Grids

The golden ratio is the relationship that the sum of two quantities is to the larger quantity as the larger is to the smaller. 1.618033989 is the approximate number of the golden ratio.

Many artists and architectures have proportioned their works to approximate the golden ratio,especially in the form of the golden rectangle which is when the ratio of the longer side to the shorter is the golden ratio. Its used because it is believed that the proportion is pleasing to the eye. Many mathematicians have studied the golden ratio because of its unique and interesting properties which can be found all around us in nature, even in ourselves.

One relationship of the golden section to the design of the human body is that there are:
- 5 appendages to the torso, in the arms, leg and head.
- 5 appendages on each of these, in the fingers and toes and 5 openings on the face.
- 5 senses in sight, sound, touch, taste and smell.

Elam, Kimberly, 2001, Geometry of Design: Studies in Proportion and Composition, Princeton Architectural Press, New York

The golden section in turn, is also based on 5, number 1.618033989, is found by using 5's, as follows:

I looked at Hokusai Katsushika's 'The Great Wave Off Kanagawa' and the concept of the golden section.
The Great Wave Off Kanagawa,
Hokusai Katsushika, 1780-1849
http://www.liquidknowledge.info/

Hokusai used compass and ruler to create this well known woodcut, as well as the concept of the golden sector also known as the most proportional and beautiful section.

The Great Wave Off Kanagawa, Hokusai Katsushika, 1780-1849 http://www.liquidknowledge.info/ (edited)

You can see in this image with the use of the grids Hokusai adds depth to the image and makes aspects of the wave more prominent then others.

Among the various cultures from the Roman to the Egyptian traditions; the harmonic proportions, human proportions, astronomical proportions , and various aspects of what was considered sacred cometary ( such as pentagram, golden ratio, and small whole-number ratios) were all applied as part design. So no one culture alone used grids in their designs, it was widespread because perhaps it is the way human beings see things as rather then just the different cultures, because to the human eye the neat order provided by a grid is is more beautiful to the eye.