The Hidden Plan of The Giza Plateau

It has long been known that many of the growth patterns in the botanical and animal worlds are based upon simple proportional additions, with some of the most pleasing being of geometric proportional increase. Under such geometric proportional growth, the organism retains its similarity of shape whilst increasing its bulk. Most plants for example, grow in a spiral arrangement, which confers self-replication whilst at the same time maintaining a dynamic balance and stability for the organism.

Leonardo da Vinci pointed out that there are considerable advantages to such a spiral growth pattern, as this results in minimal leaf overlap, allowing the maximum amount of light to reach the leaves, thereby affording maximum growth potential. It has been calculated that there is an ideal angle between the leaves or branches on a trunk, which provides the maximum exposure to light, with the least shading effect on the other parts of the plant. This `Ideal Angle' was named by Church, and later confirmed by Wiesner in 1875, and it is determined by the Golden Section.¹ Such growth patterns, as Michael Schneider points out, teach that "things" are not nouns, but processes, or dynamic "energy events." ² 

Such spiral geometric growth has been determined to be a common and essential pattern in the natural world, minimising wasted energy and maximising the moving energy of creation, providing a natural law that biological growth is an exponential pattern. The spiral that best fits this model is the logarithmic spiral, being the quintessential exposition of natural law, sometimes called the `spira mirabilis.'  The Nautilus shell, whose radius of curvature of the shell, increases according to the exponential polar equation,

provides an excellent example of this. (Where r is the vector radius, a is a constant of proportionality > 0, and ¥ is the polar angle)³

which demonstrates that a spiral obeying this formula will intersect its radii always at the same angle, and hence such spirals are more accurately termed equiangular.

The easiest method of constructing a logarithmic, or equiangular spiral, is to use a diminishing series of Golden Rectangles, which is depicted on the next page together with its most well-known form, that of the chambered Nautilus.

Notes

1 The Geometry of Art and Life, Matila Ghyka, Sheed & Ward, 1966, p 16

² A Beginner's Guide to Constructing the Universe, The mathematical archetypes of Nature, Art, and Science, Michael S. Schneider, Harper Perennial, 1995, p 173

³ If the constant of proportionality equals zero, then the spiral does not grow, and becomes a circle. Therefore a circle is in fact a special form of a logarithmic or equiangular spiral.