SIX

We encounter the Hexad, or six sided figure, in countless natural phenomena and human designs, from beehives to faucets handles, and floor tiles to snow flakes. All true insects have six legs. This arrangement of 120 degree joinery allows close-packing and true efficiency of material, time, energy and strength. Hexagonal tessellation (redundant patterning) occurs profusely in nature.

Most designs using a circle as a base will utilize hexagonal structure. Examples are the umbrella, bicycle wheels, parachutes and a camera lens, to name a few. These examples utilize different combinations of hexagonal designs for strength and efficiency. Most nuts and bolts also use hexagonal designs.

SEVEN

EIGHT

"Change has an absolute limit: This produces two modes;
the two modes produce four forms, the four forms produce eight trigrams;
the eight trigrams determine fortune and misfortune."
Confucius

The Octad weaves together the Monad's unity, expansion and cycles, as well as the Dyad's polarity and Tetrad's materialization. Eightfold geometry has long been an ancient symbol for the Mother Goddess. Depicted mythologically as an eight-legged spider or "spinner", she has created the world through her weaving of warp and woof. The Egyptian, Greek and Mayan traditions all perceived their great goddesses as spinstresses and embroiderers.

Modern physics has modeled the Periodic Table of Elements on an eightfold structure. There are eight main groups of elements. Atomic properties recur in cycles of eight. Elements in the same columns have the same number of electrons, between one and eight in the outer most peripheries of their orbits. Cell mitosis also takes place in eight stages.

Other familiar elements in our lives based on the Octad are DNA molecules, the geometry of chess (see chess article) and anything relying on the use of octaves; the musical scale; the I Ching and the eight phases of the moon, to name a few.

NINE

The Ennead, or nine pointed star, is an ancient and sacred symbol. It comprises three trinities. The Egyptian, Celtic, Greek and Christian myths all have an ennead of nine gods and goddesses, representing the entire archetypal range of principles.

The magic square is also considered sacred and full of power in the Islamic, Tibetan, Buddhist, Celtic, Indian and Jewish traditions. A magic square is when each number is used only once, but the horizontal, vertical and diagonal sums are all equal. The Chinese have patterned their architectural temples along the harmonious principles of the magic square.

TEN

According to Pythagoras ten is the "perfect number" symbolizing fulfillment and new beginnings. The Babylonian, Egyptian, Mayan, Roman, Hebrew, Greek and Arabic numerical systems all utilize a ten as a base. The study of the Tetraktys, pictured at the left, was the core teaching in Pythagorean schools of natural science of philosophy. The Tetraktys comprises the point, line, surface and volume.

The modern physics T.O.E. (Theory of Everything) or String Theory, postulates a ten dimensional universe in which the three dimensions of space (length, width and height) are a trinity, plus the dimension of time.

For a true appreciation of how the numbers one through ten impinge upon your everyday life you need to read this fascinating book. Creative mind depends upon a flexible understanding of nature and man, and how they relate. Creative problem solving also relies upon an understanding of numbers and their relationships. There is a wealth of knowledge and wisdom here that will enrich your understanding of mathematics as a basis for the arts and sciences. Thus, your relationship to these arts will be inspired and elevated as you venture to express yourself through them.

The following link is a brief synopsis of Seminars given by Michael. To contact Michael for more information on when and where his next workshop is you can email him at Michael Schneider.