# Donald in Mathmagic Land

Donald Duck learns that there is “a lot more to mathematics than two-times-two”.

Made by Disney and released in 1959, Donald in Mathmagic Land is an educational movie featuring the famous cartoon duck who discovers the beauty of mathematics and realises that there is much more to it than just numbers. The film was rolled out to school teachers to present to their class, and it proved to be one of the most popular of all educational films. Perhaps you are one of those teachers, or maybe, like me, you’ve seen it for yourself as a school child. I still remember being shown a few clips of it when I was just a teenager. I loved it so much that a few years later, I just had to watch the whole movie!

A pentagram. The coloured edges are related by the golden ratio.

Moreover, Donald Duck became my favourite Disney character, all thanks to this one film! After all, he starts off thinking maths is only “for eggheads”, but by the end of the video he understands how useful (and fun!) mathematics is. That is why I am convinced that there is so much more to Donald than the grumpy, foolish persona we see in the other Disney cartoons—and why it breaks my heart whenever I hear someone call him “stupid”.

Donald in Mathmagic Land spends much of its time showing the power of the golden ratio, first by demonstrating how it appears in a pentagram; not just once, but many times over. There is even a shape based on this beautiful proportion, and it is called the golden rectangle. But the golden ratio does not only turn up in abstract shapes—you can also find it in buildings, paintings, shells, trees, ferns and in us, too!

A petunia, star jasmine and starfish.
petunia: Andrew Bossi, CC BY-SA 2.5; star jasmine: Philippe Teuwen, CC BY-SA 2.0; starfish: Paul Shaffner, CC BY 2.0

Donald himself doesn’t fit the golden proportion, though he does manage to get “all pent up in a pentagon”! Speaking of which, nature has plenty of pentagons on offer, too: the petunia, the star jasmine and the starfish are only a few such specimens. There are thousands more examples out there.

It’s all too easy to forget that mathematics also crops up in many kinds of games. If you spent your summer watching the Euros or the Olympics, then you have seen many different geometrical areas, but probably took them for granted! For example, basketball is chock full of circles, spheres and rectangles; baseball is played on a diamond; even chess and hopscotch are games of squares. The narrator also presents a trick behind the game of billiards which relies on…you guessed it—maths!

The conic sections.
Magister Mathematicae, CC BY-SA 3.0

And then there is my favourite part of the entire movie: the mind games. Before starting, it is hilarious to see how cluttered Donald’s mind is but, once it’s cleared, he goes on a roll! He starts out with just a circle and a triangle. Donald discovers numerous inventions including magnifying glasses, wheels, propellers, gears, springs, telephones, pistons and many more—far too many to cover in one blog post! He also comes across the conic sections, from the ellipses that make up the planetary orbits to the parabolae seen in searchlight reflectors.

Yes, mathematics plays an important part in scientific discoveries and technological advances. Plenty of these doors have already opened, but there are still many more that remain locked. When I first saw the film, I was part of the next generation, waiting to unlock the doors of the future. Now it’s my turn to start unlocking and, who knows, maybe someday you will open one of those doors, too. Just remember, the key to the doors is none other than mathematics.

But don’t just take my word for it—have a look at the film for yourself. Oh, and watch out for Lewis Carroll and the visual pun on square roots!

If there is one way to end this blog post, it would be with the quote from Galileo at the end of Donald in Mathmagic Land

“Mathematics is the alphabet with which God has written the universe”.

Belgin is a data scientist having got her PhD in population genetics. When not working, you can usually find Belgin either playing the piano or playing Math Blaster. She is pictured here standing next to her copy of Zeeman’s catastrophe machine.
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