Ratio metallica

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Ratio metallica (gen. Rationis metallicae) signatur ratio (cum numero n naturale). n-ima ratio metallica definitur major radix aequationis x2 - nx - 1 = 0 quadraticae. Cifra est una at prima appellatur ratio aurea, secunda ratio argentea, tertia ratio aerea.

Ratio metallica n-ima
0 (0+√4)/2 1 1.0000000000
1 (1+√5)/2 (1+√5)/2 1.6180339887...
2 (2+√8)/2 1+√2 2.4142135623...
3 (3+√13)/2 (3+√13)/2 3.3027756377...
4 (4+√20)/2 2+√5 4.2360679774...
5 (5+√29)/2 (5+√29)/2 5.1925824035...
6 (6+√40)/2 3+√10 6.1622776601...
7 (7+√53)/2 (7+√53)/2 7.1400549446...
8 (8+√68)/2 4+√17 8.1231056256...
9 (9+√85)/2 (9+√85)/2 9.1097722286...
... ...
n

Bibliographia[recensere | fontem recensere]

  • Stakhov, Alekseĭ Petrovich (2009). The Mathematics of Harmony: From Euclid to Contemporary Mathematics and Computer Science, p. 228, 231. World Scientific. ISBN 9789812775832.