What’s the Golden Number? │ The History of Mathematics with Luc de Brabandère

Our series ‘The History of Maths’ continues with what the Greeks called the Golden Rectangle,  which led to the discovery of the Golden Number. 

Subscribe to watch all the episodes on our YouTube channel now. 

I want you to look at three rectangles. This is number one. This is number two, and this is number three. According to you: which one is the most elegant? You'll probably agree with me: it's number three. Yes, there is a connection between mathematics and beauty. Between mathematics, aesthetics and harmony.

And if you go to Athens and look at the Parthenon, the front wall of the Parthenon is elegant. Why? Because this is a beautiful rectangle. And the Greeks wanted to calculate the beauty, to conceptualise the beauty. So, the starting point for them was ‘a rectangle is beautiful’. They named it the Golden Rectangle. If, when you remove a square from the Golden Rectangle, what’s left again is a Golden Rectangle, and that's why you can find golden numbers everywhere, in a spiral, etc. 

But I told you, the Greeks loved mathematics, so they wanted to calculate what is the exact proportion between the two sides of the rectangle and they proved it is 1.618. This is the Golden Number. The Golden Number has lots of properties and they still fascinate mathematicians today. Just two of them: first, if we divide 1 by the Golden Number, you get another Golden Number. If you want to calculate exactly how much the Golden Number is, you can do it by using only 1s. Hard to believe? So, start with 1+1 which is 2. Then 1 + 1/(1+1) The outcome is 1.5. It is not 1.6 yet but it's narrowing. Next step is 1 + 1/(1+1)  ‘over’ 1+1 and then we reach 1.6666. If you do that in several steps, in the end you get the Golden Number. 

Join us next time to find out how Aristotle came up with the very first model of thinking: logic. 

Subscribe now to watch our full series of ‘The History of Maths’.