# Nautilus Shell

"The most beautiful thing we can experience is the mysterious. It is the source of all true art and science."
Einstein, Albert

## Nautilus - Living Fossil

 The Nautilus (in Greek 'sailor') has survived relatively unchanged for 450 million years and is one of the only shells to survive from the Dinosaurs era. This is why the Nautilus is sometimes referred to as a "living fossil". The Nautilus is a nocturnal creature and spends most of its time in the great depths of the ocean. The Nautilus shell, lined with mother-of-pearl, grows into increasingly larger chambers throughout its life and so has become a symbol for expansion and renewal.

## Nautilus shell and Phi

Dating back to Hindu myth, the Nautilus Shell was mentioned as a symbol of many things in the creation. It is also a symbol of the inner beauty of nature. The Nautilus shell is one of the known shapes that represent the golden mean number. The golden mean number is also known as PHI - 1.6180339... The PHI is a number without an arithmetic solution, the digits simply continue for eternity without repeating themselves. The uniqueness of the golden mean is that it can be found in all living forms such as the human skeleton, the shell, and the sunflowers seeds order. Plato called this number - "The key for the universe physics".

A similar geometric shape like the Nautilus can be found in the spiral patterns of the leaves in many plants, the arrangement of the pine cone and in cauliflower. The Concept that Phi can be found in all living things is amazing and mind-blowing. It somehow suggests that our natural world is not just a random mess, but instead contains logic and can be explained with mathematical equations.

The Golden Mean number is widely used in art, architecture and religious symbols. Artists like Da Vinci and Kandinsky have used the golden mean in their paintings. The Guggenheim Museum, planned by Frank Lloyd Wright, is shaped like the shell. Researchers found that humans will consider beautiful artwork, architecture and even a face that have the golden mean proportions. While it cannot be worked out arithmetically, Phi can be easily obtained with a compass and straightedge.

## Finding the Golden Mean

Two simple ways of finding the Golden Section geometrically are as follows:
Method one
If you take two equal squares, side by side, (a 1x2 rectangle), divide one of the squares in half, and with a compass, swing the diagonal down to the base of the other square, the point where the diagonal touches the base will be phi, or 1.6180339+, in relation to the side of the square, which is 1 (This formula also describes exactly the rectangular floor of the King's Chamber).
Method two
The other method of determining the Golden Section is by dividing a line segment, AB, at a point C, in such a way that the whole line is longer than the first part in the same proportion as the first part is longer than the remainder. AB/AC = AC/CB = 1.6180339 (notice the fractal and holographic nature of this ratio...).

## Golden Mean in Architecture

The phi ratio is found in the architecture of the Great Pyramid in the triangle formed by the height, half-base, and the apothem, or diagonal. In other words, the basic cross-section of the structure demonstrates the Golden Section. If the half - base is given a value of 1, this gives the value of phi for the apothem, and the square root of phi for the height. The Golden Section shows up again and again in Giza and in much more baffling and tedious ways (Entire volumes have been written on the geometries involved in the pyramids construction).

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