如何计算Fibonacci Sequence
learn.whatIsHeading
The Fibonacci sequence starts with 0 and 1, and each subsequent number is the sum of the two preceding ones. It appears throughout nature — in flower petals, spiral shells, and the golden ratio.
公式
F(n) = F(n−1) + F(n−2) with F(0)=0, F(1)=1; Binet: F(n) = (φⁿ − ψⁿ)/√5 where φ=(1+√5)/2
- n
- term number in sequence
- F(n)
- the nth Fibonacci number
- φ
- golden ratio — approximately 1.618
分步指南
- 1F(0)=0, F(1)=1
- 2F(n) = F(n−1) + F(n−2)
- 3Ratio of consecutive terms approaches φ = 1.618... (golden ratio)
- 4Formula: F(n) = (φⁿ − ψⁿ)/√5 (Binet's formula)
例题解析
输入
First 10 terms
结果
0, 1, 1, 2, 3, 5, 8, 13, 21, 34
输入
F(20)
结果
6765
常见问题
Where does the Fibonacci sequence appear in nature?
Flower petals, spiral seed arrangements (sunflower), shell spirals, tree branches, and spiral galaxies all exhibit Fibonacci patterns.
What is the golden ratio and its relationship to Fibonacci?
The ratio of consecutive Fibonacci numbers approaches φ ≈ 1.618 (golden ratio). It appears in art, architecture, and nature.
Is there a closed-form formula for Fibonacci numbers?
Yes, Binet's formula: F(n) = (φⁿ − (−φ)⁻ⁿ)/√5, giving exact results for any n.
准备好计算了吗？尝试免费的 Fibonacci Sequence 计算器
自己尝试一下 →