The Fibonacci sequence (1, 1, 2, 3, 5, 8, …) builds each new number by adding the two terms before it. Line up squares whose side lengths follow these numbers, and a spiral naturally appears.
The Fibonacci sequence actually comes from a puzzle about rabbits. The Italian mathematician Fibonacci discovered it while working out a problem: "If a pair of rabbits produces one new pair every month, and each new pair can start breeding two months later, how many pairs will there be after a certain number of months?" The rule turned out to be simple — add the two previous numbers to get the next one.
Here's the fascinating part: use these numbers as the side lengths of squares and line them up side by side, and a spiral shape appears all on its own. What's more, the ratio between two neighboring Fibonacci numbers (like 8÷5 or 13÷8) gets closer and closer, as the terms grow larger, to a special value called the golden ratio (φ≈1.618). The golden ratio has long been considered the most stable and beautiful of proportions.
This spiral pattern shows up outside the textbook, too — you can find similar spirals in the arrangement of sunflower seeds, pinecone scales, and the cross-section of a nautilus shell. Drag the slider to add more terms and watch how the squares grow, and how close the ratio gets to φ.