The silver ratio and other metallic ratios have rectangles of their own. In each, you block off as many squares as you can, which corresponds with the integer floor of the metallic mean.

As the video demonstrates, this is because the golden ratio is a highly irrational number, meaning it is not very well approximated by any whole number or even any fraction of whole numbers.

First described in Euclid’s Elements 2,300 years ago, the established definition is this: ... When you do the math, the golden ratio doesn’t come out to 1.6180. It comes out to 1.6180339887 ...

In Golden Meaning, a new book from London publisher GraphicDesign&, 55 designers aim to demystify the golden ratio using clever illustrations and smart graphic design.