Letter
The Metallic Right-Triangles
2020 年 35 巻 1 号 p. 33-35
詳細
2020 年 35 巻 1 号 p. 33-35
The Kepler triangle and its kin are systematically described by the unique formalism (Sugimoto, 2020). The present study affords the super-set of the formalism covering the above-mentioned triangles and other new triangles based on the metallic means and the generalised Fibonacci sequences adjoined to those means. The super-set is given by (the short leg, the long leg, the hypotenuse) = (Gn - 21/2(m), m1/2Φn/2(m), Gn1/2(m)Φ(m)), where Gn(m) and Φ(m) designate the nth generalised Fibonacci sequence and the metal mean of the metal number 'm', respectively. The initial members of the golden, silver and bronze right-triangles are presented.
