Sacred Geometries

Johannes Kepler, the man who discovered the mathematical formula for the orbits of the planets was obsessed with what he called the music of the spheres. Since ancient times men have thought that natural reveals itself in perfect harmonic proportions and that all you have to do is discover the right numbers and you will unlock the mysteries of the universe. Those secrets would be shown to be a kind of music that God plays on a grand instrument.

Pythagoras was one of the first to try to find some form of harmony in the universe through numbers.   He noticed that if you add up the numbers  1,2,3,4 you get the number 10, which he believed was a perfect number. He therefore took the ratios of the numbers 1 through 4 to be special. Some have looked at correspondence between ratios like ½, 1/3, ¼ and so on and what are termed the perfect solids. Cubes and octagons and the like.

One of the longest lasting numeric obsessions has to do with the number Phi, which has also been called the golden ratio.   One of the easiest ways to envision Phi is as one of the roots of the polynomial:   x^2 - x -1=0. If you are familiar with the quadratic equation then you know that one of the roots is:

(1+ 5^(.5))/2 = 1.618033989.

Given that I have derived this from a quadratic equation you might wonder where the ratio part of the golden ratio is.    In theory you form the golden ratio by taking two sticks of unequal length and laying them side by side. Sum the lengths of the two sticks and divide the sum by the length of the longest stick.   Form another ratio by dividing the length of the longer stick by the length of the shorter stick. Set these two ratios equal to one another.   The length of the long stick that solves this equation is the golden ratio.

You can get an approximation of the golden ratio by forming ratios of the Fibonacci sequence;   1,1,2,3,5,8,13,...   Wherein each successive number is formed by sum of the two before it. So the ratios come out to be: 1, 2,1.5,1.66667,1.6,1.625... It's interesting that the ratios are not monotonic. They go up and down but they center on the golden ratio. The golden ratio figures into proportions that artists and architects have used for centuries.

The golden ratio is found as the growth factor in the logarithmic or golden spiral. It has been used to build pyramids, Greek buildings, and Renaissance buildings.

When we are talking about the golden ratio in relation to the human body it is often called the golden section or the divine proportion. The simplest approximate golden section compares the length of the hand to the length of the hand plus the arm. Other golden sections begin with the head and compare measurements with various parts of the body.

So let's say that the Almighty, when in the process of creating all things began with the most perfect object imaginable: a circle. If you were an observer perched on the circumference of a circle then the hoop would have no discernable beginning or end. The second step in creating a universe involves creating another circle and placing a point on its circumference at the center of the first circle. Which point on its circumference is chosen for this honor, you may well ask? It doesn't matter. All points on a circle are identical. And so ends the second day of creation. On the third day a third perfect thing was needed and so another circle was formed and thus was created the tripod of life. During each successive day a new circle was added until on the on the 7th you have the seed of life. If you stack the Seeds of Life in a hexagon pattern you have the Flower of Life.

If you actually want to use mathematics to create the Seed of Life you can use a process like the following. Draw a circle. Pin the circle down at a single point on its circumference. Spin the circle about that point. Since we are not spinning the circle about its origin we are doing something that looks like drawing circles around the center of a dinner plate with each successive circle overlapping the one preceding it. If we start each succeeding circle 60 degrees from its predecessor we will wind up with the seed of life. You will see a flower pattern formed by the overlapping circles. Now form two more circles-one inside and one outside. Form the outer circle by drawing a curve through the   furthermost points on the circumferences of the overlapping circles. Form the inner circle by connecting all the innermost intersections. Now you have the Seed of Life.