Analysis of Spiral Curves in Traditional Cultures

Ryuji Takaki¹ and Nobutaka Ueda²

¹Kobe Design University, Nishi-ku, Kobe, Hyogo 651-2196, Japan
²Hiroshima-Gakuin, Nishi-ku, Hiroshima, Hiroshima 733-0875, Japan
*E-mail address: takaki-r@kobe-du.ac.jp
*E-mail address: ark-ueda@ms8.megaegg.ne.jp

(Received November 3, 2006; Accepted August 10, 2007)

Keywords: Spiral, Curvature, Logarithmic Spiral, Archimedean Spiral, Vortex

Abstract. A method is proposed to characterize and classify shapes of plane spirals, and it is applied to some spiral patterns from historical monuments and vortices observed in an experiment. The method is based on a relation between the length variable along a curve and the radius of its local curvature. Examples treated in this paper seem to be classified into four types, i.e. those of the Archimedean spiral, the logarithmic spiral, the elliptic vortex and the hyperbolic spiral.