How it is drawn

Draw a square, then a square of the same size beside it, then a square on their combined side, and keep going, each new square as wide as the two before. Their sides follow the Fibonacci numbers. Draw a quarter circle across each square and they join into the Fibonacci spiral, unwinding outward like a fern frond.

In nature

Sunflower heads, pinecones and pineapples very often carry their seeds and scales in spirals of Fibonacci numbers (34 one way and 55 the other, for example), and the leaves of many plants unfold at an angle tied to the golden ratio, so each leaf finds its own share of light. Shells, storms and galaxies wind in graceful spirals too. Nature seems to love this way of growing.

Through the ages

• Euclid described the proportion as division "in extreme and mean ratio" and used it to build the pentagon and the dodecahedron. Every point of a five-pointed star divides its lines in the golden ratio.
• Indian scholars of poetry and rhythm found the same number pattern centuries before Europe, in their study of the rhythms and meters of poetry.
• Leonardo of Pisa (Fibonacci) brought the sequence to Europe in Liber Abaci (1202) through a puzzle about breeding rabbits.
• Luca Pacioli called the proportion "divine" in De Divina Proportione (1509), a book illustrated by Leonardo da Vinci.

What it means

Since Pacioli named it divine, artists, builders and seekers have seen the golden ratio as the signature of harmony and beauty woven into the world. We read the spiral as a symbol of growth that keeps its shape as it expands, a reminder that we can grow and change and still remain wholly ourselves.

In grids and meditation

• A spiral grid winds out from a center stone, each stone a little farther from the last. It is a favorite for steady growth or for something you want to unfold in its own time.
• Trace a spiral inward to settle and outward to open, matching the breath.