A study of the concept and background of golden ratios in written sources

One of the most popular theories in aesthetics is the golden ratio theory in either theoretical or practical geometry. The golden ratio, the golden proportion which is called the extreme and mean ratio by Euclid, goes by other several various names over history. The golden ratio is well known in the artistic composition and architecture of buildings, statues, and sculptures, as still used today. There are a lot of myths about the golden ratio; Some attribute it to sacred numbers among the Pythagoreans, and some figure out an excellent placement in geometry and architecture for it, mentioning that particular ancient temples and structures were built on the basis of these numbers. The present study aims to examine the written background of the golden ratio through the written heritage of the Islamic period including accessible manuscripts and treatises as primary sources, besides the articles and reports on ancient Greek works, mainly in Greek, Latin, or other languages as secondary sources. In this article, we first explain the background of this issue in the case of ancient Greece, and then we review some textbooks of the Islamic period on the subject of arithmetic or geometry that addressed this theory directly or indirectly. Since this article relies on the Islamic period in medieval and early modern times, only the treatises and some of the efforts spared including the existing written works and the visual arts from the Islamic period to the present century are introduced. Moreover, the special shapes famed as sacred or golden due to their specific geometric properties are described