1. Symmetry and Golden Ratio in the Analysis of Regular Pentagon
- Author
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Sparavigna, Amelia Carolina, Baldi, Mauro Maria, Politecnico di Torino = Polytechnic of Turin (Polito), and Sparavigna, Amelia Carolina
- Subjects
Symmetry ,Golden Ratio ,Mathematics::History and Overview ,Geometry ,Mathematics Education ,[MATH] Mathematics [math] ,[MATH]Mathematics [math] ,Mathematics - Abstract
Regular pentagon is a geometric figure which had a relevant symbolic meaning in Pythagorean and Platonic philosophies and a subsequent important role in the Western thought, appearing also in arts and architecture. A property of the pentagon, which was probably found by Pythagoreans, is that the ratio between diagonal and side is the golden ratio. Here, we will study some links between regular pentagon and golden ratio. We will focus first on the group of five-fold rotation symmetry, to find the position of the vertices of this geometric figure in the complex plane; then, we will give an analytic method to solve the same problem in the Cartesian plane. In the analytic approach, we find the golden ratio without any specific geometric consideration. This study can be interesting also for a general education in mathematics, because it can convey and link several concepts, requiring only a general pre-college education.
- Published
- 2016