Recently, while studying technical analysis, I was reminded of that mysterious yet ubiquitous concept—the Fibonacci sequence and the golden ratio.

It's quite interesting; the origin of this set of ideas can be traced back to the 12th-century Italian mathematician Leonardo, who had a pen name called Fibonacci. He discovered a simple numerical sequence: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144… where each number is the sum of the previous two. It seems nothing special, but this sequence hides an astonishing secret.

When you divide adjacent numbers in this sequence, the ratio approaches 1.618 more and more closely. This is the legendary golden ratio. As early as 300 BC, Euclid discovered this ratio in "Elements," using it to construct a regular pentagon.

Even more amazing is that the golden ratio appears everywhere. The spiral of a snail shell, the spacing of leaves on a stem, the shape of galaxies, and even the proportions of different parts of the human body all follow this 0.618 rule. Belarusian scientist Edward Soroko studied the forms of the golden division in nature and found that everything growing in space, trying to carve out a place, is endowed with this ratio. One of the most interesting forms is the spiral twist.

So, what does this have to do with trading? This is the core logic of the Fibonacci retracement tool. Traders use this tool to find support and resistance levels. The main correction levels are three: 38.2%, 50%, and 61.8%. The intermediate levels include 23.6% and 76.4%. Extension levels include 100%, 138.2%, and 161.8%.

Using Fibonacci levels is actually simple. You just need to identify a clear trend, determine the highest and lowest points, and then draw the grid. In an uptrend, when the price pulls back, you can use Fibonacci levels to judge whether it's a buying opportunity or if you should be cautious; in a downtrend, trend confirmation usually occurs when the price retraces to 50% or 61.8%.

Why does this thing work? Because most traders are looking at the same things. They draw the grid based on the same principles, see the same patterns, and thus the market reacts at these key levels. Moreover, to some extent, the entire world tends toward this 0.618 golden ratio, so this tool indeed has a "natural" feel.

But I have to be honest—Fibonacci is not a holy grail. It’s just an auxiliary tool to help you determine the range of price movements and identify strong support and resistance levels. The best approach is to combine Fibonacci with pattern analysis, and at the same time, correctly identify the trend and truly understand the market direction.

If you want to dive deeper, you can check out A. Frost and R. Prechter’s "Elliott Wave Principle," which covers the classic wave theory fundamentals. B. Mendelbrot and R. Hudson’s "The (Un)conventional Market" discusses fractal structures and modern perspectives on price changes. B. Williams’ "Trading Chaos" explains wave counting methods in detail. R. Fisher’s "Fibonacci and the Trader" offers another angle on applying Fibonacci levels within wave counting.

In summary, Fibonacci sequences and the golden ratio are powerful tools in technical analysis, but they need to be combined with other analysis methods and solid market understanding to truly be effective.