 Hi, this is Chichu. Welcome to my channel, and welcome to our second reading for this comic book reading set number four, and for this reading set, what I've done, or for this comic book reading, what I did was picked another book from the 16 that I chose to read, and it's Donald in Math Magic Land. And this issue is the first printing of this comic. And it's Dell Four Colour 1051, and it came out in August 1st, 1959, and there's a second printing of this comic. And again, it's Dell Four Colour, but the issue number on it would be for the second printing was 1198, and you can check out the number there. Hopefully that's coming out. This is 1051, and I believe 1198 also has a number. Up there, okay? And you can tell the difference between the printings, because the first printing is 10 cents, and the second printing that came out in 1961 is 15 cents, okay? Now as far as the story in this issue is concerned, my exposure to Donald in Math Magic Land, and I think most people's exposure to Donald in Math Magic Land, came out in the animation that preceded this. And that one came out in June 26, 1959. And I probably saw that animation. I think the first time I saw that animation was in the 1980s, and it's about a half an hour animation, 27 minute animation that Walt Disney put out. And it was actually, the animation was actually nominated for an Academy of Morch for short documentary. And when I was looking this information up regarding the animation, regarding the comic book, there's a quote that was credited to Walt Disney, and it's on the wiki page anyway for the animation. It states that Walt Disney said that the cartoon is a good medium to stimulate interest. We have recently explained mathematics and film, and in that way excited public interest in this very important subject, right? It's not a groundbreaking quote, but it shows us how far we have to go, or how far back it goes where people who are interested in education, and Walt Disney was initially anyway, was interested in education. And everyone that was had a passion for this, for mathematics, was in a way trying to expose more people to the language of mathematics, right? And for the obvious reasons, for me anyway, the reason that I picked this comic book is because I am teaching mathematics and the animation when I first saw it, and I believe it was the 1980s, where I first saw it, it really did blow me away. It was fantastic, and I think I, you know, following that when I saw it in 1980s, when I was a kid, I didn't see it for a very long time until the 2000s really, when WAP 2.0 kicked into high gear, and the streaming video was available online. I believe I saw it again on YouTube, okay? So that's sort of the background of this comic, and where the story comes from. So let's crack this thing open and have a read through it. And one that, you know, when I flip through this and from what I found online, this comic has a few one-pagers, a few shorts, and a 30-page story arc of Donald entering math magic land, which is really adapted from the animation from 1959, right? And this is the cover, and it's sad. This issue's sort of mid-lower grade. It's not bad. It's got some chipping on it. As you can tell here, let me put it behind the white. You know, the corners aren't sharp. Uh, so it's sort of a mid-grade, I would assume, on this. It's not a low grade. But on the lower side, it's not a mid-high grade, I guess. And let's take it like this. There's some huge chunks missing from this. So if I was to grade this, I'd get this one somewhere around the four. And the edges, uh, the edges are fairly sharp, right? There's no real chipping going on. So it's not a bad copy. Beautiful anime. Beautiful land art animation. Beautiful, uh, beautiful artwork. And this is, uh, four-color. It's the second, uh, from what I understand, this is the second series that started in 1942. And we're hitting this with, uh, four-color 1051 in 1959. Mathematics and U. E equals MC squared, right? Einstein's, uh, relativity, I guess, Einstein's equation on the electrodynamics of moving bodies. And we did it, we did, uh, sort of a video, I put together a video of, um, Einstein's paper on, um, basically relativity. And if you're interested in a little bit more discussion on E equals MC squared on Einstein's, basically, groundbreaking paper on, uh, on relativity, which, uh, entitled, uh, on the electrodynamics of moving bodies. We did talk a little bit about this of why, uh, we can't travel at the speed of light, right? What are the other things they have here? Square root squared of, um, square root of four is equal to two. Uh, that's half your answer. The true answer to this is the square root of four is equal to plus or minus two, right? I've done some videos on, uh, on this as well for ASMR math and that for, um, the Einstein videos, well, that's also ASMR math. And we've done a whole bunch of videos on, uh, radicals and exponents for, uh, language of mathematics as well. I'm really looking forward to flipping through this while I flip through. I haven't really been looking forward to reading this, right? So let's read this first page and actually let's read this. Be consistent with what we've been doing with all the other videos. Let's read the fine print for this. Um, Walt Disney's, uh, let's see if you can see that. Walt Disney, um, Donald and math magic land number 1051 published by Dell publishing company, Inc. Um, 753rd Avenue, New York, 17, New York, Georgia and publisher, junior publisher, uh, Helen Meyer, president Paul L, Paul R. Lily, executive vice president, Harold Clark, vice president advertising and all bunch of names that goes through our vice reserves throughout the world. Nothing here and contained to be reproduced without permission, uh, Walt Disney productions, authorized edition printed in the U.S. Design and produced by Western printing and lithography company. And that's basically Dell publishing that, um, Western, uh, adapted from the Walt Disney motion picture, Donald and math magic, math magic land, copyright 1959 by Walt Disney productions. And that's the copyright for the animation. Uh, this pre-article shall, shall be sold only through authorized dealers, sales of mutilated copies or copies without covers and distribution at this, um, of this pre-article for, uh, premiums, advertisements or giveaways are strictly forbidden. And I believe the reason they put this in there, um, you can't sell this in mutilated form, um, because newsstands, when they were publishing comic books, um, for the issues that they didn't sell, they could have just removed the covers and, um, sent back the covers to the publishers. So they weren't being allowed to sell the comic book without the covers because they'd be sort of, um, I guess, lying to the publishers and pocketing the money that, uh, some, you know, some of the money that the publishers are supposed to get. Uh, so let's take a read through this first page. Mathematics and you. Every time you swing, swing to beta, dance orchestra or whistle the tune, you're acting out a mathematical equation. The principles of mathematics are applied in almost everything you do. Make use and enjoy in your life today. And without the science, the world would be in a state of almost inconceivable confusion. For instance, could you describe yourself without the use of numbers? How could you tell anyone how tall you are or how old you are, just for fun? As you read the following, supply your own figures to see how important numbers are to you. I am blank old. I was born blank. I am blank feet tall. I have blank head, eyes, uh, black eyes, blank ears, black nose, black mouth, black arm, black hands, black legs, black feet, black fingers, uh, and blank toes. I have black sisters, black brothers, black uncles, um, black hands, black cousins. I am the, I am in the black grade and I live in a house with blank rooms and a blank street. Simple way of exposing people to mathematics. Long centuries ago, Pythagoras, the Greek philosopher, observed everything is arranged according to number and mathematical shape. Hundreds of years later, Galileo, the great Italian physicist and astronomer echoed the observations with mathematics is the alphabet in which God wrote the universe. Back in the day when we first, uh, when I first started putting together, uh, math videos, I was, you know, I've had a lot of people ask me, um, why is math important, right? Sometimes in a condescending way, sometimes in a sort of general way, sometimes, you know, inquisitively, they really want to know why math is important, why they have to go through school, study mathematics for so long, uh, so what I ended up doing is putting together, uh, two videos of why math was important. Um, they're not ASMR math, one of them was sort of being pretty intense about it, uh, and another one was sort of giving, um, five reasons, five or six reasons why math is important and why has been important to me and how to percent agree with this, but even more, um, like for me, I can't even imagine my life without knowing mathematics. I wouldn't have been able to do many things without mathematics, right? So before we get started on this, let's figure out, uh, what's in this. I think this is the main storyline, Donald and math magic planned. Okay, so let's flip through this and I believe this is supposed to be 30 pages. I'm gonna definitely read this, this is the first story arc. The pages aren't numbered, but yeah, and look at the center of this, it's pretty good. I believe it's got some rusting on the staples, let's check it out. I guess so, I guess there's a little bit of rust on the staples, which is understandable, but they haven't, uh, there's no staining due to the rust, or it could be that just the staples are old. Yeah, I think so, because sometimes we're in, uh, staple rust in comic books, they sort of stain the sides, right, where it touches the paper and this one isn't. So this is in pretty good shape, actually. So this thing continues, sort of like Pascal's triangle, let's wait the back as well. We'll flip this way in the book because it looks like the whole story arc is from the beginning, right? Um, math magic pyramid puzzle, this sort of like Pascal's triangle, I guess. Let's check it out. Like the great pyramids of early Egypt, this pyramid is a puzzle to Donald and his nephews. Can you help them? Place small markers such as a button or papercliffs on all letters except A. Now, by jumping, I'll bring this closer so we can read it together, um, now by jumping, try to remove all the markers except one, which in the last move must be left on the letter A. To do so, jump one marker over another to end to an empty spot. I remove the marker that has been jumped over. Markers must be jumped along the lines only. For instance, you may jump, jump, jump marker E to A, E to A, where is E? E to A. So you can jump from there to there jumping over the sky, but not E to I. Where is I? Oh yeah, because there's no line connecting this, right? So you can go along the lines but you can't go this way. If you need to, turn the page upside down for the solution. These solutions are good. So basically you put markers everywhere except on A and then you start doing the jumps. So if you jump from E to A, you would remove this one and you would have two empty spots. And then you could go from here to from B to E. Oh no, you couldn't go from B to E. You would have to go start from here. Where would you go from here then? Oh yeah, you would have a marker here but there's one wouldn't be empty. So how does that work? Place small markers such as buttons or papercliffs on all letters except A. Now by jumping, try to remove all the markers except one. Oh yeah, you would just go from C, C to E. That's right and you would take off D. So that could be one move where you could go from G to E and remove F. For sure we should be able to figure this out. Nice little fun game. Fascinating fun with numbers. Let's check out the fascinating fun with numbers. The back cover. All ducks double talk. I can prove that seven goes into 28, 13 times. Reminds me of what happened in Costello video as well when they were trying to do mathematics. So Donald, I can prove that seven goes into 20, 13 times. Seven only goes into it four times. That's Huey, Dewey and Louis I believe. Right. That's so. First, I'll prove it by multiplication. Three times seven is 21, right? Right. You admit seven times one is seven. Well, of course. So there you are. Seven plus 21 plus seven is 28, which just goes to prove what I said. Seven goes into 28, 13 times. Math, the magic, the room. Of course, this is all just a trickery, trickery confuser and not really accurate the mathematics, but you can make it sound almost right. If you talk fast enough, then prove it with the following addition. Let's check out how he does it with addition. Here we have seven, 13s. Now I'll prove again that all this goes into 28. Seven threes out of the 21 and seven ones out of the seven, 21, seven equals 28. This is almost identical to an Avanon Costello routine. I believe it's Avanon Costello. Check this out. So the top staple is detached from the cover, right? So that sort of reduces the value a little bit on this. So let's not put any more strain on it. Let's do it like this. That's the way I should have been holding it. Fascinating fun with numbers. Let's read these ones too. These one pages are a kick. Fascinating fun with numbers. Huey, Dewey and Louise. Mind reading stunt. Look, ice cream cones. Yum yum. One which sure tastes good now. And that's Uncle Scrooge. You can stop hinting kids, I'm not buying cones. Ten cents an ice cream cone. If we tell you how much change you have in your pocket, will you buy us a cone? What are you, pocket spies? He swings. He swings his cane. He's so greedy. Such a miser. No, no. We'll just read your mind. You couldn't do that in a million years. So go ahead. Okay. Write down how much change you have. Double it and add five. So he writes down 40, 40 times to his 80, plus five is 85. Now multiply by 50. Then subtract the number of days in the year. Multiply by 50. So 85 times 50 is 4,250 minus 365 is 3885. There's the answer. And it doesn't mean a thing. Just so confident. He knows his math well though. He did 85 times 50 in one line multiplication. I guess he would. He's going to go Scrooge. Oh, yes it does. 3885 plus 115 equals 40,000 or 4,000 in two decimal places. So 40 cents. You have 40 cents enough for all of us to have cones. Kids are too smart these days. Oh, again I'm sweating. Use the same math, mathematics stunt to tell friends their age and month of birth. Tell one to write down his age. Double it and add five. Multiply that by 50. Then subtract the number of days in the year and add number of his birth month. To the answer you add 115, the first two numbers will be his age. The last two is birth month. Have fun. And there's tricks like this available online. Let's read this little pledge. This little plaque here. A pledge. A pledge. Dell comics to parents. A pledge to parents by Dell comics, I guess. Read this. The Dell trademark is and always has been a positive guarantee that the comic magazine bearing it contains only clean and wholesome entertainment. The Dell code eliminates, eliminates entirely, rather, what? Eliminates entirely, entirely rather than regulations. Objectionable material. Okay, so they're censoring their own stuff. That's why when your child buys a Dell comic, you can be sure it contains only good fun. Dell comics or good comics is our only credo and content goal. And this little disclaimer here. This was published in 1959. And this little disclaimer here is basically the witch hunts that went, that were started in, I believe, in the mid-1950s with Seduction of the Innocence, the book that came out, and Congress got involved. And they were basically saying that comic books, and does this have to seal the approval, comic books were polluting children's minds. And after Seduction of the Innocence, and basically comic book publishers were scared that Congress was going to pass laws to start censoring comic books. And there's different stories involved in this too, where some comic book publishers, specifically the ones who were producing superhero comic books, really pushed for this. But basically they came up with a little code. And we've seen the code, comic book code, approved, and it's usually put on the top, where it's supposed to be censored for content that at the time they deemed to be polluting kids minds. And the stuff that they did were like censor wars like vampire horror and stuff like this. And that was sort of the death knell for the comics. As far as I'm concerned, some of the greatest comic books ever published. And as far as I'm concerned, probably the greatest comic book publisher of all time, which was EC Comics. The work that they produced was absolutely brilliant. And we've done some readings of EC Comics. But once the comic code came into effect, EC Comics wound up. Well, they sort of stayed with Mad Magazine, so they kept on producing their humor comic books, but they stopped producing horror and science fiction comic books. And the horror and science fiction for EC was absolutely brilliant. Fascinating fun with numbers. So here's another one of the same thing here, this type of story. And as far as this is concerned, I guess Dal was preemptively making sure that parents appreciated their G rated comics. And here's, I guess, a shorter story. Let's go to the beginning and read through Donald and Math Magic Land. Hopefully we get a chance to go through this whole thing. Yeah, I think so. So Uncle Scrooge, Donald and Math Magic Land. After deducting your 15 cent payment for this week, Donald, your balance still owing is only up to $14.73 up. If I keep paying on my loan, it's supposed to get less Uncle Scrooge, not more. I borrowed only a measly 89 cents from you in the first place, but at 30 per cent interest only. 30 per cent interest computed on a monthly basis, compounded weekly. We talked about this compound interest in the ASMR math video, where we talked about interest rates and how interest rates affect our society. And this is sort of an extreme version of what we talked about with differential accumulation. Wow, 30 cents, 30 per cent interest compounded on a monthly basis, compounded weekly. It's simply a matter of mathematics, nephew. Unless you can raise your weekly payment, the balance has such a lovely way of growing, but it can't, can it? And this is something that payday loans does. You borrow money from them, and this is a little bit more extreme, this interest rate, but wow. Once you get stuck in that trap, there's almost no way out. Figures don't lie. You can see for yourself, mm-hmm, mumble mumble. Look at Donald, he's got question marks. Uncle Scrooge is showing the mathematics. Yes, just as I thought, at your present rate of payment, you'll owe me $37.92, but your birthday, it's highway robbery. Actually, that is the, I'm not sure what the $5.98, so this is Dell Comics number 1051. For sure, at the beginning of the 51, right? But I'm not sure what the other number means. You agreed to the terms, nephew. Now you're stuck with them. You have to watch your figures. That's you, Dewey, and Louis coming out. You have to watch your figures. Uncle Donald, whenever you do business with Uncle Scrooge, remember, we said you should brush up on your mathematics. Mathematics, there's too much mathematics here already. On my budget, I need to be a magician. I'm going to get out of Uncle Scrooge's clutches somehow. Just leave me alone, boys, to do some figure. That's the spirit, Uncle Donald. Let's see now, if I can get half a dollar for my jackknife and maybe two bits for my rabbit's foot, and gee, it's going to take a lot of figure. Uncle Donald, here's our book on mathematics. It might help you some, so they're bringing their textbook, I guess. Well, maybe just to check up on the compound interest angle, and a few of Uncle Scrooge's figures. Good luck, here we do in Louis' sleeping. 85 plus 9 times 6, carry the 5, 794. No, that's wrong too. Decimal point comes about here, I think. Numbers, figures, nothing but trouble. I wish mathematics had never been invented. Lightning sound, I guess. Thunder. Not lightning sound, thunder sound, preceding lightning. I heard your words, small one. Huh? What? Who? I'm the spirit of mathematics. The torchbearer of progress since civilization began. Shake my tail and call me shivers. Mathematics, the key to achievement, to all sciences, to the arts, to music. I'll chuck it, Charlie. You're just talking about a lot of numbers. Remember? You doubted the truth, Donald. Then you had better come with me. There's so much you should know. Come with you where you shall see. You shall see. It will be a great adventure. There you are, all ready for the trip. Put on his adventure hat. Well, okay, adventure is my dish, chum. But wait, if you want me to come with you, quit fading away. Where are you going? Slipping back into the fourth dimension of time. Do not fear. I'll be with you. I can take you anywhere. I slip through the portal. Just follow my voice. Follow, follow. To math magic land. I'm following, I'm following. My tail at least. It's the roots of the tree. Oh my gosh. What kind of a square root? Square roots, Donald. Of course. You know, five is the square root of 25. Square root. Roots. And six is the square root of 36. Okay, okay. You don't have to tell me that stuff. I'm not tummy. And two is the square root of four. And four is the square root of cats. The whole routine is strictly for squares. You're more interested in pie then. Now you're talking. Trot it out. Any flower will do. Toot toot in mathematics. Pi is the greek letter used to designate the relation of the circumference of a circle to a diameter. Trigonometry. We've done a whole bunch of trigonometry videos, right? Very important circles, right? Triangles used to basically, for us anyway, to appreciate the power of cyclic functions. And that's what we've been creating for the trigonometry playlist, right? Pi is 3.1451, 14159265. Or to put it more briefly, just 3.3. You can't put it briefly enough for me. What do I care about the circumference or diameter of a circle? That one wasn't even big enough. It's just like I said, the whole mathematics business is just a lot of trouble and nuisance. Donald, oh no, you are still so wrong. Oh, I knew it. His nibs, the spirit, is in again. If we judge it by the value received mathematics as the queen of all sciences, yet the greatest servant of man, tuk-tuk, perhaps the best way to convince you is to take you back to the world before mathematics. Well, at least now maybe you're talking some adventure stuff. Putting on his hat again. Ho, trouble, you mean. Here, look back to days before man could count and see the problem, quantity of anything represents. I give, I give you my bare skin. Mungu, you're supposed to gather me many sticks of wood from my fire. This is many enough. Your idea of many, not my idea of many. Or is that so? Give them, you may give them, you my idea of many in lumps. Oh, he's picking up the stick, they're gonna fight. Charms, wait. If you want my idea, why don't you? That's Donald, right? His clothes changed. Club, his hat's changed. His clothes has changed. You keep out nosy. Already we've got too many ideas of how much many is. So we bang them over the head. I guess one thing, violence was okay with the comma code, right? Smacking people on the top of the head. That's G-rated. See, Donald? There just had to be some definite way of measuring quantities. So inevitably counting in numbers evolved. Oh, I wish they got with it before I got here. Developing civilization came the need for some shorthand way of expressing numbers in visual terms. However, put down this much. And this much. Trying to figure out the language, right? The symbols of mathematics. Those numbers are our modern place value system in which each digit's place in a number determines its value is easy. Thousands, hundreds, tens, singles. 9,537. But writing numbers was not always so simple. Go ahead, give this early Egyptian a number to record. This is Donald now. He's got the gear Egyptians, the clothes. Hey, Buster, let's you put down 6,741. I'm going to write 6,741. 6,700. Just be patient. Feather one. It will take a while. You understand? I guess that's the symbol for thousands. So that's the symbol, Egyptian symbol for thousands. And that one is 400s. Right, we got six of those. We got seven of those. And then he's got to do 7,741. I guess those are tens in Egyptian. Hopefully it's accurate. Yes, yes. Now four tens, four tens to make the 40 and then merely a single one. Oh, brother. It's a good thing I didn't ask him to write 6 million. He couldn't have done it in a day. Even centuries later, Romans were struggling with the same problem. Here we go, Donald. All roads lead to Rome nowadays. Rome. So Donald's clothes have changed again. And this is all in form, a uniform. And I think that's sort of a take the concept all roads lead to Rome because Romans built some amazing roads that I believe they're still around now. That's how well constructed they were. Look, this Roman is writing your number for a higher one. He would need a much bigger wall. He's doing the same thing. He's writing down 6000. I'm sure why he only has D. Wow. I'm beginning to appreciate our little old one, two, three, four, five, six, seven, eight, nine. Later, the Romans later, the Romans added great range to their system by simply deciding that a line over a letter multiplied it by 1000. Thus, 10 is the X. Let's show this. 10 is X. And a line over the X is 10,000. The L is 50. A line on top of the L is 50,000. Nowadays, with the mathematics symbols that we use, a line on top of a letter means not that letter. And we talked about this in for the real number set, right? Where Q is representing rational numbers and Q with a line on top represents irrational numbers, meaning not rational, right? Interesting. I didn't know it came from there. Well, different interpretation of it anyway. We still use Roman numbers to number book chapters or a succession of kings. But think what a Roman schoolboy faced in arithmetic. Just multiply them down. Today, you can do the same problem easily with our place value system. You said it. You said it, spirit. It's easy as pie, even for me. 1,947 times 739 is going about it. Our versatile digits were invented by an unknown Hindu. But we call them Arabic numbers because Arabs introduced them to the European world in about the ninth century. Among the Arabs, there were many learned mathematicians in Baghdad, Damascus, even the Arabic universities of Concord, Spain. They made great progress in an advanced form of mathematics. They called algebra algebra. I'm not sure how you pronounce that. Algebra meaning to bind together. That's where the word algebra comes from. Algebra, you recognize it, Donald? Algebra, algebra. Oh no. Here's where I get off, Mr. Spirit of Mathematics. A willing to admit arithmetic comes in handy. But next, you'll be ringing in geometry and trigonometry and all those complicated flavors. Every branch of mathematics was developed to meet a need, Donald. Geometry, for instance, is from a Greek word meaning measurement of the earth because that was the great need that produced it. Even long before the Greeks made geometry and exact science, the Egyptians developed knowledge of it to help re-establish property lines wiped out by frequent flooding of the river Nile. They learned a lot about triangles, rectangles, and other shapes dealt with in geometry. I know the boundaries of my field can be cited from these markers and by extending the lines of this right angle, hold on, Roma, ho. There's the property boundaries. And one thing I should have mentioned about this book or about the animation is that there were a lot of scientists or there were some well-known scientists that were involved in creating this. So it gave a lot of creatives to the animation and to the comic book because it's sort of adaptation of the animation where a lot of this information, I believe all of this information or most of it at the time that we knew is accurate. So let's continue with our property lines. Anybody can see your markers do not make a right right angle. It does not meet the triangle test. I say it's a right angle. Check out what they do. I leave it to you, stranger. Should not a true right angle fit a triangle whose size measure five by four by three. And that is accurate. That's one of the special triangles, three, four, five. Or well, when it comes to this kind of mathematics term, it's my day off. Huh. I'm just a tourist. You see, look out that marker. Oh, he's leaning on the marker. Oops. Sorry. Oh, you clumsy off. Now you've moved it in Rama's favor. My favor. Whose toe did it land on? But fellas, scramble your own interloper. I didn't do it on purpose. I don't know a right triangle from a kepper keppered herring. Donald Donald wait. He's like, God, there's some rocks out of the zooms way zigzags. Smart way to go. Siding on top of the pyramid. At least you pick the fine spot to appreciate how well the Egyptians applied their knowledge of the triangle and the great pyramids. Triangles fully. They come to a point in the most uncomfortable places. I just as soon as never see one again to Donald. You can't escape them. The triangles verse versatile dependable qualities are used throughout the world. Structurally, it is the perfect shape. As long as the size of a triangle remain the same, it cannot change its shape as squares, rectangles and other forms. As long as the size of the triangle remain the same, it cannot change its shape as squares, rectangles and other forms. That's right. All the sides are same, but you change the angles. You can still keep the sides the same. That's why triangles are a basic part of all heavy construction. From now on, just notice how often you see them, Donald. Say that's right. And especially there are loads of them in those geosomething domes. Geodesic domes. Yes, you're so right, Donald. The framework of these structures consists exclusively of triangles, each exerting such equal weight and stress that no uprights are needed for support. Any reasons they use triangles and construction are one of the most stable. And we've talked a little bit about this, but I think no, this part of it, right? As long as the size of a triangle remain the same, it cannot change its shape as squares, rectangles and other forms can. Onions of a geodesic dome construction say there is theoretically no size limit. A dome a mile across would be possible. If they've never tried it, silly. They just figure it out mathematically. There's a squirrel popping his head from a tree holding a tree. It's the spirit. Even from squirrels, I get it today. Squirrels laughing. But it's true, Donald. All construction is figured out mathematically. That's how architects, engineers and builders are sure of results before construction starts. That's how tunnel builders build and cruise. No, they will meet underneath, no, they will meet underneath a river from one side to the other. As long as the mathematics done correctly, there's construction sites where bridges starting from one side to the other, they don't meet the same place and same with tunnels and stuff where they didn't do the mathematics properly. Yes, you will have to look hard to find a job where mathematics is not important. Scientists, sailors. It enables astronomers to measure our universe. I'd say that third star from the left is exactly 16 million trillion miles away. My, our figures agree precisely, Donald. That's well, except for one thing. Chance, I haven't the foggiest idea how I did it. Why? It's really quite simple, my boy. Here's the angle of our sighting six months ago when we were at this point in the Earth's orbit. And here's the angle of our sighting tonight. So with those known angles and with diameter of the Earth's orbit as the baseline, we construct this imaginary triangle to that star and easily determine the height of the triangle. They're figuring out the height of the triangle here with their, man, these triangles sure keep, sure keep busy. They do. You know trigonometry is a branch of mathematics dealing just with triangles and other shapes involving them. We'll originally develop just eight astronomers. Trigonometry is a basic tool in countless fields of modern science and industry today. A computer there, right? And this was published in 1959 with a huge computer little scientist that designing its construction of supersonic planes in optics, sonics, acoustics, and light in hundreds of military ways. Spirit of mathematics, that's enough. So now I'm convinced about trigonometry. It sure is a very mathematical world, all right. Indeed, it is, Donald. There are mathematics in every atom of our existence. All right, Mr. Spirit of mathematics, you think you've got all the answers, but I'm tripping you, tripping you up on one thing. It's what you said about mathematics and music. Just turn on your ears for a musical sample and tell me where the mathematics is in this. Donald is singing. We're going to go from a jolly good fellow, from a jolly good fellow. Well, I don't quibble, Donald. If you want to call that music for the mathematics of it, we must go back to ancient Greece, the time of Pythagoras. Huh, I still say music isn't numbers. It's getting the Greek uniform. Pythagoras it was, for it is recognized as the father of math, for he is recognized as the father of mathematics and music. Father of, we'll show you, Donald. First, he took a string. There's a little mouse here, pulling on his little string from his, from his clothes, right? That's it. And now, with the string pulled tight, pluck it, Donald. Music tune comes out. Now, hold the string exactly in the middle and pluck it again. It's the same musical tone, one octave higher. Divide the next section in half. That's it. Now, pluck it again, or pluck again. By what's left and pluck again. Each time you notice one octave higher, pluck. Donald, that was a great time. Well, what do you know? After discovering that the octave had a ratio of two to one, Pythagoras used simple fractions to measure the length of additional strings and eventually created mi fa so la ti do. I guess that's the harp, right? Pluck, pluck, pluck, pluck. You see, Donald, the fractions of Pythagoras created our whole musical scale, which is the basis of all occidental music. Well, I'll be doggone. You find mathematics in the darnest places and music coming out of there. Speaking of music, what the thing Donald said, it must be a meeting with Pythagoras and his followers. Their ideas were so advanced, they found the best to meet secretly. He a cat, I don't blame them. I guess the music he doesn't like. Their gatherings usually dealt with serious and weighty subjects, but it sounds as if Pythagoras' musical scale is tonight's topic. Musical, oh brother. Thought combo was strictly from square land. Music, oh brother, that combo is strictly from square land. Let yourself go chum. Here, I'll give you something with a beat. Ah, it's bringing the, it's mathematic. Now you're with it. Yahoo! For Pythagoras, you're all reet, reet. Just so you give your stuff a beat. He would do it, Louis. You boys here too? Sure thing. Uncle Donald, why not? It's just logical. It was our mathematics books that you borrowed. Or, oh sure, logical. Here in Math Magicland, I won't be surprised at anything anymore. You speak with wisdom, young friend. I hear pride proclaim you a fellow Pythagorean. Thanks, Pythag old boy. Congratulations Donald. You have one year Pythagorean. Pythagorum, the secret symbol of Pythagoras and his followers. It's just a five point star. About history, the Pythagoras were persecuted during the time when they were coming out, because a lot of the establishment, the people who were doing controlling information, didn't like the new ideas, the changes that were coming. And I believe Pythagorean was forced to commit suicide, or it could be Galileo thinking about. Oh, it's much more than that Donald. Within the Pythagorum, Pythagoras discovered mathematical properties which influenced art and architecture from then on, magical. The two shorter lines making up the length of the third line, and the second and third lines making up the length of the fourth. Give them the properties and the proportions of their famous golden section. Hidden within the Pythagorum is also the secret for creating from its golden triangle and golden rectangle, which the Greeks admire for its beautiful proportions and its magic qualities. This particular rectangle is a most remarkable shape. It can mathematically reproduce itself over and over indefinitely, simply by swinging a short side to create a smaller brother, or by swinging a long side to create a larger one, and still larger ones. Large or small, they always retain the same proportion. And what they're talking about here is the golden rectangle, right, and using the golden ratio. Fantastic. And we did for math and real life, we put together a couple of videos about this when we're talking with Dirk, my friend as an artist, and he showed us how he creates the golden rectangle basically from the outside in, right, starting off from the outside and spiraling in, spiraling in, and creates the golden spiral, right? And I create the golden rectangle the way I've known how to create is starting with the Fibonacci sequence and working from the inside out, right? So if you're interested to know a little bit more about this or see this work in motion, there's a couple of videos that we have out creating this, and how my friend is incorporating the golden rectangle and the golden ratio into his art. Ah, fantastic work, fantastic work. To the Greeks, the golden rectangle represents a mathematical law of beauty. We find it in all their classical architecture. Well, I'll be dog-gone as a Parthenon, I believe. Your right spirit. I can see oodles of golden rectangles in these old Greek buildings, and you can see them in Greek sculpture. For hundreds of years, the golden rectangle dominated the idea of beauty in the Western world, in architecture, Notre Dame in Paris, in the works of great painters, Mona Lisa, I believe. And even today, the golden rectangle is very much a part of our modern world. The influence of mathematics persists not just in the creation of man, it is in nature, too, where mathematical forms are limitless. In the symmetry of living growth, we see the mathematical proportions of the pentagrams. Quadrants, hexagons, say, looks like a giant sample of the honeycomb. You mean, now, we're in a beehive. Yo, no doubt about it, Uncle Donald. This fellow still requires some mathematical figuring, boys. According to present laws of aerodynamics, it is impossible for the bumble bee to fly. Tell him, tell him. And I don't know if this is true anymore, but according to physical calculations, the physics we understand, at some point, the reason or how bees are able to fly is unknown to us. We can't mimic it. We're first starting examples of mathematical perfection. We have only to turn to a fluffy fall of winter snow. What now? Snow? But the bee is small now. Microscopic enlargements of snowflakes reveal exquisite displays of perfectly matched angles, infinite variety, never a duplication, yet each and every arrangement always adheres to a certain mathematical order, every snowflake being different. Reminding us of the worlds of Pythagoras. Everything is arranged according to number, to number and mathematical shape. Boy, you said it, spirit. Now, this is my kind of mathematics. Look at Donald look crazy with the beauty queen. What does that say? Miss Cookie Week? Miss Cookie Week. Look at you doing a Louis trying to stop him. Uncle Donald, whoa, simmer down. I just want to study the subject more closely, boys. I'm really getting help to mathematics. A lot here in Math Magicland. Even before you came along, I'm the one who really got the whole tour. The whole tour, Donald? Ho, ho. We've hardly scratched the surface, but suffering cyclones, Mr. Spirit. How much more is there? We've done the numbers bit, algebra, geometry, trigonometry, the triangle, the golden rectangle. What about that important relative of the triangle who doesn't look at all, look at all like him? Relative? The circle. No, we're in nature. Do we find a perfect circle? So it is a product of man. Try to visualize one if you can. A perfect circle. Okay, that's easy. Your part is, is sagging, Uncle Donald. Don't rush me, I'm working on it. There, that's fine. Now put a triangle in it. All right, just leave this to me, boys. I'll show you some real mathematical thinking. So they're visualizing it. Fine, spin the triangle like a propeller, and the circle like a weather vane, or just a sink. Now, what do you have? A ball. Yeah, it's a ball. The shape of a thing. The shape of all things is first discovered in the mind. Now, just imagine yourself retracing the thoughts of some of history's greatest thinkers. That's for me, he puts on his graduation little hat. You ask yourself what you could do with a shape like a ball. Bounce it. Oh no, try slicing off the top, and you have a lens. Say, not bad. For reading glasses, binoculars, microscope, the thickness of a lens and its curves may be altered, but always to precise mathematical calculations. Take another slice of that ball, Donald, and you have a wheel, a very useful invention. Yep, a lot of possibilities in a gimmick like that. Look at the carriage. I don't know if that's from real history or not. Let's set aside the circle. Let's set aside the circle, though, and now spin the triangle like a weather vein. The result? A cone. But with our mind, even now, let's slice the cone and we have gears. Well, what do you know? Slice the cone differently several times at any angle, and we have, oh boy, satellite orbits. Right, all possible satellite orbits can be found in the cone. This is in mathematics called conics, basically, something that they used to teach in my part of the world in grade 12, but they removed it from the curriculum, unfortunately. They're how you slice it. It's always mathematics, but keep slicing, Donald. Right now, yours is the mind of all men. Look at Donald's face, searching through the ages and finding the reflector, the spiral, the telescope, the spring, machinery, the piston, the cylinder, everything coming from a cone. The triangle in the circle, and your searching mind, Donald, you have created all things, all these wonders and more, but they were only the beginning, the proof that from certain basic form and principles, there are no limits to what the mind can conceive and create. Every new day, doors are swinging wide on new scientific achievements, all these doors, access to all these information, right? Cool visual. Doors that are locked today will be open tomorrow with the same key. Mathematics opens the doors, right? Brother, what a workout. Puff puff. Ho ho. You've covered thousands of years in just a few minutes, Donald. But mathematics isn't all work. It's play. Play too. It's the basis for most games, games where you keep score or play on a geometrically shaped area, like baseball, football, basketball, checkers, chess, hockey, hopscotch, and billiards. Here is a game where actual arithmetic can be used on every play. These tables always remind me of how I wish our front lawn would look. In billiards, the playing area equals two squares. The cue ball must hit both of the other balls, contacting at least three cushions before it hits the final ball. This is specifically the game of billiards for very few places you can play this now, right? Most of it is either 8-ball or 9-ball. Only an expert can make several shots in succession, but these diamond markings on the rail are his mathematical guide. Yeah, cats. How do they help him? And there's always, if you look at any pool table, there's little diamonds that breaks, you can see them here, little markers, that breaks the pool table into segments, right? Let's learn about that. They contain a formula for making perfect shots. They contain a formula for making perfect shots, enabling the expert to figure out each shot in his mind before making the play. Now, there it goes, and it is hitting the cushions exactly as planned. So the person, that's the person's hand, thinking about it in his mind, visualizing it right, and then here, he does it. And then, hooray, he did it. Yeah. Gee whiz spirit. Gee whiz spirit. The only trouble is, seeing like mathematical games, mostly called for fancy setups, like billiard tables and chess boards and football fields. Not at all, Donald. Lots of the fun and mathematics calls for no more equipment than some knowledge of arithmetic, and perhaps a paper and pencil. Fun with arithmetic, of course. Fun with numbers is a fascinating pastime, especially if you know a few of their amazing tricks. Here's a trick. We can do it, Uncle Donald. The wizard of numbers. Brain teasing made easy. Amaze your friends. Wait, boys. This must be interesting. Interesting, indeed, Donald. With all of man's inventions, none can produce more intriguing results than simple mathematics. He's got a sign outside, says your friends. Hewie, Dewey, Louis, where? Think of a number from 1 to 10, then add 8 and double the result. Or, okay. So you pick 16, add 8, this 14, double it, you get 28. All right, now divide that, answer by 4, and then subtract half of the original number. 28 divided by 4 is 7. Let's see. Half of 6 is 3, 3 from 7 is, he's confused. Ho-ho, don't tell me. I can look right into your mind and tell you the answer is 4. Well, I'll be a ruffled duck, that's right. Oh, I didn't read your mind, Donald. It's a trick, of course. Show it to me, wizard. Please. So I could catch my Uncle Scrooge flat-footed with some figures just once. The sign actually said, amaze your friends. Up here, right? It's not your friends, but amaze your friends. I will, but you must never scorn the magic of mathematics again. Never ignore the strength and understanding it can give you. I won't, I promise. This whole trip through math magic land has been a terrific adventure, but if I could just learn something that would get me out of my Uncle Scrooge's clutches, oh boy. So be it, ho-ho. It's about to learn some math magic to free himself of his debt. I'll show you some tricks your Uncle Scrooge never heard of. He's been too busy to have fun with his figures. Say, these are all good ones, wizard. Wait till you see this one. Mumble, mumble. You see? Here's the idea. Mumble, mumble. Yahoo! This'll do it, wizard. With this one, I'll flat, I'll flabber gasp him. We, from now on, numbers are my dish. Bring on Uncle Scrooge. Uncle Donald, wake up. Wake up. You've been dreaming. Boys, what are you doing in your night? Night shirts. We want to strike while the iron is hot. Come on, let's get over to Uncle Scrooge's house. But Uncle Donald, what's got him and what's gotten to him? Search me. Something sure got him steamed up. Uncle Scrooge, wake up. I want to settle my deal with you. Pay off your loan at this ridiculous hour? Well, I'm always ready to accept money. Where is it? Where? Where? Have you ever heard the story of the ancient king and the grains of wheat on his chessboard? Of course not. I don't have time for silly stories. Fine. I mean, here's my offer. The balance I still owe you is about $15 by now. I expect. So I'll give you my whole house to pay it off. Oh no. Uncle Donald, our house is worth more than that. He'll have to pay me a little something extra to make up the difference naturally. But I won't pay much. At least a few pennies, Uncle Scrooge. Here. Here's your chessboard. I'll settle, settle if you'll just put a penny on the first square and two pennies on the second square and four pennies on the third. Just double the number of pennies each time until you've given me some for every one of these 64 squares. Pennies. Oh no. He's flipped his lid. The house. That house of his is worth a few thousand at least. He. I could rent it back to him for a nice profit too. Look at Uncle Scrooge. He doesn't know the scale. All right. It's a deal, Donald. Here. We've got it all done down in black and white, and now we'll sign. Both copies. Oh, you're making a big mistake, Uncle Donald. There. All signed. Fine. And now there's no use piling all the pennies on this chessboard. I'll just run out the total on my computer. 4,096 pennies on the 13th square. Gosh. It doubles pretty fast at that. 4,000 pennies is only $40. Just keep going, Uncle Scrooge. At least you have to give me as much as our deal calls for. If you're so impatient, Donald, my electronic brain will give us the total in a jiffy. Click, click, click, click. His computer is processing, spitting out paper. Here it comes. All I owe you for your house is gulp. You're doing a little freaking out. What? Oh no. Yep. That's the figure we agreed on, Uncle Scrooge. Look at the number. It's like huge. Oh my gosh. How many thousand trillion dollars? No, this can't be right. Electronic brains don't make mistakes. Wow. Uncle Scrooge's shoe has just flew off his feet. Bottom staple got detached as well during this reading. That's okay. Price was worth it. The price is worth it. Isn't that much money in Allah? There isn't that much money in all my money vaults. Not even this much in the whole world. Sigh. And to thank you, owe me all. You owe it all to me. Donald is happy. No, no. Give me your copy of your our agreement, Donald. Please, let me out of it. I'll buy it from you. Make me a cut rate. You mean a nice round figure and even trillions? You just call things square on my loan and I'll tear up this whole deal. Oh yes, you don't owe me a thing, nephew. You're so sweet, so kind. He is kind. And all of a sudden, so smart. Uncle Donald, it isn't anywhere in our mathematics books. Where did you even learn that terrific dabbling routine? How can you boys ask such silly questions? Why? I learned it back in Math Magic Land, of course. A magic land? Uncle Scrooge asks. There's no such thing. It's impossible. Haha. Oh, come on, Uncle Scrooge. Look, I'm all square with you. That's sure ought to prove, huh? In mathematics, anything is possible. Haha. Walks away happy. Let's start it. We've read almost everything. The only one we haven't read is this one. So let's read this one as well. That way we've gone from cover to cover for this reading. Fascinating fun with numbers. The secret of the wizard's trick. Pick a number from 1 to 10. Pick 6. Add 6 to your number and double the result. 6 plus 6 is 12. 12 times 2 is 24. Now divide your answer by 4. 24 divided by 4 is 6. Now subtract half of the original number you picked. 6 minus 3 is 3. Your answer is 3. By golly, you're right. Here's the secret. No matter what number is picked, the answer will always be half the amount of the number you tell them to add to the number they picked. If you tell them to add 3 to their number, the answer will be one and a half. If 4, the answer will be 2. Try it and see. Pick a number from 1 to 10. And it only works from the number from 1 to 10, eh? Cool. Nice little trick. That was a fun read. Really? And we detached our comic book and it's really well worth it. Well worth it. Very fun read. I think I might go online and watch the animation again. And there's a little bits of it. I'm not sure if you can see this, right? And that's where I'm there for comic books. That's fun. And if you're interested in math games, just reading off the last little bit, if you're interested in math games, we did put together a video of a grid game that one of my students showed me. And it's a really fun game where you create a square grid, 10 by 10, 100 square, then you start with the number 1, you follow certain types of moves, and you try to complete, fill in the whole square from the number 1 to 100. And it's fun and there's a video of us putting that puzzle together and actually trying one out. Okay, if you're interested in math games, sort of pattern recognition games, okay? And that's Dao, four color number 1051 from 1951, right? Sort of an adaptation of Walt Disney's animation that came out in the same year in June of 1959, right? I hope you enjoy it and I'll see you guys in the next video. Bye for now.