A deduction of the Golden Spiral equation via powers of the Golden Ratio ?

• Autores: Maurício Zahn
• Localización: International journal of mathematical education in science and technology, ISSN 0020-739X, Vol. 48, Nº. 6, 2017, págs. 963-971
• Idioma: inglés
• DOI: 10.1080/0020739x.2016.1172741
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• Resumen

  • This paper presents an interesting deduction of the Golden Spiral equation in a suitable polar coordinate system. For this purpose, the concepts of Golden Ratio and Golden Rectangle, and a significant result for the calculation of powers of the Golden Ratio ? using terms of the Fibonacci sequence are mentioned. Finally, various geometrical considerations that help us deduce the sought equation are presented.