Saturday, August 24, 2013

Sacred Geometry

     The term 'geometry' means 'measure of the earth', a Greek word inherited from ancient Egypt. The yearly flooding of the Nile caused chaos in the fields and each year, after the waters had receded, 'geometry', the redefining and re-establishment of boundaries, was carried out. It was the re-establishment of the principle of order and law on the planet.

     This 'measurement of the earth' evolved into the basis for a science of natural law, embodying the archetypal forms of square, circle and triangle. This led to the belief that 'God created the universe according to a geometric pattern': Plato: 'God geometrizes continually'; Gauss: 'God arithmetizes.' And, in a way, this is true.

     Nature is geometric, often symmetric from the 'simplest' snowflake to the most beautiful flower. In ancient Egypt, it was the god Thoth (Djehuti) to whom were attributed many aspects including science, religion, philosophy, magic and the mediating power between good and evil; responsible for the calculations that made the heavens, stars and earth.
The Geometry of
a Snowflake
     Note that, in English, the spelling of the name 'Thoth' is itself near-symmetric. The Greeks adopted this deity and added to his attributes, the science of mathematics and geometry among others.
     Thoth, the 'ibis (sometimes baboon)-headed' deity (see post: What Did They See?) became especially known for magic, writing, judgement of the dead and the development of science. The 'golden ratio' is a ratio studied since ancient Greece and first remarked upon because of its frequency in nature.
     A 'golden ratio' is present, in arts and mathematics, when the ratio of the sum of the quantities to the larger quantity is equal to the ratio of the larger quantity to the smaller one; a ratio of approximately 3:2. Within this, there is a certain appealing beauty that is caught by the eye.
Kolam-South India

     The mathematics of the 'golden ratio' are intimately related to the Fibonacci (named after Leonardo of Pisa-a.k.a. Fibonacci) sequence, a number theorem.

Christ with Compass
     The Fibonacci sequence appears to be a 'rhythm' that is inherent in nature. It is seen in ancient Indian mathematics as well as in Sanskrit poetry. In many cultures, geometric patterns are still considered sacred, powdered onto the doorstep each morning (kolam).
     By definition, in the Fibonacci sequence, each number is the sum of the previous two. It is a sequence that appears throughout nature, such as in the the arrangement of leaves on a stem, the branching of a tree; and is applicable to computer algorithms, graphs, data structure.
The Golden Ratio

     'Sacred Geometry', the 'Golden ratio', the 'Fibonacci Sequence'...It's beautiful, it's natural, it's everywhere. It's all one more way to have 'Fun with Numbers' (see posts: Fun With Numbers and Geomatria-Fun With Numbers Again).
The Geometry of a Low Pressure
Weather System

     To create symmetry, to create a perfect geometry that reflects the natural world, mankind created tools that allowed him to build pyramids, castles, spaceships.
     These tools were the magical implements of the builder, the architect, the engineer: the compass, the planer and the set-square.
     *Sacred geometry: subject of research for the novel The Tao of the Thirteenth God - Amazon Kindle

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