Of course, the Greeks knew this long before modern psychologists tested it, which is why they used golden rectangles, as well as other golden shapes and proportions adhering to the golden ratio, in their architecture and art.įor example, almost 2500 years ago, a Greek sculptor and architect named Phidias is thought to have used the golden ratio to design the statues he sculpted for the Parthenon (note the word “phi” in Phidias’ name-that isn’t a coincidence and actually inspired the naming of the number in the 20th century). We won’t go into the details right now, but there is evidence that people tend to perceive one particular shape of rectangle as being most pleasing to the eye. What’s the most beautiful rectangle? More specifically: What’s the ratio of this “most beautiful” rectangle’s height to its width? This question seems strange, but it isn’t crazy. But how did this number come to be of such importance? Oddly, it started as a question of aesthetics. If you’re interested in seeing how the actual value of phi is obtained, check out this week’s Math Dude “Video Extra!” episode on YouTube.

Phi isn’t equal to precisely 1.618 since, like its famous cousin pi, phi is an irrational number-which means that its decimal digits carry on forever without repeating a pattern. This number is now often known as “phi” and is expressed in writing using the symbol for the letter phi from the Greek alphabet. So, what is this golden ratio? Well, it’s a number that’s equal to approximately 1.618. One such place is particularly fascinating: the golden ratio. But the numbers in Fibonacci’s sequence have a life far beyond rabbits, and show up in the most unexpected places. And, save a few complicating details like the fact that rabbits eventually grow old and die, this sequence does an admirable job at modeling how populations grow. Each successive number in this sequence is obtained by adding the two previous numbers together.

Fibonacci number examples