Donald in Mathmagic Land

Transcript

 * Donald: Mighty strange. Ha! That's an odd-looking creature. What kind of a crazy place is this? Well, what do you know! Square roots!
 * Pi Creature: Pi is equal to 3 point 141592653589747 Et Cetra, Et Cetera, Et Cetra.
 * Donald: Huh? [Echoing] Hello!
 * Spirit: Hello, Donald.
 * Donald: That's me! Where am I?
 * Spirit: Mathamagic Land.
 * Donald: Mathamagic Land? Never heard of it.
 * Spirit: It's the land of great adventure.
 * Donald: Well, who are you?
 * Spirit: I'm a Spirit. The true spirit of adventure.
 * Donald: That's for me. What's next?
 * Spirit: A journey through the wonderland of mathematics.
 * Donald: Mathematics? That's for eggheads.
 * Spirit: Eggheads? Now, hold on, Donald. You like music, don't you?
 * Donald: Yeah.
 * Spirit: Well, without eggheads, there would be no music.
 * Donald: Aww!
 * Spirit: Come on. Let's go to Ancient Greece. To the time of Pythagoras. The master egghead of them all.
 * Donald: Pythagoras?
 * Spirit: The father of mathematics in music.
 * Donald: Mathematics in music?
 * Spirit: Ah, you'll find mathematics in the artist places. Watch. First, we'll need a string. Stretch it good and tight, plunk it. [Plunking] Now, divide in half, plunk again. You see? It's the same tone, one octave higher. Now divide the next section, and the next. The Pythagoras discovered the octave had a ratio 2 to 1. With simple fractions, he got this. [Harmony Music Playing] And from this harmony in the numbers developed the musical scale of today. [Music Playing, Breaking]
 * Donald: Oh, goody! You do find mathematics in the goodness gracious.
 * Spirit: You can imagine how excited Pythagoras was. When he shared his findings with his pals of fraternity of eggheads, known as the Pythagoreans. [Whispers] They used to meet in secret to discuss their mathematical discoveries. Only members were allowed to attend. They had a secret emblem: the pentagram. Let's see what the topic is for today. [Harp Music Playing] [Flute Music Playing] [Harp Music Playing] [Music Playing]
 * Donald: What's going on?
 * Spirit: [Whispering] Shh, it's jam secion.
 * Donald: Give me something with a beat.
 * Spirit: [Whispering] Shh. [Music Playing, Bongo Music Playing, Music Playing] So, from these eggheads, the Pythagoreans, with their mathematical formula, came the bases of our music of today. [Cello Music Playing] [Saxophone Music Playing] [Horns Music Playing] [Horns Music Playing, Violin Music Playing] [Trumpet Music Playing] [Horns Music Playing] [Music Playing] [Piano Music Playing] [Violin Music Playing] [Cymbal Crashing] [Tympani Playing] [Cymbal Crashing] [Violin Music Playing] [Cello Music Playing] [Harp Music Playing] [Music Ending]
 * Donald: Pythag, old boy. Put it there. [Sparkling] Well, I'll be a gosh-darn egghead. [Laughing]
 * Spirit: It was our old friend, Pythagoras who discovered that the pentagram was full of mathemagic. The 2 shorter lines combine, exactly equal the third. And this line shows the magic proportions of the famous golden section. The second and third lines exactly equal the fourth. Once again, we have the golden section. But this only the beginning, hidden within the pentagram is a secret for creating a golden rectangle which the Greeks admire for its beautiful proportions in magic qualities. The star contains the golden rectangle many times over. It's a most remarkable shape. It can mathematically reproduces itself indefinitely. All these rectangles have exactly the same proportions. This figure also contains a magic spiral that repeats the proportions of the golden section into infinity. To the Greeks that golden rectangle represented a mathematical law of beauty. We find it in their classical architecture: the parthenon. Perhaps one of the most famous of early Greek buildings contains many golden rectangles. These same golden proportions are also found in their sculpture. In the centuries that followed, the golden rectangle dominated the idea of beauty in architecture throught the western world. The cathedral of Notre Dame is an outstanding example. The Renaissance painters knew this secret well. Today, the golden rectangle is very much apart of our modern world. Modern painters have rediscovered the magic of proportions. Indeed this ideal proportion is to be found in life itself.
 * Donald: Boy! Oh, boy, oh, boy! This is mathematics! I get mathematical figures like that!
 * Spirit: Uh, uh, uh, Donald.
 * Donald: Let me try it.
 * Spirit: No, no.
 * Donald: Ideal proportion.
 * Spirit: Not quite. Uh-uh. No, I'm afraid not. Well, we can't all be mathematically perfect.
 * Donald: Oh, yeah? [Grunting] There. I knew I could do it.
 * Spirit: Now that you're all pent up in a pentagon, let's see how nature uses it's same mathematical form. The petunia. The Star Jasmine. The starfish. The wax flower. There are literally thousands of members and good standing, and natures Pythagorians suicide of the star. All nature's works have a mathematical logic and her patterns are limitless. The magic proportions of the golden section are often found in the spirals of nature's designs. The prefusion of mathematical forms brings to mind the words of Pythagoras. "Everything is arranged according to number and mathematical shape." Yes, there is mathematics in music in our art, and just about everything, and as the Greeks had guessed, the rules are always the same. Well, Donald, did you enjoy your geometrical journey?
 * Donald: Gee, Mr. Spirit, there's a lot more to mathematics than 2 times 2!
 * Spirit: That's right, Donald. And you can find mathematics in games, too?
 * Donald: Games? Oh, boy!
 * Spirit: Let's begin with the game that's played on squares.
 * Donald: Checkers?
 * Spirit: No. Chess.
 * Donald: Chess?
 * Spirit: A mathematical contest between 2 minds. It's a game that is been enjoyed the centers by Kings and Commoners. In fact, Louis Carol, a famous mathematician the literary mind used chess as a setting for his classic tale through the looking glass. Alice. Found herself face to face with line to friendly group of chess pieces.
 * Queen: Good heavens, what's this?
 * King: Upon my soul, it appears to be a lost pawn!
 * Donald: Ain't no pawn! I'm Donald Duck!
 * Queen: He says, "He's Donald Duck!"
 * King: Preposterous!
 * Queen: Or it could be an Alice.
 * Donald: Alice?
 * King: No, no, no! It's a lost pawn!
 * Queen: Lost pawn? Stop that pawn!
 * Donald: Hey, Mr. Spirit! Help, help, help! [Banging] [Donald looks at "Hurry. Eat One.", but Donald eats one treat and growing bigger]
 * Donald: Oh, whew. That was close.
 * Spirit: Now you can look at this game from a safer prespective. Chess is a game of calculated strategy. And since the board is geometrical, the moves are mathematical. Checkmate, and the game is over.
 * Donald: That's very interesting. What's next?
 * Spirit: Pratically, all games are played on geometrical areas. The baseball field is a diamond.
 * Donald: Oh, boy!
 * Spirit: And without mathematics, we couldn't ever keep score. Football is played on a rectangle divided by yard lines. Basketball is game of circles, spheres, and rectangles. Even hopscotch has its multiple squares.
 * Donald: What's next? [Licking] Tiddlywinks?
 * Spirit: No. A mathematical game played on a field of 2 perfect squares using 3 perfect spheres and a lot of diamonds. In other words, billiards.
 * Donald: Oh, boy! That's for me!
 * Spirit: You know the game, don't you, Donald?
 * Donald: Of course! The cue ball has to hit the other 2 balls like this!
 * Spirit: Now, let's see how an expert of 3 cushion billiards uses his head.
 * Donald: 3 cushion?
 * Spirit: Yes. The cue ball not only has to hit both the other balls, but it must contact at least 3 cushions before it hits the final ball. 1, 2, 3. 1, 2, 3. It takes an expert to make several shots of succession. 1, 2, 3, 4, 5, 6.
 * Donald: Wow! That was a lucky shot!
 * Spirit: Luck? No. It's skill. For this game, you have to know all the angles.
 * Donald: 1, 2, 3, 4, 5, 6, 7! That's amazing! How does he do it?
 * Spirit: First, there's technique. He's striking the cue ball low, so it'll spin backwards. Hitting the ball on the right side, it will make it tug the rail. These trick shots take a lot of practice.
 * Donald: [Laughing] He missed it! [Laughing]
 * Spirit: 1, 2, 3.
 * Donald: What's so mathematical about that?
 * Spirit: Oh, this game takes precise calculation. He figures out how each shot in his head. He could play it like this, but it calls quite a bit of luck. There is a better choice. For this, he uses the diamond markings on the rail as a mathematical guide. First he figures the natural angle for hitting the object balls, and then he finds at his cue ball must bounce off the number 3 diamond. Next, he gets ready for the shot and he needs the number for his cue position. This cause for a different set of numbers.
 * Donald: Very confusing, isn't it?
 * Spirit: Not when you get the hang of it. You see the cue position is 4. Now simple subtraction: 3 from 4 is 1. So he shoots for the first diamond. He should make it. It's called playing the diamond system. Natural angle 2. Cue position. 1 and a 1/2 2, 2 and a 1/2 3, 3 and a 1/2. 2 from 3 and a 1/2 is 1 and a half. So, shoot halfway between the first and second diamonds.
 * Donald: There's nothing to it! Let me try! Let's see now. If I hit it here, hit and it'll bounce there, and uh--no, here. If I hit it here... 4 and a 1/2 minus 3. 3 and a 1/2 plus 4. Add the 2. [Mumbling] Divided it to, uh, to, uh... I guess I should shoot about here.
 * Spirit: No, no, Donald. There's no guesswork to mathematics. It's quite simple. Natural angle for the hit. 2. Cue position. 3 and a 1/2. How much is 3 and a 1/2 minus 2?
 * Donald: Uh, 1 and a 1/2! Hey! It works! Oh, boy! It's a cinch! [Mumbling]
 * Spirit: You're making it tough for yourself, Donald.
 * Donald: How do you like that for mathematics, Mr. Spirit?
 * Spirit: Wonderful, Donald. And now you're ready for the most exciting game of all.
 * Donald: Oh, boy!
 * Spirit: And the playing field for this game is in the mind. Uh-oh. Look at the condition of your mind. "Antiquated Ideas. Bungling. False Concepts. Superstitions. Confusion." To think straight we'll have to clean house. There. That's more like it. A nice clean sweep. This game is played with circles and triangles. Think of a perfect circle. A perfect circle. Perfect circle. Perfect. Ahh, put a triangle inside, and turn it. Now, spin the circle and what have you got?
 * Donald: A ball!
 * Spirit: Yes, a sphere. The shape of things is first discovered in the mind. Slice off the top, and we have a...
 * Donald: A magnifying glass!
 * Spirit: That's right. A lens is a section of a sphere. All optical instruments are created through mathematics. You see, there's a lot more to mathematics than just numbers and equations. [Camera Snapping] Let's get back to our circle and triangle. Roll it, and we have a...
 * Donald: A-- A wheel! [Transforms into Wheelbarrow, Car, and Train] [Engine Chugging]
 * Spirit: The circle has been the basis for many of man's important adventures. [Transforms To Planes] [Propellers Running] The mind can create the most amazing things. If we spin the triangle, we have a--
 * Donald: Cone!
 * Spirit: Slice the cone. [Donald Quacks] The cone is full of useful mathematical shapes. Slice it again. Slice it several times. The orbits of all planets and satellites can be found in the cone. No matter how you slice it, it's always mathematics. A slice like this, gives us the reflector of a searchlight. A slice like this, the mirror of a giant telescope. A line on the cone, and we have a drill. And a spring. [Boing] [3x] Now, you're ticking.
 * Operator: Number, please.
 * Spirit: [Record Music Playing, Drums Music Playing] The mind is the birthplace for all of man's scientific achievements. The mind knows no limits when used properly. Think of a pentagram, Donald. Now, put another inside, a third, and a fourth. No pencil is sharp enough to draw as fine as you can think. And no paper large enough to hold your imagination. In fact, it is only in the minds that we can conceive infinity. Mathematical thinking has opened the doors to the exciting adventures of science.
 * Donald: I'll be dog-goned! I've never seen so many doors before.
 * Spirit: Each discovery leads to many others, an endless chain.
 * Donald: Hey! Hey! What's the matter with these doors? Hey! These doors won't open! They're locked!
 * Spirit: Of course, they are. These are the doors of the future... and the key is--
 * Donald: Mathematics!
 * Spirit: Right. Mathematics. The boundless treasures of science are locked behind those doors. In time, they will be open by the curious and inquiring minds of future generations. In the words of Galileo, "Mathematics is the alphabet with which god has written the universe."

Characters

 * Donald Duck
 * Mr. Spirit, the Narrator
 * Pi Creature
 * Queen Chess Piece
 * King Chess Piece
 * Horse Chess Piece

List of languages

 * English
 * Spanish
 * French

Shapes

 * Circle
 * Triangle
 * Square
 * Rectangle
 * Pentagram
 * Pentagon

Clips Include

 * Beginning
 * Music
 * Pentagram and Golden Rectangle and Pentagon
 * Chess
 * Billiards
 * Circle and Triangle
 * Doors with ending