Golden Ratio‎: ‎The Mathematics of Beauty

Document Type : Original Scientific Paper


Faculty of Mathematical Sciences, Department of Statistics, University of Kashan, Kashan, Iran



‎Historically, mathematics and architecture have been associated with one another. Ratios are good example of this interconnections. The origin of ratios can be found in nature, which makes the nature so attractive. As an example, consider the architecture inspired by flowers which seems so harmonic to us. In the same way, the architectural plan of many well-known historical buildings such as mosques and bridges show a rhythmic balance which according to most experts the reason lies in using the ratios. The golden ratio has been used to analyze the proportions of natural objects as well as building’s harmony. In this paper, after recalling the (mathematical) definition of the golden ratio, its ability to describe the harmony in the nature are discussed. When teaching mathematics in the schools, one may refer to this interconnection to encourage students to feel better with mathematics and deepen their understanding of proportion. At the end, the golden ratio has been statistically examined using its first 100000 decimal digits to show that the golden ratio decimals can be used as a random number generator.


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