The Fibonacci sequence (1, 1, 2, 3, 5, 8, โฆ) builds each next number by adding the two before it. Line up squares whose sides are these numbers, and a spiral shape appears naturally.
The Fibonacci sequence actually originated from a problem about rabbits. The Italian mathematician Fibonacci is said to have discovered this sequence while solving the problem: "if a pair of rabbits gives birth to one new pair every month, and each new pair can start reproducing after two months, how many pairs of rabbits will there be after a certain number of months?" The rule is simple โ add the two previous numbers to get the next one.
What's remarkable is that if you use these numbers as the side lengths of squares and line them up side by side, a spiral shape appears on its own. And the ratio of two neighboring Fibonacci numbers (for example, 8รท5, 13รท8) gets closer and closer to a special value called the golden ratio (ฯโ1.618) as the terms get larger. The golden ratio has long been considered the most stable and beautiful of proportions.
This spiral pattern shows up often outside of textbooks too. You can find similar spirals in the arrangement of sunflower seeds, the scales of a pine cone, and the cross-section of a nautilus shell. Use the slider to increase the number of terms and watch how the squares grow, and how close the ratio gets to ฯ.