# The Nautilus Shell Spiral

The shell of the chambered nautilus is a symbol of beauty and proportional perfection. In this exercise you will experience the essence and energy of the spiral displayed in the unfolding of the nautilus shell.

The proportion of this nautilus shell is consistent through all of the relationships of the shell, so once you discover the secret ratio, you will see clearly why this particular gem of nature is such a treasure.

The nautilus shell spiral is a logarithmic spiral similar to other spirals such as the Golden Mean or phi spiral, but with slightly different proportions. A close approximation of a Golden Mean spiral, based on the Fibonacci whole number sequence is illustrated below.

The spiral of the chambered nautilus as well as other logarithmic spirals can be found throughout the human body and nature. The drawing of the inner ear and the photo image of a star cluster nebula shown to the right are just two examples which can be seen with a microscope or a telescope. There are many examples which can be seen without magnification. See what you can find.

**This beautiful spiral can be easily drawn on a piece of grid paper with a pencil. Refer to the drawings below as you work.**

## STEP 1

Begin with a small single square, one unit per side, near the lower right-hand corner of the page. Continue adding larger and larger squares in a counterclockwise direction using the following number sequence: 1, 1, 2, 3, 5, 8, 13… as illustrated in the example. This number sequence is often referred to as the “Fibonacci series.

## STEP 2

Draw diagonals through every square in a counterclockwise direction. Use the diagonals as guides and draw a smooth spiraling curve from the smallest, one-unit square, outward through your largest square. The proportional relationship of the squares quickly begins to approach the Golden Proportion of 1:1.618…

If you have a drawing compass, you can set the point at the corner of each square, opposite the diagonal, and construct a beautiful spiraling curve out from the smallest square. The center is known as the “eye of the spiral.”

This inspiring and energetic form is common throughout nature. You can easily find it in the plant and animal kingdoms and in cloud patterns and whirlpools if you look.