スギモト タケシ   Sugimoto Takeshi
  杉本 剛
   所属   神奈川大学  工学部 情報システム創成学科
    神奈川大学大学院  工学研究科 工学専攻(情報システム創成領域)
   職種   教授
言語種別 英語
発行・発表の年月 2020/04
形態種別 学術雑誌
査読 査読あり
標題 The Kepler Triangle and Its Kin
執筆形態 単著
掲載誌名 Forma
掲載区分国内
出版社・発行元 Soc. Sci. Form
巻・号・頁 35(1),pp.1-2
概要 The Kepler triangle, also known as the golden right triangle, is the right triangle with its sides of ratios '1 : phi^1/2 : phi,' where phi denotes the golden ratio. Also known are the silver right triangle and the square-root-three phi right triangle. This study introduces the generalised golden right triangle, which have sides of lengths closely related to phi and the Fibonacci numbers, Fn: '(Fn-2)^1/2 : phi^n/2 : (Fn)1/2 phi' for any natural number n. This formalism covers all the known phi-related right triangle, i.e., the Kepler triangle and its kin. As n tends to infinity, the ratios of the sides goes to 'phi^-1 : 5^1/4 : phi.' Our model plays an important role in the classroom to study the golden ratio, the Fibonacci numbers and the Pythagorean theorem.