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How Donald Duck created an Urban Myth

Credit cards, Greeks and Golden Rectangles

If you wanted to pick a rectangle that was the most aesthetically pleasing, the "rectangle's rectangle" if you like, what would you choose?

A sheet of A4 paper perhaps?  Or maybe a playing card?  Or how about a credit card?

There are those who claim that the most pleasing rectangle is the so-called Golden Rectangle, whose sides are in the proportion of the golden ratio, a little over 1.618.  And if this is true, then the surprising answer (to me, at least) is that of the examples of rectangles I listed above, it is the good old credit card that wins.  Because, I was told this week, the credit card is an everyday example of the Golden Rectangle.

How amazing that after all these years hearing stories about golden rectangles, I had never heard that the credit card is based on it.  Being a bit of a skeptic, I thought I'd take out my Mastercard and measure it.  Sure enough, when I divided the length (85 mm) by the width (53mm) it came to just over 1.6, close enough to the golden ratio to suggest that this is indeed the basis of the dimensions of our flexible friend.

So why on earth did the inventors of credit cards choose the golden ratio?  Was there a closet mathematician in the design team who wanted to sneak in this symbol of eternal beauty? Or did the shape of the credit card emerge almost as a force of nature, because it is the 'best' shape?  The history of the credit card dimensions seems to be shrouded in mystery, but after a bit of surfing one thing becomes apparent.  The unusual metric dimensions used today are just a conversion from the more straightforward imperial dimensions. The length is 3 3/8 inches, and the width 2 1/8 inches. That means the ratio is precisely 27/17, about 1.59.  It might be close to the golden ratio, but it's certainly not the same.

Meanwhile, the ratio of the sides of a regular playing card (bridge size) is 14/9, or 1.56, while the sides of a sheet of A4 have an irrational ratio, the square root of 2 (about 1.41).

Which of these rectangles is the most aesthetically beautiful?  Well, that is entirely subjective.  But it's an urban myth that most people choose the golden rectangle ahead of other rectangular shapes. And in my view, the fact that A4 paper retains its same proportions when folded in half (to make A5 paper) makes it by far the most beautiful of the rectangles.

Where does this widespread belief in the superior beauty of the golden rectangle come from? Blame Donald Duck.  In 1959, Disney released a short animation called Donald in Mathmagic Land, about the beauty of mathematics.  It was a huge hit, and for years it was a staple in US classrooms.  Nine minutes into the cartoon (watch it on Youtube!), Donald learns that the Parthenon was deliberately built to the proportions of the golden ratio, as was Notre Dame cathedral and countless other structures.  "Boy, oh boy, oh boy!" exclaims Donald. And if it came from Walt Disney, then surely it was true.  Except of course it wasn't, Disney was using the same artistic licence he used in all his adaptations of traditional stories.  

The golden ratio has many genuine and beautiful connections with the real world, but alas Greek architecture and credit cards aren't among them.