Original scientific paper

Non-standard Visualizations of Fibonacci Numbers and the Golden Mean

Gunter Weiss ; University of Technology Vienna, Vienna, Austria
Sybille Mick ; University of Technology Graz, Graz, Austria

Abstract

Fibonacci numbers and the Golden Mean are numbers and thus 0-dimensional objects. Usually, they are visualized in the Euclidean plane using squares and rectangles in a spiral arrangement. The Golden Mean, as a ratio, is an affine geometric concept and therefore Euclidean visualizations are not mandatory. There are attempts to visualize the Fibonacci number sequence and Golden Spirals in higher
dimensions [11], in Minkowski planes [12], [4] and in hyperbolic planes (again [4]). The latter has to replace the not existing squares by sequences of touching circles. This article aims at visualizations in all Cayley-Klein planes and makes use of three different visualization ideas: nested sets of squares, sets of touching circles and sets of triangles that are related to Euclidean right angled triangles.

Keywords

Cayley-Klein geometries; Fibonacci numbers; Golden Mean

Hrčak ID:

133845

URI

https://hrcak.srce.hr/133845

Publication date:

30.1.2015.

Article data in other languages: croatian

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