There
is practical geometry which sees a relationship between mathematics and geometric
forms and there is symbolic sacred geometry which sees a relationship of geometric
forms with the structure of the world as created by God. "According to
this discipline, the basic patterns of existence are perceived as sacred:
for by contemplating and communing with them one is thereby contemplating
the Mysterium Magnum, the patterning relationships of the Great Design."**
(Sacred Geometry: wikipedia.org)**

The fundamental geometric
form is the circle which is a shadow of a globe. Mathematicians have noticed
that when you divide the diameter of a circle into its perimeter you wind
up with a number which goes on without end. This they call an **irrational
number** because it cannot be expressed as the ratio of two whole
numbers. In its essence a circle exists in a dimension that transcends the
linear rationality that it contains. There is here a greater wisdom than can
be expressed by our limited ideas alone. "The sphere
is an ultimate expression of unity, completeness, and integrity. There is
no point of view given greater or lesser importance, and all points on the
surface are equally accessible and regarded by the center from which all originate.
Atoms, cells, seeds, planets, and globular star systems all echo the spherical
paradigm of total inclusion, acceptance, simultaneous potential and fruition,
the macrocosm and microcosm." **(website:
geometrycode.com by Bruce Rawles)**

Islam by using basic Euclidean geometric forms and by removing certain line portions and overlapping of lines was able to create intricate geometric patterns as you can see if you study these images. "The Islamic designs echo quasicrystalline geometry [e.g. snowflake] in that both use symmetrical polygonal shapes to create patterns that can be extended indefinitely without repetition." Islam ever so fearful of Idolatry and wishing to establish the Oneness of Allah developed sacred Geometry to a fine art. These patterns engendered order and harmony in the viewer and a sense of the Infinite.

Then
in God's providence came Benoit M. Mandelbrot who followed an unorthodox path
in mathematics and discovered fractal geometry. He wrote, **"Clouds
are not spheres, mountains are not cones, coastlines are not circles, and
bark is not smooth, nor does lightening travel in a straight line." **In
other words, nature is much more complex and does not follow the abstract
forms of Euclidean geometry.

Mandelbrot developed,
with the aid of computers and complex numbers, a new geometry of nature encompassing
the fourth dimension of space and time. In essence, he demonstrated that patterns
in nature are repeating themselves at all different levels of magnitude. For
example, the tree pattern is also found in the leaf at ever diminishing scale
but each leaf is unique. There are invisible self-similar forms embedded in
the fabric of nature in motion waiting to be revealed as you can see in the
Mandelbrot Set. God is infinite, that is, has no beginning and end and this
infinity is present and reflected in the seeming countless creatures coming
into being. **This is the true Sacred Geometry of
Creation.**