Fibonacci Sequence: From Rabbits to Stock Charts

If you have ever stared at a number on a form and wondered where it came from, you are not alone. 1, 1, 2, 3, 5, 8, 13... A simple add-the-last-two rule that appears in flowers, hurricanes and trading charts.

The rule

F(n) = F(n−1) + F(n−2). Start with 0, 1.

The golden ratio link

Ratio of consecutive terms approaches φ = 1.618... as n grows.

Where it really appears

Sunflower seed spirals, pinecone scales, branching patterns. Less often where pop-sci claims it does.

Pro tips

• Fibonacci retracement levels in trading are mostly self-fulfilling; treat with caution.
• Binet's formula gives F(n) directly without iteration — uses φ.

Frequently asked questions

Is the golden ratio everywhere? Less than internet posts claim. Confirmation bias is strong.

What about the spiral? A logarithmic spiral approximates the Fibonacci squares — same family, not identical.

Run your own numbers before you trust a rule of thumb. Two minutes saves a lot of regret.