The Golden Ladder

An alternating harmony of φ
1 = φ¹ – φ⁻¹
3 = φ² + φ⁻²
4 = φ³ – φ⁻³
7 = φ⁴ + φ⁻⁴
11 = φ⁵ – φ⁻⁵
18 = φ⁶ + φ⁻⁶
etc.

Interestingly, the Luca numbers show up in this golden ladder.

⇨ More number facts.