Elam, Kimberly. Geometry of Design: Studies in Proportion and Composition. New York: Princeton Architectural, 2001. Print.
“German psychologist, Gustav Fechner…. investigated the human response to the special aesthetic qualities of the golden section rectangle… Fechner limited his experiment to the man-made world and began by taking the measurements of thousand of rectangular objects such as books, boxes, buildings, matchbooks, newspapers, etc. He found that the average ratio was close to a ration known as the golden ration, 1:1.618, and that the majority of people prefer a rectangle whose proportions are close to the golden section.” p. 6-7.
Most preferred rectangle 5:8 according to Fechner (1876) and Lalo (1908).
Read The Curves of Life by Cook, Theodore Andrea, Sir, (1867-1928)
“there is an attempt in biological growth pattern proportion to approach but never reach golden spiral proportions.” p. 9
“the ration of any two lines within a star pentagram is the golden section proportion of 1:1.618.” p. 9
“The numbers 8 and 13 as found in the pine cone spiral and 21 and 34 as found in the sunflower spiral and 21 and 34 as found in the sunflower spiral… adjacent pairs in the mathematical sequence called the Fibonacci sequence.” p. 10.
“Vitruvius advised that the architecture of temples should be based on the likeness of the perfectly proportioned human body where a harmony exists among all parts.” p. 12
See Vitruvius (born c. 80–70 BC, died after c. 15 BC)
A 1684 depiction of Vitruvius (right) presenting De Architectura to Augustus. Sebastian Le Clerc. Via wikimedia.
See statue Doryphoros (Δορυφόρος)
See statue Artemision Bronze
See Leornardo Da Vinci’s Human Figure in a Circle and Albrecht Dürer‘s Man Inscribed in a Circle
See facial proportions p. 18-19
“The Parthenon in Athens is an example of the Greek system of proportioning. In a simple analysis the façade of the parthenon is embraced by a subdivided golden rectangles.” p. 20
On the Cathedral of Notre Dame “The rectangle around the cathedral façade is in golden section proportion.” p. 21
“The clerestory window is in proportion of 1:4 to the major circle of the façade.” p. 21
“Even the earliest and most primitive architect developed the use of a regulating unit of measure such as a hand, or foot or forearm in order to systemize and bring order to the task.” p. 22-23.
Gnomon (figure)
Gold, silver, and bronze rectangles arranged vertically so that they are all the same width. Squares marked with dotted lines and arrows. Via Wikimedia.