Recently, while studying technical analysis tools, I discovered that the ancient mathematical concept of the Fibonacci sequence is truly fascinating in trading.

This sequence originated in ancient India, but it was the Italian mathematician Leonardo of Pisa, known as Fibonacci, who popularized it in Europe in the 12th century. He published this simple yet elegant series under a pen name: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144… Each term is the sum of the previous two. It looks simple, but it hides the most harmonious ratio in nature—the golden ratio 1.618.

This number was discovered as early as Euclidean times and used to construct regular pentagons. Interestingly, the golden ratio appears everywhere: snail shells’ spirals, the spacing between leaves, galaxy shapes, and even human body proportions all follow this mysterious number. A Belarusian scientist, Edward Sorocho, studied this phenomenon deeply and found that all things growing and competing for space in nature are endowed with the golden ratio.

How is it used in trading? Fibonacci levels are derived from this golden ratio as key levels. The main retracement levels are 0.382, 0.5, 0.618; intermediate levels are 0.236 and 0.764; extension levels are 1, 1.382, 1.618. The method is straightforward: identify a clear trend, find the high and low points, and draw the grid.

In an uptrend, when the price pulls back, these Fibonacci levels can help you find buy opportunities. In a downtrend, the opposite applies; strong rebounds often occur at 0.5 or 0.618 levels. Why are they effective? Because most traders are watching the same levels, creating self-fulfilling prophecies. Plus, the fact that everything in our world tends toward the golden ratio 0.618 makes Fibonacci a quite “natural” tool.

But to be clear, Fibonacci is not a holy grail. It’s just an auxiliary tool to help determine price ranges and support/resistance levels. The best approach is to combine it with pattern analysis and correctly identify the trend direction.

If you want to learn more, I recommend a few books. Frost and Prechter’s “Elliott Wave Principle” covers classic wave theory fundamentals. Mandelbrot and Hudson’s “(Un)conventional Markets” interprets market rhythms from a modern fractal perspective. Williams’ “Trading Chaos” and Fisher’s “Fibonacci and Trading Strategies” offer practical methods for wave counting and Fibonacci levels.

Overall, the Fibonacci sequence and golden ratio are powerful tools for understanding market structure and are worth studying.