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Файл:M&Ms. Movies and Maths. Учебно-методическое пособие
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3. In Russia, East and West fuse together in a way that is surprising to observe.
a. to join or become combined
b. to deal with
4. That you have been chosen in the contest seems divine intervention.
a. relating to God
b. dividing
5. Can you give any evidence to support your claim?
a. a statement that something is true
b. a false accusation
6. Calculus can be used to calculate such things as rates of change, the area bounded
by curves, and the volume bounded by surfaces.
a. adding numbers
b. a branch of mathematics
D. If you are interested in this topic, go to The Golden Ratio and Fibonacci in Music for
more information –
https://www.youtube.com/watch?v=9mozmHgg9Sk&ab_channel=SoundField
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Appendix Scripts
Unit 1
Gifted
Mary: So, what's this problem I am supposed to look at?
Mary’s grandmother: I don't know.
Mary: Is it like the problems Mom worked on?
Mary’s grandmother: Your mother didn't work on problems. She worked on just one
problem.
Mary: Just one? Her entire life?
Mary’s grandmother: Most of it. Look. These are the Millennium Problems. Seven
great and meaningful problems. Some mathematicians have worked their entire lives
to prove them.
Mary: Who's the dude with the beard?
Mary’s grandmother: That's not a dude. That's Grigori Perelman. He proved
the Poincaré conjecture. The only one of the seven proved. This...This is your mother's
problem.
Mary: Na... vi...
Mary’s grandmother: Navier-Stokes.
Mary: No picture. She didn't solve it?
Mary’s grandmother: No. She was close. She would have won the Fields Medal...and
probably shared a Nobel... considering what it would have meant for physics.
Mary: Maybe I'll have my picture up here someday.
Mary’s grandmother: If you really desire it...you can have your picture there, darling.
I can help you. It takes focus and hard work, but if you succeed...your name will live
forever. ….Don't be smug, Seymore.
Seymore: Well, she's had plenty of time.
Mary’s grandmother: She traveled yesterday. She slept in a strange bed. Give her
a chance. At six years old she read Zimmer.
Seymore: Outstanding. How much did she comprehend? …So, Mary... I see you're
looking at our little problem.
Mary: Little? It's big.
Seymore: Yeah.
Mary: Why are you so mad all of a sudden?
Mary’s grandmother: I'm not mad. I'm annoyed. Not with you, dear. With that
pompous ass, Shankland.
Mary: I knew that guy was gonna have a beard before we even went in there. Math
teachers like to grow beards.
Mary’s grandmother: I should never have agreed to this in the first place. Did he
really expect you to just walk in and be able to dissect ... some random, massive
problem?
Mary: Not much to dissect, if you ask me.
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Mary’s grandmother: Why? Why do you say that?
Mary: It was wrong.
Mary’s grandmother: What?
Mary: Well, for starters, he forgot the negative sign on the exponent. It went downhill
from there. The problem was unsolvable. Maybe this school isn't as great as you think
it is.
Seymore: Mary, you knew the problem was incorrect. Why didn't you say anything?
Mary: Frank says I'm not supposed to correct older people. …Nobody likes a smart-
ass.
Unit 2
A Beautiful Mind
The Principal: Mathematicians won the war. Mathematicians broke the Japanese
codes…and built the A-bomb. Mathematicians... like you. The stated goal of
the Soviets is global Communism. In medicine or economics, in technology or space,
battle lines are being drawn. To triumph, we need results-- publishable, applicable
results. Now who among you will be the next Morse? The next Einstein? Who among
you will be the vanguard... of democracy, freedom, and discovery? Today, we bequeath
America's future... into your able hands. Welcome to Princeton, gentlemen.
Man 1: It's not enough Hansen won the Carnegie Scholarship.
Man 2: No, he has to have it all for himself.
Bender: It's the first time the Carnegie Prize... has been split. Hansen's all bent.
Neilson: Rumor is he's got his sights set on Wheeler Lab, the new military think tank
at M.I.T.
Bender: They're only taking one this year.
Neilson: Hansen's used to being picked first.
Man 1:Oh, yeah, he's wasted on math. He should be running for president.
Nash: There could be a mathematical explanation... for how bad your tie is.
Neilson: Thank you. Neilson, symbol cryptography.
Bender: Neils here broke a Jap code. Helped rid the world of fascism. At least that's
what he tells the girls, eh, Neils? The name's Bender. Atomic physics. And you are?
Sol: Am I late?
Neilson: Yes. Yes, Mr.Sol.
Sol: Oh, good. Uh, hi. Sol. Richard Sol.
Hansen: The burden of genius…
Sol: There he is.
Hansen: So many supplicants, and so little time. Mr. Sol. How are you, sir? Ah,
Bender. Nice to see you.
Bender: Congratulations, Mr. Hansen.
Hansen: Ah, thank you. I'll take another.
Nash: Excuse me?
Hansen: A thousand pardons. I simply assumed you were the waiter.
Bender: Play nice, Hansen.
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Neilson: Nice is not Hansen's strong suit.
Hansen: Honest mistake.
Nash: Well, Martin Hansen. It is Martin, isn't it?
Hansen: Why, yes, John, it is.
Nash: I imagine you're getting quite used to miscalculation. I've read your pre-prints…
both of them. The one on Nazi ciphers, and the other one on nonlinear equations, and
I am supremely confident... that there is not a single seminal... or innovative idea in
either one of them. Enjoy your punch.
Hansen: Gentlemen, meet John Nash, the mysterious West Virginia genius. The other
winner of the distinguished Carnegie Scholarship.
Bender: Oh, okay.
Sol: Oh, yeah?
Bender: Of course.
Unit 3
Einstein and Eddington
Dyson: What are you reading? You look overcome.
Eddington: Come to supper.
Eddington’ sister: For what we are about to receive, may the Lord make us truly
thankful.
Eddington: Amen.
Eddington’ sister: Amen.
Eddington: It’s called general relativity. It’s a theory of gravity. And…everything. He
has done it. Let me just…Sorry. Let me just show you.
Eddington’ sister: What … are you doing? Have you gone mad?
Eddington: Dyson, the other end. Pick it up. Pick up the table cloth. Space. The table
cloth is space. The sun. What’s happening?
Eddington’ sister: What?
Eddington: What’s happening with the sun and space?
Eddington’ sister: The bread is sinking into the table cloth.
Dyson: The sun makes a shape around it in space.
Eddington: Yes! Now what happens if I do this? It wants to travel in a straight line
but it can’t. Why not?
Eddington’ sister: Because the bread is making shape.
Dyson: The apple follows the curves made in space made in space.
Eddington: Yes. Yes. Space is shaped. And that is how gravity works. Space tells
objects how to move. Objects tell space what shape to be. And there’s a way to prove
it. When statrlight comes near to the sun, what will happen to it?
Eddington’ sister: It will bend
Eddington: Yes. That’s what he says. That’s what Einstein says. Starlight will bend.
Every theory needs proof. And I am the man to prove it.
Dyson: The English observer and the German theorist.
Eddington: Hand in glove.
55
Dyson: We are at war, Eddington. Germany is our enemy.
Eddington: I love my country very deeply. But my country is my country, and this…
This is so much more. Will you help me?
Unit 4
Hidden figures
Scene 1
Katherine: The problem is when the capsule moves from an elliptical orbit to
a parabolic orbit. There’s no mathematical formula for that. As we can calculate launch
and landing but without this conversion, the capsule stays in orbit, we can’t bring it
back home.
Mr Harrison: Maybe we’ve been thinking about this all wrong.
Paul Stafford: How’s that?
Mr Harrison: Maybe it’s not new math at all.
Katherine: It could be old math. Something that looks at the problem numerically,
and not theoretically. Math is always dependable.
Mr Harrison: For you it is.
Katherine: Euler’s Method.
Paul Stafford: Euler’s Method?
Katherine: Yes.
Paul Stafford: That’s ancient.
Katherine::But it works! It works numerically.
Mr Harrison: That's it!
Paul Stafford: Let’s type it up.
Scene 2
Mr. Harrison: This is Katherine Goble with our Trajectory and Launch Window
Division. Her work is pertinent to today’s proceedings. Come on. Get her a chair. We
have a confirmed launch window.. Give her your chair. We have a confirmed launch
window for Friendship 7. Let’s discuss a landing zone.
Speaker 1: The Navy needs a singular landing zone.
Speaker 2: 20 miles square is what we can service for retrieval. Outside of that, we
risk the capsule’s recovery.
Paul: We’d like 3 possible recovery areas.
Speaker 2: We can’t cover half the damn ocean.
Mr. Harrison: With all due respect our capsule’s being altered daily. We’re orbiting
the Earth at... what’s the speed now?
Katherine: 17,544 miles per hour. At the time the rocket delivers the capsule into low
space orbit.
Colonel Glenn: That’s one hell of a speeding ticket.
Speaker 3: OK. So we have the vehicle's speed, the launch window and for argument’s
sake, the landing zone is The Bahamas. Should be enough to figure the Go/No Go?
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Paul: Yeah! In theory, sir.
Speaker 3: We need to be past theory at this point.
Mr. Harrison: We’ll be able to calculate a Go/No Go with that information.
Speaker 3: When exactly is that gonna happen?
Mr. Harrison: Katherine. Have a go at it?
Katherine: The Go point for re-entry is 2,990 miles from where we want Colonel
Glenn to land. If we assume that’s The Bahamas. At 17,544 miles per hour.. upon
reentry.. 37o feet.. At a descent angle.. of 46.56 .. degrees.. distance.. Velocity square
… sin… gravity… 32 feet… distance… 20 530 372 feet or 2 990 miles or 46.33
degrees OK! So, that puts the landing zone at... 25.0667° North, 77.3333° West.
Which is here! Right here. Give or take 20 square miles.
Colonel Glenn: I like her numbers.
Katherine: Thank you.
Speaker 3: That of course is assuming the .. capsule hits the reentry point exactly. How
do we ensure that?
Mr. Harrison: That’s the math we don’t have yet, gentlemen. We’re working on it.
Katherine!
Unit 5
Pi
Professor: Syracuse, eh? …The King asks Archimedes to determine if a present he
has received is actually solid gold – unsolved problem at the time! It tortures the great
Greek mathematician for weeks – insomnia haunts him, and he twists and turns in his
bed for nights on end. Finally, his equally exhausted wife – she is forced to share a bed
with this genius – convinces him to take a bath, to relax. While he is entering the tub,
Archimedes notices the bath water rise. Displacement – a way to determine volume,
and, thus, a way to determine density: weight ver volume. And, thus, Archimedes
solves the problem, he screams “Eureka!” And he is so overwhelmed, he runs dripping
naked through the streets to the King’s Palace to report his deiscovery. Now, what is
the moral of the story?
Max: That a breakthrough will come.
Professor: Wrong! The point of the story is the wife. You listen to your wife, she will
give you perspective, meaning you need a break, you have to take a bath or you will
get nowhere. There will be no order, only chaos. Go home, Max, and you take a bath.
57
Unit 6
The GR
The sequence begins with the numbers 1, 1, 2, 3, 5, 8, 13, 21, 34, and continues
indefinitely. Each number is obtained by adding the last two digits together. If we were
to take a perfect or golden rectangle, break it down into smaller squares based on
Fibonacci sequence and divide each with an arc, the patterns begin to take shape. We
begin to see Fibonacci spiral. The spiral in and of itself is insignificant, its importance
is revealed in where we find it. Take for example the sunflower. Its florets are in perfect
spirals of 55, 34 and 21, the sequence of Fibonacci. The fruitlets of the pine-apple
create the same spiral based on the sequence. The pine-cone does the same. As currents
move through the ocean and the tide rolls on to the shore, the waves that bring in
the tide curve into a spiral that can be mathematically diagrammed onto a plot at
the points 1, 1, 2, 3, 5, 8, 13, 21, 34 and 55. Buds on trees, sand dollars, starfish,
petals on flowers, and especially the nautilus shell are formed with this exact same
blueprint. With each segment of growth, the nautilus adds to itself one more value on
Fibonacci scale. This blueprint can be seen around us on a small scale every day. But
the greatest example of all is directly above our heads. At an average of 100 000 light
years across even the spiral of the galaxies above us are formed with the exact design
that the tiny shell is formed.
Учебное издание
Шилова Валентина Владимировна
M&Ms: MOVIES AND MATHS
Учебно-методическое пособие
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