From regular pentagons to the icosahedron via the golden ratio - part I

Jagadeeshan, Shashidhar (2019) From regular pentagons to the icosahedron via the golden ratio - part I. At Right Angles (4). pp. 5-9. ISSN 2582-1873

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Abstract

This series of articles will explore an amazing connection between three different objects in mathematics: the regular pentagon, the Golden Ratio and the icosahedron. Obviously, if the Golden Ratio is involved then the Fibonacci sequence can’t be far behind and, if the icosahedron is, so is its dual the dodecahedron! In the first of these articles we will begin with the question of how to construct regular polygons, and restrict our attention to the regular pentagon and some of its properties. The regular pentagon serves as a doorway to a veritable treasure house of interconnected mathematical ideas and it never fails to astonish me. At the outset I would like to acknowledge that almost all the ideas discussed here can be found in [3]. In this series of articles we expand on some of the ideas and take a few digressions along the way.

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Articles in APF Magazines

Authors:

Jagadeeshan, Shashidhar

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