Math Mysticism: is Hurricane Shape a Fibonaci Spiral?

By Xah Lee. Date:
fibonacci spiral girl
When a attractive girl flips her wet hair, the water stream formed is a Fibonacci spiral.

Please beware of the golden ratio math mysticism spreading online.

Fibonacci spiral hurrican Irene
Illustration giving the impression that hurricane Irene has a shape of so-called “Fibonacci spiral” image source

Many people are sharing this image online. It is true that the hurricanes have the general shape of a spiral. In particular, it's a equiangular spiral (aka logarithmic spiral), which is the shape that many (but not all) natural growth takes (For example, Seashells), but saying that hurricane has golden-spiral is completely baseless, it's like seeing Jesus face on Mars.

The so-called “Fibonacci spiral” (aka golden-spiral) you see in the pic is made up of parts of circles, stacked on blocks of squares. It is not a spiral in a math sense. This “spiral” has curvature discontinuity at every connection point. (this means, if you are driving fast on such road, you'll need to adjust your steering wheel ABRUPTLY at every connection point.) This “spiral” is only a approximation of one particular equiangular spiral.

equi spiral def
A example of equiangular spiral with angle 80°.

(equiangular spiral is a family of spirals. See: Equiangular Spiral.)

Also, hurricane does not really have a definite shape, we can only say it's roughly that of equiangular spiral based partly on physics and appearance.

If you don't have a degree in math, you might be all confused about this Fibonacci number , the Golden ratio, and the various spirals. It is true that mathematics is mysterious, and many shapes in nature are well described by math, but if you see any online blog or math popularizing books that carelessly connect it with mysticism, about how some numbers or shapes is everything in the universe, beware, it's stretched to garbage.

For highschool-level explanation of the equiangular spiral, see: Equiangular Spiral. For other spirals, see: Archimedean Spiral, Lituus.

For debunking of the Fibonacci number and “golden” this that, see:

See also: Math: Fibonaci Sequence Video Fallacy 📺.