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.

8. The Human Pattern