Fibonacci in the Mona Lisa and in Markets

by Michael Lebowitz, 1/26/26

Michael LebowitzAdvisor Perspectives welcomes guest contributions. The views presented here do not necessarily represent those of Advisor Perspectives.

Did you know there is a type of technical analysis that shares structural similarities with hurricanes, nautilus shells, sunflowers, music, and human dimensions? These examples — along with countless others — follow proportions related to the sequence of numbers: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89...

This endless sequence of numbers that form ratios, known as the Fibonacci sequence, provides a technical analysis tool for managing financial securities. Before you assume we've lost our minds —relying on biology or, even worse, mysticism to predict stock prices — let us explain.

Fibonacci Surrounds Us

If you draw quarter-circle arcs connecting the opposite corners of squares with side lengths following the Fibonacci sequence (1, 1, 2, 3, 5, 8, 13, 21…), you generate a spiral that expands outward, resembling a nautilus shell. Each number in this sequence is the sum of the two preceding numbers.

Notably, the ratios of consecutive Fibonacci numbers approach the golden ratio, 1.618, represented by the Greek letter Phi. To arrive at Phi, divide a number in the sequence by its predecessor; conversely, dividing a number by the one following it approaches 0.618.

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Below are a few other examples of natural occurrences following the Fibonacci sequence and the golden ratio:

  • Spiral galaxies: Some galaxies have arms that extend outward at distances resembling the Fibonacci spiral.
  • Sunflower spirals: Seed spirals in a sunflower — 34 clockwise; 55 counterclockwise (or sometimes 55 and 89).
  • Cauliflower florets: Count the spiraling florets, which are often five, eight, or thirteen per cluster, reflecting Fibonacci growth.
  • Piano keys: In an octave, there are a total of 13 keys (8 white and 5 black, arranged as 2 and 3).
  • Mona Lisa, according to Math Central:

The Mona Lisa has many golden rectangles throughout the painting. By drawing a rectangle around her face, we can see that it is indeed golden. If we divide that rectangle with a line drawn across her eyes, we get another golden rectangle, meaning that the proportion of her head length to her eyes is golden. There are other golden rectangles that can be drawn on the rest of her body, like from her neck to the top of her hands.

sunflower image

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mona lisa

Furthermore, it’s widely believed that the Fibonacci sequence and the golden ratio form the foundation of the brain's structure and thought processes.

Professor Adrian Bejan of Duke University, published in The Atlantic magazine, noted:

This is the best flowing configuration for images from plane to brain and it manifests itself frequently in human-made shapes that give the impression they were 'designed' according to the golden ratio.