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Mathematics Goes to the Movies
by Burkard Polster and Marty Ross
C'est la tangente que je prefere (LOVE, MATHS AND SEX) (1997)
Opening sequence shot
SABINE (THINKING): Why are these three points aligned? This one's the middle of the segment. How was that one drawn up? Ah, it's the centre of the circle.
(walking across a circular roundabout.)
SOME GUY: 3818 multiplied by 132...3818 multiplied by 132...
SABINE (THINKING): We have that vector. I've already used the equilateral hypothesis. It can be used twice. So why does it work? Ah, these two angles are equal. Then this one is equilateral. Which gives us a rhombus. The two vectors are equal. This one, is a third of that one. So the three points are aligned.
(Looking down a row of "aligned pillars)
CLASSMATE: Careful, the maths teacher!
TEACHER: Sabine, can I see you a minute? (telling her about some international maths Olympiad, poster)
The best from each county go to Brussels for a year. I'm sure you have a good chance.
SABINE: But... do we have to pay?
TEACHER: Just the journey and three nights in a hotel for the competition. But you know...you have to be picked for France first.
SABINE (THINKING): This meant planning long term. A lot of work, more than two hours a day and unpaid, a loss of about 15O francs. I'm good at finding solutions, not only in maths. I'll sleep two hours less.
SABINE: You replace b with its value, that makes 16...
CLASSMATE: You do it.
SABINE: It's like in class, just stick to the formula. If it's positive you have 2 solutions, or else no solution in real numbers. It's easy when you explain it. And if you weren't so lazy. 5 francs. You're lucky, a parabola is 15.
CLASSMATE: I've scored 15O million! I've broken all records! Better than your equations!
OTHER CLASSMATE: She won't buy it.
SABINE (THINKING): Luck would have it that Josephine's parents got back late, setting off a chain of events. No more buses so I walked home, obsessed with my exercise. Then I wandered of my route. (SEES THE MYSTERY MAN ON THE BUS AGAIN. FROM WHAT HE DOES SHE CONCLUDES) So he was a cop. Was it simply a coincidence? No, there was a meaning to it all. Who was that man who crossed my path? ... I didn't see him that day, three times in a row can't be accidental.
(SEE HER DOING AN EXPERIMENT. TOSSING SOME CRACKER IN THE AIR AND CHECKING WHETHER WHICH WAY IT LANDS, COUNT BY PUTTING CROSSES ON A PIECE OF PAPER)
It's a twist of fate, the chances of it falling face up: one in ten. Face up three times running: one in a thousand. The probability of meeting him again: infinitesimal.
(meets the stranger again)
SABINE (THINKING): Three times running! I've never trusted probabilities, I should have used statistics. Tossing bread and butter isn't destiny.
SABINE (THINKING): If they question me, I'll lie while telling the truth, like in logic. After all, when I say: "I am telling a lie" am I lying or telling the truth?
FATHER (a bad gambler): I could have won a fortune with Jean-Pierre. Then there'd be no summons. He's bad luck for me. High stakes pay off, he says, so I double my losses!
SABINE: Sure. You halve your chances.
SABINE: But you'd have won double if you'd won. You're more likely to win by playing lots of columns, not a lot on one column.
FATHER: If you're so smart where's my 3OOO francs?
LITTLE SISTER: If there's no money, Sabine can write a cheque.
SABINE calculating on the wall how many times she has to do something for her classmates to earn 3000 francs.
By 5: 6OO 2nd degree equations,
By 15: 2OO parabolas,
By 3O: 1OO derivatives.
A good exam exercise, but even if I up my prices and only coach 6th formers
to make 3OOO francs I'll have to speed it up.
CLASSMATES: Sabine's too fast for us. We're not machines. We need time to think. This isn't the Einstein competition. Want to apply, Emile?
(SOME GOOD BLACKBOARDS)
TEACHER: The selection is still open. Take it again; a - 2, factor of...
SABINE CONTINUES: Factor of
a squared + a + 2 = O.
Delta = b squared -4 ac.
a - 4 x 2 = - 7.
l didn't think a man could be so good, So gentle, so strong, so geometrical. What's the nearest shape? The trapezium? More like a heptagon topped with a circle,00:37:15
TEACHER: You must get to work for this exam. You haven't been selected yet. It's not easy! You must work! I'll set you some new problems. We've discussed the real numbers, there's also the complex numbers, an even more abstract notion. A beautiful construction, purely mathematical... you'll never find it in nature. Geometry in space needs imagination. I'm sure you'll enjoy it.
SABINE thinking: How does it apply to masculine and feminine? I can admit they're two different sets, but are they disjoint or do they have an intersection? Unless they're overlapping? No, the situation is more symmetrical. So what's the intersection? It can't be an empty set! There are mutual points, even if we are different.
Working in the theatre gave him time to meet people, the parameters had changed, the configuration cop + hooker worked. But this form was more complex. How would it turn out?
JIRI: That my life now is as empty as this glass?
SABINE: Define empty. This glass isn't an empty set. It's empty now, but it could contain vodka. It's simple: an empty set is a set of elements with incompatible properties. Like white blackbirds! It looks quite normal to me (the glass). No cracks or chips, it doesn't seem to leak.
SABINE (thinking): A man of 4O with a girl less than half his age, 4O - 15 = 25, 25 is a lot! What's the common factor? 4O over 15 cancelling by 5 gives 8 over 3. Only 5 years difference!41:47
Sabine doing some calculations in front of some committee (get blackboard)
AO squared + OE squared = AE squared according to Pythagoras's theorem.
We know OE = A root of 2 over 2... so OE squared = small A squared over 2... = half of AC.
Finished with the test
SABINE: I don't know. I did it but...
CLASSMATES (CHEERING HER ON): Sabine to Brussels! \
SABINE: They only take 6 from each county.
CLASSMATE: 6! Disgusting!
SABINE: If we're 15O,OOO, the odds are 1 in 25,OOO.
CLASSMATE: Give yourself a break.
OTHER CLASSMATE: The teacher's backing you!
SAME GUY FROM THE BEGINNING of the movie: 3818 x 132... 3818 x 132.00:44:12
CLASSMATE (Sabine is helping her): Now I look for the limit that y curves towards. We won't finish this exercise today. ...
SABINE: What are they (some of the classmates relatives) playing?
CLASSMATE: Backgammon... since childhood. Shall we continue? Call me when you've got a perfect example.
ONE OF THE PLAYERS: Let's go! l, 2... 3.
(Sabine sticks around to watch them play)
SABINE (thinking): They played two moves in advance, I could see four.
SABINE (giving advice): Not there.
SABINE (thinking): Even if I took them both on they couldn't beat me. Two against a girl: easy! Next step: get them playing for money.00:46:21
TEACHER: Great news, you've been selected!
SABINE: I'm one of the 6?
TEACHER: I'm so proud of you!
SABINE: When is it?
TEACHER: The 3rd, 4th and 5th in Brussels. Now you have 1 chance in 4. Stimulating, eh? A year with others on your level.
SABINE: What do I do now? Work hard! Your parents must write a letter.00:49:02
Thank God he was there. He was my vector.
I thought I'd smothered the pain but it kept coming back, worse than ever, the coefficient of the slant had been low but now it was rising. And I realized that the slant was inverted and the angle was sharper. The 2nd derivative was negative, Now what? Do I let myself slide? (drawing)
some math pictures on the wall
SABINE (lost at backgammon): The problem with games of chance is chance, At 8 to 1, I could have cleaned up, 4OOO in one game! But not a single 6. Not one double throw. It wasn't my game. Why didn't I see it in time?
SABINE (thinking): The equation was simple while he was the unknown quantity. I surprised myself. Now there were 2 unknowns. Was there still a solution? For the first time he said "I love you", and I believed him.
TEACHER: We've never discussed topology. See this? It's a Möbius strip. It joins a point on the inner surface to the outer without changing sides. Run your finger along the inside of the strip, you're inside... keep going and bingo! You're on the outside. You always come back changing sides.
Get shot and movie
SABINE (THINKING): They could do what they liked. I was invincible. I threw myself into maths. It had always been my refuge, and to my joy the mechanism functioned as perfectly as ever. I had to win the competition. Theatres are everywhere and exile would solve the legal problems. (GET SHOTS OF GRAPHS ON THE WALL)
SISTER: Is it complicated, Sabine?
SABINE: Very. But I must get it right.
SABINE: We can plot this curve differently. It must have a function. A function is more precise than your word, grace.
JIRI: It doesn't have the same ring. It doesn't tell us about the aesthetic quality. Is beauty a question of proportions for you?
SABINE: Beauty is harmonious. Geometry never betrays.
JIRI: Function opposing grace. How can we communicate?
SABINE: By drawing! Symbols! It's the same for everyone!
JIRI: That can be very dangerous.
How do you symbolise freedom? The joy of being together?
SABINE: By space! We're here. But if I do that? We're here. No, we're here. (DRAWING IN THE SAND)
And if I do that... 1, 2, 3... Then we're here! It depends the frame of reference.
JIRI (TO SOMEONE WALKING ACROSS HER DRAWINGS) Hey, sir, don't walk there please. You're trampling over her odalisque... Please.
SABiNE: The sea will wash it away. I'll remember it.
The maths competition
TEACHER: You couldn't have known. We do that next year. You had to express numbers in base 2. It's a tough problem. Don't lose heart, you can take it again next year. (blackboard)
SABINE: No one's mentioned base 2 since primary school!01:34:45
What now? Was life like the Möbius strip? You think you've crossed over, found a way out, then you're back at the beginning? It's not possible, there must be a way out.