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1959 - Donald Duck - Donald in Mathmagic Land

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    Very strange.
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    Huh, that's an odd-looking creature
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    What kind of a crazy place is this?
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    Well, what do you know? Square roots!
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    Pi is equal to 3.141592653589747 etc. etc. etc.
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    Hello? (echo)
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    Hello, Donald.
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    That's me! Where am I?!
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    Mathmagic land.
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    Mathmagic land? Never heard of it.
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    It's the land of great adventure.
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    Well, who are you?
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    I'm a spirit, the true spirit of adventure.
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    That's for me! What's next?
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    A journey through the wonderland of mathematics.
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    Mathematics? That's for eggheads!
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    Eggheads? Now hold on, Donald.
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    You like music don't you?
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    Yeah.
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    Well, without eggheads, there would be no music.
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    Bah.
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    Come on, let's go to ancient Greece, to the time of Pythagoras, the master egghead of them all.
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    Pythagoras?
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    The father of mathematics and music.
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    Mathematics and music?
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    Ahh, you'll find mathematics in the darndest places.
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    Watch
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    First we'll need a string
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    Hey!
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    Stretch it good and tight; pluck it!
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    Now divide in half. Pluck again.
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    You see? It's the same tone, one octave higher.
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    Now divide the next section.
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    And the next.
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    Pythagoras discovered the octave had a ratio of two to one.
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    With simple fractions, he got this [major triad]
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    And from this harmony in numbers, developed the musical scale of today. [major scale]
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    By golly, you DO find mathematics in the darndest places.
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    You can imagine how excited Pythagoras was,
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    when he shared his findings with his pals and fraternity of eggheads, known as the Pythagoreans.
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    They used to be meet in secret to discuss their mathematical discoveries.
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    Only members were allowed to attend.
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    They had a secret emblem, the pentagram.
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    Let's see what the topic is for today.
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    [major scale]
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    [music]
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    What's going on?
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    Shh! It's a jam session.
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    Gimme something with a beat!
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    Shhh!
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    [percussion]
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    So from these eggheads, the Pythagoreans,
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    with their mathematical formula
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    came the basis of our music of today.
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    [big band]
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    Pythag, old boy, put her there
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    Now I'll be a goshdarned egghead [laugh]
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    It was our old friend Pythagoras who discovered that the pentagram was full of mathemagic.
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    The two shorter lines combined exactly equal the third
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    and this line shows the magic proportions of the famous golden section
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    The second and third lines exactly equal the fourth
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    Once again we have the golden section
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    But this is only the beginning
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    Hidden within the pentagram
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    is a secret for creating a golden rectangle
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    which the Greeks admired for its beautiful proportions and magic qualities
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    The star contains the golden rectangle many times over
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    It's a most remarkable shape
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    It can mathematically reproduce itself indefinitely
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    All these rectangles have exactly the same proportions
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    This figure also contains a magic spiral
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    that repeats the proportions of the golden section into infinity
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    To the Greeks, the golden rectangle represented a mathematical law of beauty
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    We find it in their classical architecture
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    The Parthenon, perhaps one of the most famous of early Greek buildings,
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    contains many golden rectangles.
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    These same golden proportions are also found in their sculpture.
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    In the centuries that followed
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    the golden rectangle dominated the idea of beauty in architecture throughout the Western world.
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    The Cathedral of Notre Dame is an outstanding example.
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    The Renaissance painters knew this secret well.
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    Today, the golden rectangle is very much a part of our modern world.
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    Modern painters have rediscovered the magic of these proportions.
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    Indeed, this ideal proportion is to be found in life itself.
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    Boy, oh boy, oh boy!
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    This is mathematics? I like mathematical figures like that.
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    Ah, ah, ah, Donald.
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    Let me try it!
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    No, no.
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    Ideal proportion
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    Not quite
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    Uh uh. No, I'm afraid not.
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    Well, we can't all be mathematically perfect.
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    Oh yeah?
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    There, I knew I could do it.
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    Now that you're all pent up in a pentagon
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    let's see how nature uses the same mathematical form.
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    The petunia
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    The star jasmine
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    The starfish
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    The wax flower
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    There are literally thousands of members in good standing
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    in nature's Pythagorean society of the star.
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    All nature's works have a mathematical logic
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    and her patterns are limitless.
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    The magic proportions of the golden section
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    are often found in the spirals of nature's designs.
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    The profusion of mathematical forms brings to mind the words of Pythagoras:
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    "Everything is arranged according to number and mathematical shape."
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    Yes, there is mathematics in music,
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    in art, in just about everything.
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    And as as the Greeks had guessed, the rules are always the same.
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    Well, Donald, did you enjoy your geometrical journey?
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    Gee, Mr. Spirit, there's a lot more to mathematics than two times two!
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    That's right, Donald
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    And you can find mathematics in games, too!
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    Games! Oh, boy!
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    Let's begin with a game that's played on squares.
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    Checkers?
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    No, chess.
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    Chess?!
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    A mathematical contest between two minds.
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    It's a game that has been enjoyed for centuries by kings and commoners.
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    In fact, Louis Carroll, a famous mathematician with a literary mind,
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    used chess as a setting for his classic tale, Through the Looking Glass.
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    Alice found herself face to face with a none-too-friendly group of chess pieces.
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    Good heavens, what's this?
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    Upon my soul, it appears to be a lost pawn!
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    I'm no pawn, I'm Donald Duck!
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    He says he's Donald Duck!
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    Preposterous!
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    Or, it could be an Alice.
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    Alice?!
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    No, no no. It's a lost pawn.
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    Lost pawn? Stop that pawn!
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    Ow, Mr. Spirit! Help, help, help!
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    Whew, that was close!
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    Now you can look at this game from a safer perspective.
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    Chess is a game of calculated strategy,
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    and since the board is geometrical,
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    the moves are mathematical.
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    Checkmate, and the game is over.
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    That's very interesting. What's next?
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    Practically all games are played on geometrical areas.
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    The baseball field is a diamond.
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    Oh boy!
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    And without mathematics, we couldn't even keep score.
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    Football is played on a rectangle divided by yard lines.
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    Basketball is a game of circles, spheres and rectangles.
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    Even hopscotch has its multiple squares.
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    What's next?
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    Tiddlywinks?
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    No, a mathematical game played on a field of two perfect squares
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    using three perfect spheres
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    and a lot of diamonds.
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    In other words, billiards.
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    Oh boy! That's for me!
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    You know the game, don't you Donald?
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    Of course, the cue ball has to hit the other two balls
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    like this!
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    Now let's see how an expert at three-cushion billiards uses his head.
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    Three-cushion?
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    Yes. The cue ball not only has to hit both the other balls,
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    but it must contact at least three cushions before it hits the final ball.
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    One, two, three
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    One, two, three
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    It takes an expert to make several shots in succession
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    One, two, three, four
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    five, six.
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    Wow! That was a lucky shot!
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    Luck? No. It's skill.
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    For this game, you have to know all the angles.
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    One, two, three, four, five, six, seven.
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    That's amazing! How does he do it?
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    First, there's technique.
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    He's striking the cue ball low, so it'll spin backwards.
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    Hitting the ball on the right side will make it hug the rail.
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    These trick shots take a lot of practice.
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    Hahaha! He missed that time!
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    One, two...
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    three.
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    What's so mathematical about that?
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    Oh, this game takes precise calculation.
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    He figures out each shot in his head.
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    He could play it like this, but it calls for quite a bit of luck.
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    There is a better choice.
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    For this, he uses the diamond markings on the rail as a mathematical guide.
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    First, he figures the natural angle for hitting the object balls.
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    And then he finds that his cue ball must bounce off the number three diamond.
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    Next, he gets ready for the shot and he needs a number for his cue position.
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    This calls for a different set of numbers.
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    Very confusing, isn't it?
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    Not when you get the hang of it.
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    You see, the cue position is four.
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    Now, a simple subtraction.
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    Three from four is one.
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    So, if he shoots for the first diamond, he should make it.
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    It's called "playing the diamond system".
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    Natural angle, 2.
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    Cue position, one and a half, two, two and a half, three,
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    three and a half.
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    Two from three and a half is one and a half.
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    So, shoot halfway between the first and second diamonds.
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    There's nothing to it! Let me try!
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    Let's see now.
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    If I shoot it here, and it bounces there, and uh, no there.
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    If I shoot it here...
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    Four and half minus three, three and a half plus four...
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    Add it to two...
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    And dividing it.. and...
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    I guess I should shoot about here.
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    No, no, Donald. There's no guesswork to mathematics.
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    It's quite simple.
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    Natural angle for the hit: two.
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    Cue position: three and a half.
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    How much is three and a half minus two?
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    Uhhh... one and a half!
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    Hey! It works! Oh boy!
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    It's a cinch!
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    If i hit it here, add three and a half plus four
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    Four and a half minus three... [???]
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    You're making it tough for yourself, Donald.
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    How do you like that for mathematics, Mr. Spirit?
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    Wonderful, Donald. And now you're ready for the most exciting game of all.
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    Oh, boy!
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    And the playing field for this game is in the mind.
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    Uh oh, look at the condition of your mind!
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    Antiquated ideas, bungling, false concepts, superstitions, confusion!
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    To think straight, we'll have to clean house.
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    There, that's more like it.
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    A nice clean sweep.
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    This game is played with circles and triangles.
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    Think of a perfect circle.
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    A perfect circle. Perfect. Circle.
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    Perfect. Ahhhhh.
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    Put a triangle inside and turn it.
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    Now spin the circle, and what have you got?
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    A ball!
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    Yes, a sphere.
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    The shape of things is first discovered in the mind.
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    Slice off the top and we have a...
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    A magnifying glass!
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    That's right.
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    A lens is a section of a sphere.
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    All optical instruments are created through mathematics.
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    You see, there's a lot more to mathematics than just numbers and equations.
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    Let's get back to our circle and triangle.
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    Roll it and we have a...
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    A... a wheel!
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    The circle has been the basis for many of man's important inventions.
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    The mind can create the most amazing things.
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    If we spin the triangle, we have a...
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    Cone!
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    Slice the cone.
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    giggle
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    The cone is full of useful mathematical shapes.
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    Slice it again. Slice it several times.
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    The orbits of all planets and satellites can be found in the cone.
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    No matter how you slice it, it's always mathematics.
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    A slice like this gives us the reflector of a search light.
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    A slice like this, the mirror of a giant telescope.
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    A line on a cone, and we have a drill.
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    And the spring.
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    Now you're ticking.
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    Number, please?
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    The mind is the birthplace for all of man's scientific achievements.
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    The mind knows no limits when used properly.
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    Think of a pentagram, Donald.
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    Now, put another inside.
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    A third. And a fourth.
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    No pencil is sharp enough to draw as fine as you can think
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    and no paper large enough to hold your imagination.
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    In fact, it is only in the mind that we can conceive infinity.
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    Mathematical thinking has opened the doors to the exciting adventures of science.
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    I'll be dog-darned!
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    I've never seen so many doors before.
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    Each discovery leads to many others.
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    An endless chain.
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    Hey! Hey! Whatsa matter with these doors?
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    Hey! These doors won't open! They're locked!
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    Of course they're locked.
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    These are the doors of the future,
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    and the key is...
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    Mathematics!
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    Right. Mathematics.
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    The boundless treasures of science are locked behind those doors.
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    In time, they will be opened by the curious and inquiring minds of future generations.
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    In the words of Galileo:
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    "Mathematics is the alphabet with which God has written the universe."
Title:
1959 - Donald Duck - Donald in Mathmagic Land
Description:

Donald wanders into a magical land where the beauty of the laws of mathematics unfold before him.

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Video Language:
English
Duration:
27:36
dmoncangel added a translation

English subtitles

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