GART

Fibonacci Spiral

Squares whose sides are the Fibonacci sequence. A quarter-circle in each chamber is the golden spiral; an inset at 1/φ is the septum.

Fibonacci Spiral: Squares whose sides are the Fibonacci sequence. A quarter-circle in each chamber is the golden spiral; an inset at 1/φ is the septum.Fibonacci Spiral: Squares whose sides are the Fibonacci sequence. A quarter-circle in each chamber is the golden spiral; an inset at 1/φ is the septum.

About this pattern

Leonardo of Pisa (Fibonacci), 1202

Fibonacci Spiral, fibonacci sequence, drawn by GART: Squares whose sides are the Fibonacci sequence. A quarter-circle in each chamber is the golden spiral; an inset at 1/φ is the septum.
Fibonacci Spiral · CC BY 4.0

Liber Abaci (1202) gave Europe the sequence 1, 1, 2, 3, 5, … Each new square’s side is the sum of the two before it. A quarter-circle in each square is the golden spiral; an inset at 1/φ reads as a shell chamber. Motion unfurls the tiling: each square buds from the last, the spiral follows, the frame zooms out with φ, then the sequence recedes.

TopicsFibonacci sequence (opens in a new tab)Golden spiral (opens in a new tab)

Squares
1, 1, 2. Each new square’s side is the sum of the two before it.

Behind the mathematics

Leonardo of Pisac. 1170–c. 1240–50

Fibonacci sequence

The Italian mathematician known as Fibonacci popularised Hindu–Arabic numerals in Europe; his famous sequence produces ratios that approach the golden mean.