Symmetry and the Golden Ratio in the Analysis of a Regular Pentagon

Autor/inn/en	Sparavigna, Amelia Carolina; Baldi, Mauro Maria
Titel	Symmetry and the Golden Ratio in the Analysis of a Regular Pentagon
Quelle	In: International Journal of Mathematical Education in Science and Technology, 48 (2017) 2, S.306-316 (11 Seiten)Infoseite zur Zeitschrift PDF als Volltext Verfügbarkeit
Zusatzinformation	ORCID (Sparavigna, Amelia Carolina) ORCID (Baldi, Mauro Maria)
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	0020-739X
DOI	10.1080/0020739X.2016.1233587
Schlagwörter	Geometric Concepts; Geometry; Mathematical Concepts; Problem Solving; Comparative Analysis; Numbers; Methods + Suchen Sie Ihr Suchwort? Elementare Geometrie; Geometrie; Problemlösen; Zahlenraum; Method; Methode
Abstract	The regular pentagon had a symbolic meaning in the Pythagorean and Platonic philosophies and a subsequent important role in Western thought, appearing also in arts and architecture. A property of regular pentagons, which was probably discovered by the Pythagoreans, is that the ratio between the diagonal and the side of these pentagons is equal to the golden ratio. Here, we will study some relations existing between a regular pentagon and this ratio. First, we will focus on the group of fivefold rotational symmetry, to find the position in the complex plane of the vertices of this geometric figure. Then, we will propose an analytic method to solve the same problem based on the Cartesian coordinates, a method where we find the golden ratio without any specific geometric consideration. This study shows a comparison of the use of complex numbers, symmetries and analytic methods, applied to a subject which can be interesting for general education in mathematics. In fact, the proposed approach can convey and link several concepts, requiring only a general pre-college education, showing at the same time the richness that mathematics can offer in solving geometric problems. (As Provided).
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Erfasst von	ERIC (Education Resources Information Center), Washington, DC
Update	2020/1/01