high School⏱ 4 min

Fibonacci and Golden Ratio

Fibonacci sequence and φ = 1.618...

○Not Started
φ = 1.6180F2/F1F3/F2F4/F3F5/F4F6/F5F7/F6F8/F7F9/F8F10/F9F11/F10
n = 10
11235813213455
φ=1+52≈1.618034\varphi = \frac{1+\sqrt{5}}{2} \approx 1.618034
Fn=Fn−1+Fn−2,lim⁡n o∞\ racFn+1Fn=\ arphiF_n = F_{n-1} + F_{n-2}, \quad \lim_{n\ o\infty}\ rac{F_{n+1}}{F_n} = \ arphi

The ratio of consecutive Fibonacci numbers converges to the golden ratio φ≈1.618. The golden ratio appears in shell spirals, leaf arrangements, and Greek art.