The Fibonacci Sequence is a series of numbers where each number is the sum of the two preceding ones, starting with 0 and 1. It’s typically written as:
0,1,1,2,3,5,8,13,21,34,55,89,144,…
Formally:
Named after the Italian mathematician Leonardo of Pisa (aka Fibonacci), who introduced it to the West in his 1202 book Liber Abaci, it originally modeled rabbit population growth but has since been found in nature, art, and finance.
How It Works
The sequence starts with the base cases (0 and 1), then builds recursively:
- 0+1=10 + 1 = 1
0 + 1 = 1(third term), - 1+1=21 + 1 = 2
1 + 1 = 2(fourth term), - 1+2=31 + 2 = 3
1 + 2 = 3(fifth term), - 2+3=52 + 3 = 5
2 + 3 = 5(sixth term), and so on.
How to Use It
The Fibonacci Sequence has practical applications across domains, especially when paired with its ratios (e.g., 0.618, 1.618, or percentages like 23.6%, 38.2%, 61.8%).
Mathematics and Nature
- Modeling Growth: It describes recursive processes, like plant branching or bee genealogies (males have one parent, females two, mirroring the sequence).
- Golden Ratio: Used in geometry and design for aesthetically pleasing proportions (e.g., the Parthenon or a nautilus shell).
Trading and Finance
- Fibonacci Retracement: Traders use Fibonacci levels to predict support and resistance in price movements. After a significant price move (up or down):
- Key levels are calculated: 23.6%, 38.2%, 50%, 61.8%, and 100% of the move.
- Example: If a stock rises from $100 to $200, a 61.8% retracement is $161.80 ($200 – 0.618 × $100). Traders watch these levels for potential reversals.
Fibonacci Extensions: Predicts price targets beyond the initial move (e.g., 161.8% or 261.8% of the original range).
Works because markets often reflect human psychology, and these levels act as self-fulfilling prophecies where traders act.
Programming
Algorithm Practice: Coding the sequence (recursively or iteratively) tests loops and recursion. Example in Python:
Optimization: The sequence appears in dynamic programming problems or search algorithms (e.g., Fibonacci search).
Art and Design
- Proportions: Architects and artists use the Golden Ratio for balance (e.g., in the Mona Lisa’s composition or modern logos).
- Spirals: Drawing squares with Fibonacci side lengths (1, 1, 2, 3, 5, …) and connecting their corners forms a logarithmic spiral.
Why It Matters
The sequence isn’t just a math curiosity—it’s a bridge between order and chaos. In trading, it’s a tool for timing entries and exits. In nature, it explains efficient growth. In code, it’s a simple yet profound pattern. Whether you’re charting stocks or counting petals, it’s a universal thread tying numbers to reality.