ok, so we are looking for a door in the floor? Pomps: That is what the old man said. [They continue looking] Pomps: Hey, look, a door. [They all come over and look] Tim: Hey, and there is a lock on it.] Harry: Looks pretty old…lets try to pull it off. [The team pulls…the lock comes of really easily] Harry: Wow! That was easy. I wonder why they never bothered to just open the door before. [The team shrugs] Pomps: Let’s get this door open. [They all pull on the door, and swing it open] Tim: Before we go down, what do you think we will find? Harry: I don’t know…if they have been down there as long as Mr. Resnick said, they must be dead by now. Pomps: Man, this is super freaky. Berman: Take a Scooby snack and calm down. Justin: What if we find bones down there? Tim: Well, then I guess we are out of luck. Harry: We will have to go see for ourselves. Pomps: Let’s go! [We see the team sending the first person down into the basement…the camera fades] ---------------------- [We zoom in on the boys wondering around the basement, hearing all sorts of weird sounds and noises] Justin: What was that? Pomps: Probably just the water pipes. Justin: I'm afraid to close my eyes, I'm afraid to open them. I'm so scared. [snort] [Justin stands and quivers] Tim: Come on, we have to find these people…we don’t have much time left. [They approach a tunnel] Harry: They must be through here! Pomps: I’ll go first. [The group travels through the tunnel, navigating it as it changes direction] [They come out of the other side of the tunnel] [As they come out, they are in a room filled with boxes. They look across and see two men standing and arguing] Calculus: No, no, no…You can’t push the door from the sides…It is too far from the center of gravity. You won’t be able to get enough force to push the door out. It will slam back in your face! Statistics Teacher: I disagree. There is a good chance it won’t based on the 95% confidence interval. The p-value proves it! Calculus Teacher: No, no…It is all about velocity…you know the first derivative…you have to push through the lock, which is a formidable task. Statistics Teacher: Yes, indeed…but let us analyze the strength of the lock using a difference test…when you do so, you find out that there is a 68% chance that you can break the lock by pushing it. Calculus Teacher: On what model of decay are you basing these numbers on? If it were exponential, I would agree. But if it were logarithmic, there is not a chance in the world. No, way. [At that point, Tim comes up and says] Tim: Ahemm…Ach..Ahhemm. Teachers: Ahh! Team: Ahh! [After yelling, there is a long pause] Calculus Teacher: What are you doing here? Tim: We are here to set you free. Teachers: Yeah! Alright! [the screen goes black] ----------------------- [Next, we see the group walking through the hall] Harry: So what have you been doing down here all of this time? Calculus Teacher: Well, mostly we have spent most of our time arguing how to mathematically open the door. Pomps: How did you survive? Statistics Teacher: Well, mostly, we ate rations from the old bomb shelter. I still think that pudding tastes better when it is 40 years old. Team: Ewh! [Drummer sounds a rimshot] Pomps: No, I meant how did you survive talking about math for all these years…I mean, I practically die after 10 minutes in math class. [Focus on the class nodding] [Focus on a drummer. Does a rimshot] Berman: What is that? Tim: I believe it is a drummer. Pomps: [looking up] Could you not do that, please…it interrupts our conversation. Drummer: Make me. [We see Tim run off the screen…He then runs on to the drummer’s screen…he tackles him out of his chair…Tim comes back in, brushing himself off] Tim: Anyway, why didn’t you just push on the door a long time ago? The lock looked like it was rotted out for many years… Statistics Teacher: Told you… Calculus Teacher: You got lucky that it was exponential decay. Statistics Teacher: You and your "Exponential Decay." Hah! Anyway, to answer your question, the thought of pushing on the door never came to mind…we were so busy trying to think of a way of opening the door, we never tried to push. Drummer: [with drum ring around his head] I guess the moral is to not use math, just common sense! [Tim runs off again…he comes up to the drummer, and starts kicking him vigorously…he runs back again] Tim: It had to be done. Anyway, what are your names? Statistics Teacher: My name is Lawrence Jackson…his is Tony Jones…but I am called "Stat Boy"…he is "Integral Man". Harry: Stat Boy…Integral Man…we haven’t much time. We need your help. [Scene zooms to fade] --------------------------- [Scene zooms in on the boys and the teachers in one of the classrooms] Pomps: So that is why we broke you out of the basement…we are going to need your help to beat Seaford. Justin: Real badly! Stat Boy: We would like to help you, but we are condemned to a life of living in the basement. Integral Man: We can’t help you otherwise we will get into real trouble. Harry: Think for a minute…if you help us, and we beat Seaford, we can use that as a reason to get you freed for good. [Just then, we see a shadow lurking through the window…his black gloved hand opens the door of the classroom…he then flings protractors into the room] Integral Man: Look out! All: Aghh!!!! Harry: What was that? Stat Boy: That was the infamous "Derivative Baby"… Justin: Who is that? Stat Boy: He is the one who stole the information from Integral Man. Pomps: So it wasn’t you? Stat Boy: No…I was framed. Tim: Oh, my! Stat Boy: He is going to follow your every move…you are marked people. Justin: Why did he want the theorem? Stat Boy: We don’t know. Integral Man: And, now, since we are working on it again, he will want this new theorem, too. Tim: Do you know his name? Stat Boy: He goes by the initials R.N. Other than that, we don’t know. Tim: Oh. Justin: So, anyway, can you help us? Integral Man: We can...but only so much. Justin: What do you mean? Stat Boy: We will give you the tools you need to beat Seaford...you must do the experimentation and field work yourselves. Tim: Why can't you come with us? Integral Man: We are condemned people. We cant be seen in public, or we will be caught. Harry: Well...I guess we'll have to use math, and integral man and stat boy's help to beat seaford. Pomps: Lets do it! [We fade out] -------------------------------- [We are in a classroom. We see a blackboard full of math equations. It is lengthy statistics work] Stat boy: It is quite simple, actually, this part...you must cross multiply, and solve for N. Tim: And what is "N" again? Stat boy: Simply put, it is the amount of flings of the pigeons you need to make in order to make an equation in which you will be 95% confident that the next fling of the pigeon will be adequately close to fitting the model. Tim: Oh...ok. Stat boy: Lets go over this again...in order to be sure, you must use the confidence interval, and determine the amount of throws... [Throughout the speech, the boys are starring blankly at the teacher and his board work, with mouths wide open, and non-changing facial expressions] -------------------------------------- [The boys are sitting at a table going over equations, when they are approached by Integral Man] Integral Man: Ahh, boys...good thing I found you...today, I must tell you the procedure for solving your dilemma. Pomps: Lets do it! Integral Man: Ok. Now, you went over with Stat Boy how to find out how many throws of the pigeon you have to make to get an accurate equation, right. Tim: Yup. 50, or so. Integral Man: Good. Now, simply, when you shoot at clay pigeons, you want to hit them when they "stall" at the peak of their flight path, right? Boys: Yeah Integral Man: Well, if we were to find equations for the trajectory of the pigeons, we could figure out when the pigeon stalls. We would use the derivative function, and figure out when the vertical velocity is equal to zero. Tim: Oh, I see...when it is equal to zero, you hit it at that time, right? Integral Man: Precisely! Justin: Go further, Integral Man! Integral Man: Well, first you need to get two graphs. One is the relation of the location of the pigeon in flight to the rest of the field when compared to time. [He holds up a diagram of a field, which has work drawn onto it] The other is the relationship between the height of the pigeon and time. [He holds up another diagram]. From the gathering of data from the 50 tosses, we can find an equation for both vertical height with relation to time, and location above the field. Justin: Further...FURTHER! Integral Man: You will need to collect the following data: [We watch the hands on the clock go around and around, jumping through time like a chronoskimmer] Integral Man: Ok, so that is how you are going to figure that out in the field. Tim: Wow. That is a lot of work to do. But, we better get started soon if we are going to finish...there are only 5 days left until the competition. [Just then, we see a shadow coming from outside the class. It is Derivative Baby. He opens the door, and flings rulers at the team. Tim: Look out! Berman: Agh!!! [Justin gets hit] Justin: Ow…that had a sharp corner on it [We fade out] -------------------------------------- [We see a truck pull up to a field. From the back of the truck, the group pulls out a trap. They fumble it as they carry it to the field. They then take the pigeons and bring them over to the trap. From there, they bring notebooks, tape measures, and oak tag.] Pomps: Ok...where do we start? Tim: Well, first, lets put the trap where we want it. Harry: [swollen from moving the trap earlier] Aughh! [They move the trap to where they want it to go] Tim: Then, since we are trying to eliminate all "lurking variables..." Justin: What does that mean again? I forgot! Tim: Well, your in luck...it is already conveniently printed on this card. [Holds up card] Tim: A lurking variable is is a variable that has an important effect on the relationship among the variables in a study but is not included among the variables studied. Berman: Wow...we sound like mathematicians already. Tim: We should place each pigeon an equal distance from the edge of the arm to eliminate trajectory factors. Justin: How about 3 centimeters. Harry: No, silly...This is America...Metric isn't wanted here! How about 1 inch from the end. Berman: Sounds good to me! [Tim puts first one on] Tim: Well, now that that is squared away, we must fling 50 targets, and measure their distance from the target when it lands, total time of flight of the pigeons, how many horizontal degrees off from center the pigeons are after landing, at what time the pigeons reach their peak, and how many degrees they are vertically at their peak. Once we get all of that data on paper, we can analyze it, and make some functions. Berman: Then, using these functions, we can take the derivatives and vector geometry and figure out where we need to point the gun in the competition, and at what time to fire. Harry: So lets get started throwing those pigeons! Pomps: Before we do, let me consult with the director. [Pomps walks over to the director, away from the filming area...he is in a chair, with a directors outfit on] Pomps: Now, next we fling 50 pigeons, right? Director: Yah. Pomps: And the audience has to sit and watch us do this? Director: Of course. Pomps: Why, though? Director: Because I said so! Pomps: I have a much better idea...a hoe-down! Director: Yes...that is much better! Yee-haw! [Country music starts to play out of nowhere. Everybody starts to square dance frantically around. The scenes of dancing are interwoven with the music, the firing of pigeons, the measuring of figures, and the writing down of figures.] [As the song plays on, we see the page is being filled with more and more numbers. When the song ends, the page is filled with data.] Pomps: Now, wasn't watching that much better than us firing these badboys one at a time? Director: You betcha, buckaroo! Pomps: Also, stop making me say "Let’s Go!"…it gets annoying after a while. Director: You’ve got it! -------------------------------------------------- [Back at the school] [The group sits in front of a desk with the page filled with the pertinent data from the experiment.] Tim: Ok...what we need to do now is make two equations...the first is the relationship of the sides of the field to where the pigeon actually landed. Justin: Why is this important? Harry: So we know where to aim the gun. Tim: First, since this is an imperfect world, we must make a few assumptions. First, we are going to assume that the pigeon remains at the same horizontal speed for the total duration. Second, we are going to assume that the pigeon traveled in a straight line. Third, we are going to assume that it goes at the same rate up as coming down. [Aside to camera] Mrs. Speigel, we must apologize...since this planet has things like air resistance, we know that none of these things is true. Please be kind in the scoring of this...Thank you. [Back to table] So, if we use the south side of the field as the x-axis,and the west side as the y-axis, we can make a relationship between the two. If we lay over a coordinate plane with the center of the pigeon being (0,0), we can get points to which we can base a relationship on...y is the total distance traveled Berman: And x is how far off-center the pigeon was upon landing. Harry: Precisely...We can use these points to make a regression line equation to fit the data well. Justin: And, if we take the average flight time and the average speed of all 50 tosses, we can determine just how long the regression line is. Tim: And, since we are assuming so much, halfway down the regression line is where the pigeon "stalls" in mid-air. Thus, that is the point to which we must shoot. [Throughout the entire sequence, overheads are laid on the diagram to correlate with what the person is saying.] Tim: Ok, Berman...here is what you are going to do with the data...look at the first column of data. Berman: Ok. Tim: Take the first point, and draw it on the piece of paper. Berman: Like so? Tim: Yup...now, make a triangle with that point, the line of flight, and a straight line to the x-axis. Berman: So, I am making a triangle. Tim: Exactly...now, use Pythagorean Theorem to figure out how long that line from the x-axis has to be. Berman: Ok...sin of...divide by this...Ok...I got it. Tim: Now, figure the distance along the x-axis from that straight line to flight line. Berman: Ok, cosine...divide...calculate...alright...all done. Tim: The distance of those two make up the pigeons resting point on the coordinate plane...if we get all 50 of these coordinates, we can use them to make a best fit regression line...a line that will help us to make an intelligent guess where the next shot will go. Berman: Awesome...I'll get going with those numbers. [We see the clock pass again...the rest of the team is sitting anxious outside the room where Berman works...some twiddle thumbs...others use weird site objects to pass time...the door spins with time...finally, Berman comes out and says:] Berman: Its time to make a regression line! Team: Yeah! Pomps: Let's go! [Off-screen] Director: I couldn't resist! Pomps: Tim, I think you know what to do! [Tim runs up to the director and sacks him] [Tim comes back, brushing himself off] Pomps: Thanks Tim. Harry: Hey, wait…no director…we are totally improv! [Team looks at each other…they start doing all of these weird dancing styles, like the funky chicken, and the monkey…camera zooms in and out and pans wildly…Harry raises one arm…they all stop dancing…Harry says:] Harry: Well that was fun…ok, back to work. ---------------------- [The team sits in front of a TI-89 calculator] Berman: Ok…I entered the data…it is going to give us a regression line any second… [The team waits impatiently, except for Berman, who looks bright eyed at the calculator…the camera occasionally shows the "busy" bar…it finally gives a regression line] Berman: There we go…All done…now, lets graph it. ------------------------------ [We see an overhead with the regression line and the points on a coordinate plane] Tim: Ok…now that we have graphed it, we need to make endpoints for the graph…Berman, what was the average time of flight and the average speed. [Berman looks at a chart] Berman: The average time of flight was [fill in] and the average speed was [fill in]. Tim: That means that, on average, the pigeons traveled [fill in] feet. So, the pigeon traveled from zero to [fill in] on the regression line. [Tim erases extra part of regression line] Harry: That means that the midpoint of the regression line, which is where you want to shoot, it at [fill in] feet? Tim: Right! Berman: Awesome! Harry: Next, we need to plot time versus the pigeons vertical height traveled. [The scene fades] -------------------------- Tim: Integral Man, we need your help! We need to plot the vertical height of the pigeons travels versus time! Integral Man: It is actually quite easy…do you have the data with you? Harry: Sure do, Integral Man. Integral Man: Very good. To the "Math Cave." [At this point, we hear a trumpet call, and the zoom fades] ----------------------------- [The scene is the math cave, which is just a desk in the middle of an empty basement room] Berman: Wow! This is awesome! [Camera shows the desk] Integral Man: Yes, indeed it is. Tim: Why did you re-relocate yourselves to the basement? Stat Boy: Well, since our last few experiences in the class led to us being dragged away and put in the basement, or being threatened with mathematical instruments, we figured that it was best to move down here, and create an environment where we can work freely. Justin: Leaping Logarithms, Stat Boy! Stat Boy: Yes…Leaping Logarithms, indeed! Justin: Uh…Ok…If you say so, Stat Boy. Stat Boy: I believe I did. [silence falls in the math cave] Tim: Anyway…we need you help to graph the vertical height of the pigeons in relation to time. Integral Man: It is quite easy, you see. First, make the x-axis time and make the y-axis height, like so. [Integral Man works all of the math out on oak tag] Integral Man: Then, you take the data that you used on the first equation, and you recall at what time the pigeon reached its peak. Harry: That was at [fill in with time] seconds. Integral Man: Ok…that is the maximum point of your new graph. What was the pigeons height at that point? Harry: We didn’t figure that out yet. Integral Man: Oh, ok…how many degrees high was the pigeon on average for the trials when it reached its peak? [Harry sits and figures out all of the numbers] Harry: It was [fill in] degrees high. Integral Man: Ok…Berman, use Pythagorean Theorem and figure out the height of the pigeon using this graph I have here, which is also conveniently printed out (wink, wink). Berman: [looking at diagram] Sine of this…divide…the height at that point was [fill in] feet. Integral Man: Ok… Justin: Do you have to say ‘Ok’ so much? Integral Man: Fine…I’ll say fine, instead…are you fine with that? Justin: I give up. Integral Man: Anyway, the high point of your function is the height of the pigeon, which you just figured out, and the time when it got there. Plug this in on the coordinate plane. [Justin goes over to a large diagram of the coordinate plane and plugs it in] Integral Man: Fine…You can also fill in y=0 for time [fill in], because the pigeon has landed. Also, put in y=[fill in] at time zero to represent the starting point of the pigeon. If you look at the new graph, you will realize that it looks like a cosine curve, correct? Justin: Yes, Integral Man! Integral Man: So, lets use a compass and draw the cosine graph using the three points. [Intergral Man uses the compass and makes this arc] Integral Man: We are then going to figure out the equation of this graph. Justin: [Excited] We can do this by using the calculator! Integral Man: [Under his breath] Lazy kids! Tim: Huh? Integral Man: Oh, I just called you lazy, that’s all. Tim: [Angry] For the most part, that is true…but we aren’t lazy enough to not put you back in the basement! Integral Man: Integral Man is sorry. Tim: Accepted. Justin: I got an equation! I got an equation! Integral Man: Good. We are going to need that equation to find the derivative. Harry: What is the "derivative", Integral Man? Integral Man: [sighs with pleasure] Come team, and gather around Integral Man, for he will teach you about "The Miracle of Derivatives." [Team gathers around Integral Man. He pulls out a book from his desk. The team sits Indian Style around him. He shows the team the cover of the book like they are in a kindergarten class] Integral Man: When a function gets older with time, it goes through many changes. There are ups, and downs, and sometimes no change at all. Team: Oh…Ah! [Integral Man flips the page] Integral Man: In order to find out how a function is changing at a specific time, you find its derivative. [He flips the page] Integral Man: In order to find this rate of change, you must do something magical - you take the exponent, move it to the front, and lower the exponent by one. [He flips the lage…the kids have smiles on their faces] Integral Man: And, when you do this, the stork comes and brings another entirely different function. When it is positive, the original function is increasing…when it is negative, the original function is decreasing…when it is equal to zero, there is no change at all in the original function. [The team is happy…Integral Man flips the page] Justin: Oh…Ohhh! Integral Man: Yes, Justin? Justin: Where do cosine curves come from? Integral Man: Well, that is a good question…there are certain "special cases" where function has trouble having its own derivative, so it is given one. For instance, some cases functions have to go to L’Hospital to have a derivative…and, in the case of cosine curves, they come from sine curves. Tim: So, that means that any particular time, the derivative of our function will be a sine function? Integral Man: Exactly. Team: Wow! Integral Man: And, you can use the derivative of your function to figure out when the pigeon stalls in mid-air. Harry: How? Integral Man: Just take your function, take the derivative, and set equal to zero. At that time, the pigeon will be at its maximum flight path. Team: Yeah! Integral Man: So, now you kids know "The Miracle of Derivatives". Pomps: I want to have a derivative! Integral Man: Oh, sorry Pomps…not until your older. Pomps: Oh, man! [Scene ends in dark] ------------------------------ [The scene is the basement…they are at Integral Man’s desk] Tim: So, we used the power of the derivative, just like Integral Man said, and we have the exact time where the pigeon stalls. [Integral Man comes into the room] Tim: Integral Man…we have the best-fit function, and the time when the pigeon stalls. Integral Man: Good, now we can begin the real training. [The scene closes on a dark note] ---------------------- [A sign is held up that says "Four Days Later". We see the kids seated at desks in one of the classrooms. The blackboard reads "Final Exams Today. We see Integral Man come into the class dressed as Groucho Marx.] Tim: What is with the outfit? Integral Man: It is a disguise…Remember, I can’t be seen up here! Tim: Well, then…to that I say "I never forget a face, but in your case, I’ll make an exception!" Team and Integral Man: What? Tim: Didn’t any of you see the Marx Brothers movie "Animal Crackers"? Team and Integral Man: No. Tim: Oh, then you are missing out on pure wit…Groucho says that line in the movie, and it seemed like an appropriate remark, since he is dressed like Groucho Marx, and we are supposed to forget his other face…Get it? Huh, huh? [Team and Integral Man stare blankly] Tim: No…trying to forget Integral Man’s face…Groucho Marx…you don’t get it? [Stares remain] Tim: Oh, forget it! Berman: With pleasure! Integral Man: Anyway, boys, I think that you are ready for your final exam. Berman, you are up first. Team: Go, Berman, Go! Integral Man: Your task is to find the time when the pigeon is at the peak of its flight using just the equation of the height of the pigeon in relation to time. GO! [Berman goes up to the board, and starts writing furiously. The team looks on in wonder.] Berman: Ok, the answer is at t=[fill in]. Integral Man: That is correct. You are ready for the finals. Berman: Thanks Integral Man! Oh, and give Stat Boy my regards! He kind of just disappeared there for a while, didn’t he? [We go to Stat Boy, in the basement, eating pudding] Integral Man: Will do…Tim, your up next. [Tim walks up to the blackboard] Integral Man: Tim, I want you to determine how far off center you must stand in relation to the trap with your gun so that if you aim straight ahead, you will hit the pigeon. Tim: Oh, that is easy. [Tim turns on the overhead…he draws the graph…he finds the halfway point, and drops the perpendicular…he determines the point, and the distance from the trap.] Tim: You must be [fill in] feet to the [fill in] of the trap in order to shoot straight and hit the pigeon. Integral Man: Very good…Harry, your next. [Harry goes up to the board] Integral Man: Harry, I would like you to figure out exactly at what angle you must aim the barrel of the gun from the point that Tim identified before if it is 6 feet above the ground. [Harry goes up to the board and does geometry with diagrams…he comes up with an answer.] Harry: The answer is [fill in] degrees. Integral Man: That is correct. You are good to go. Pomps, you are next. [Pomps rises and walks to the front of the room] Integral Man: I want you to figure out exactly what angle the pigeon leaves the trap after it is flung to satisfy the vertical height of the pigeon versus time equation. [Pomps writes out on the board all of the math work] Pomps: The answer is [fill degrees]. Integral Man: Very good. Now, finally, Justin. [Justin rises from his chair…we hear somebody say "Dead man walking!" He goes to the board and picks up chalk] Integral Man: You wont be needing that…your challenge is a field one, and it is the hardest challenge of them all. Justin: [scared] Uh…I just remembered…I took calculus last year. In fact, I already did this video…yeah, we were on the beach…it was great fun. In fact, I should be going, anyway. I haven’t been home in 5 days. [Justin heads for the door…Tim gets in the way] Justin: Oh, phooey! Integral Man: Getting back to your challenge…you must go in the field and aim directly at a clay pigeon. [Justin interrupts] Justin: Oh, that’s not so bad…I have done that plenty of times with the trap team. Integral Man: Not so fast; this time you will be using math as your guide. [Scene fades] ------------------------- [The scene is a clay pigeon field that we say earlier in the movie] Integral Man: What I have done here is I have set up a trap. I have also set up an auto fire devise for the gun, except, instead of shooting buckshot, it shoots pictures. You must use the trap and the auto fire device to hit the pigeon dead on. Justin: Eep. Integral Man: Let calculus be your guide! Justin: [Under his breath] Fraud…[Loud] Hey, I though Newton created calculus? Integral Man: Uh…that isn’t true at all…I did…it was all me…yeah, pure Integral Man! Justin: [under his breath] He’s a pure loon! Ok, maybe this challenge isn’t so bad. [Justin sits and thinks] Justin: Ok…well, here is what I know…Pomps said that the pigeon has to come off the trap at [fill in] degrees, so let me set that. [He goes over to the trap and sets it] Justin: Then, Tim said that the gun had to be [fill in] feet to the [fill in] of the trap. [He moves the autogun] Justin: Then, Harry said that the gun had to be at an angle of [fill in] degrees when it is 6 feet above the ground. [Justin goes over and sets the auto gun camera at the right angle and height] Justin: Then, Berman said that the length of time that the pigeon took to reach the top was [fill in] seconds. [Justin sets the egg timer on the auto gun, and holds the nob] Justin: Now, to put it all together…Harry, when I say so, let go of the pigeon on the trap. Harry: Ok… Justin: 3…2…1…release! [Harry lets the pigeon fly…at that exact moment, Justin lets go of the timer nob, letting the timer count. We watch the pigeon fly. Then the screen goes blank. We hear a pop. The screen reveals the barrel camera view at the exact moment. It is a perfect shot.] Team: Yes! [Camera to Integral Man] Integral Man: You have all passed the test…good for you all…if you shoot just like that at the tournament, you can’t lose! Team: [hoisting Justin up] Alright! Pomps: Let’s go to the tournament! ------------------------------- [We are in the classroom…the camera is zoomed on a note written on the board that says that the Wantagh trap team was the County champs beating Seaford 180 to 63. A footnote says "Thank you, Integral Man!" Another says "You rock, Stat Boy." We then see the team celebrating with the two teachers in the classroom. The two teachers aren’t in disguise.] Tim: Wow…I guess all of this business of you being condemned is over…the school board will have to release you now! [Then, we see the luminous body of Derivative Baby come into the room…he has the black gloves, a large black cap, and a cloak over his face…] Derivative Baby: Not so fast! [He throws cardboard plus symbols at the group] Stat Boy: Derivative Baby! Get him! [The whole group gets up and chases him around and about, a la "The Breakfast Club". They catch up and reveal his face…It is Richard Nixon] Tim: Richard Nixon? Richard Nixon: I am not a crook! Harry: Tell us, why did you do it? Richard Nixon: The motive was so clear…I didn’t want the Commies and Castro to get hold of this "calculus". With it, they could stop our missles. Berman: But why would you shut down a small school operation just to prevent something that never would have happened anyway? Richard Nixon: Richard Nixon always does things on a grand scale. He will go to any lengths to get the job done. Pomps: What did you do with the "Mathgate Papers"? Richard Nixon: I burned small portions of them…I figured then nobody could guess what was going on. Harry: Why didn’t you burn the whole thing? You left it out in the open, like the Watergate Tapes, didn’t you? Richard Nixon: I don’t know why I don’t burn the whole thing…I suppose I should start…anyway, there are a lot of things people don’t know about Watergate…The real reason I sent them into that hotel was to get me some maple syrup for my pancakes. I figured that nobody would notice if I some from there. Well, I guess I was wrong. Justin: Why didn’t you come clean? Richard Nixon: Because "Watergate" sounds better than "Pancakegate", now doesn’t it? Justin: I guess that’s true. Nixon: Anyway, I have to go…good thing this wrapped up nicely. Integral Man: Not so fast…get him! Nixon: AHH!!!! [At the end of the credits, we see the old man in his room, still on the ground trying to get up…he says:] Mr. Gordon: Help! Somebody please help me up! When I get up I am going to smack all of you good for not helping me up! Lazy kids! |
