This article was automatically translated from the original Turkish version.
The golden ratio (approximately 1.618) is a mathematical proportion regarded as a symbol of aesthetic harmony in nature and art. This ratio has been observed in numerous structures, from architecture and painting to living organisms in nature and the human body. Interestingly, traces of the golden ratio can also be found in the geometric structure of the Turkish flag.
The golden ratio establishes a relationship between the parts of a whole such that the ratio of the smaller part to the larger part is equal to the ratio of the larger part to the whole. Mathematically, this ratio is expressed as approximately 1.6180339887…. Used by artists and architects since antiquity, this proportion has served as a vital tool for creating compositions that are visually pleasing.
The design of the Turkish flag is based on precise measurements and proportions defined in the Turkish Flag Law of 1983. The ratio between the flag’s width and length, as well as the placement and dimensions of the crescent and star, are grounded in mathematical principles. These measurements not only ensure visual balance but also create conditions conducive to the emergence of aesthetic ratios such as the golden ratio.
An important study on this subject was published by Veli Akarsu in 2009. In Akarsu’s study, the flag was modeled with a width of 70.00 meters and a length of 105.00 meters; the positions and dimensions of the crescent and star were analyzed geometrically. Some of the ratios obtained from the research are as follows:
The ratios obtained for the star are very close to the golden ratio. This indicates that the design of the Turkish flag reflects not only symbolic intent but also aesthetic and mathematical consideration. These ratios can be interpreted as deliberately chosen to achieve visual harmony rather than occurring by chance.
The fact that the Turkish flag is designed with proportions close to the golden ratio demonstrates that it is not merely a national symbol but also an aesthetic work of art. This design, conceived within a framework of mathematical harmony, is compelling both historically and artistically.
Akarsu, Veli. "Türk Bayrağı ve Altın Oran İlişkisi." *Erciyes Üniversitesi Fen Bilimleri Enstitüsü Dergisi* 25, no. 1 (2009): 437-448. https://dergipark.org.tr/tr/download/article-file/236312"Türk Bayrağı ve Matematik." *Matematik Kafe*. Accessed April 25, 2025. https://www.matematikkafe.com/?pnum=113&st=T%C3%BCrk+Bayra%C4%9F%C4%B1+ve+Matematik
What Is the Golden Ratio?
The Geometric Structure of the Turkish Flag and the Golden Ratio
Scientific Analysis and Findings
Conclusion: The Flag Beyond a Symbol
