文章基本信息

标题：Non-standard Visualizations of Fibonacci Numbers and the Golden Mean
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作者：Weiss, Gunter ; Mick, Sybille
期刊名称：KoG
印刷版ISSN：1331-1611
电子版ISSN：1846-4068
出版年度：2015
卷号：18
期号：18
页码：36-44
语种：English
出版社：Croatian Society for Geometry and Graphics
摘要：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.
关键词：Cayley-Klein geometries; Fibonacci numbers; Golden Mean