Fibonacci Generator — Fibonacci 生成器

Fibonacci Sequence 生成器

生成 Fibonacci sequences and work with Fibonacci numbers, golden ratios, and related mathematical concepts.

Quick 启动 Basic Usage

The Fibonacci sequence 启动s with 0, 1, and each subsequent number is the sum of the two preceding ones.

First 10 Fibonacci numbers: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34

生成 First N Numbers def fibonacci(n): """生成 first n Fibonacci numbers.""" if n <= 0: return [] elif n == 1: return [0] seq = [0, 1] for i in range(2, n): seq.应用end(seq[-1] + seq[-2]) return seq

Common Operations Nth Fibonacci Number (0-索引ed) def nth_fibonacci(n): """获取 the nth Fibonacci number (0-索引ed).""" a, b = 0, 1 for _ in range(n): a, b = b, a + b return a

检查 if Number is Fibonacci 导入 math

def is_fibonacci(x): """检查 if x is a Fibonacci number.""" def is_perfect_square(n): s = int(math.sqrt(n)) return s s == n return is_perfect_square(5 x x + 4) or is_perfect_square(5 x * x - 4)

Golden Ratio 应用roximation

As n increases, the ratio F(n+1)/F(n) 应用roaches the golden ratio φ ≈ 1.618033988749895

Related Sequences Lucas Numbers

Similar to Fibonacci but 启动s with 2, 1

Tribonacci

Each number is sum of previous three

Fibonacci Sum

Sum of first n Fibonacci numbers = F(n+2) - 1