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'''Ratio metallica''' (gen. Rationis metallicae) signatur ratio <math>1:\frac{n+\sqrt{n^2+4}}{2}</math> (cum numero ''n'' naturale). ''n''-ima ratio metallica definitur major radix [[Aequatio quadratica|aequationis]] ''x''<sup>2</sup> - ''nx'' - 1 = 0 [[Aequatio quadratica|quadraticae]]. Cifra est una at prima appellatur [[ratio aurea]], secunda [[ratio argentea]], tertia [[ratio aerea]].

{| class="wikitable" style="float:right"
|+ 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...
|-
! ...
| colspan="3" style="text-align:center" | ...
|-
! ''n''
| colspan="3" style="text-align:center" | <math>(n+\sqrt{n^2+4})/2</math>
|}

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

[[Categoria:Metalla]]
[[Categoria:Notiones mathematicae]]