Golden Ratio | Examples, Definition, & Facts - Encyclopedia Britannica

Trang chủ » Phi 1 618 » Golden Ratio | Examples, Definition, & Facts - Encyclopedia Britannica

Có thể bạn quan tâm

Mathematics

The golden ratio occurs in many mathematical contexts. It can be constructed using classical geometric methods—equivalent to straightedge and compass constructions—that go back to Euclid. For example, it can be shown in dividing a line or in forming a golden rectangle.

The golden ratio is closely connected with the Fibonacci sequence—1, 1, 2, 3, 5, 8, 13, …—where each number is the sum of the two before it. As the sequence grows, the ratio of one number to the previous one gets closer and closer to ϕ. Thus ϕ is the limit of these ratios. The golden ratio can also be expressed as an infinite continued fraction: ϕ = 1 + 1 1 + 1 1 + 1 1 + 1 1 + 1 1 + . . . . ​ .

In modern mathematics the golden ratio occurs in the description of fractals, figures that exhibit self-similarity and play an important role in the study of chaos and dynamical systems.

Financial Markets

Price chart with Fibonacci levels shown.
Fibonacci retracements and extensionsRetracement and extension: Retracement numbers are set at key levels starting from the high price of the sample stock. If the stock were to fall beyond the low price of the current move (100 percent retracement), Fibonacci traders would begin looking at Fibonacci extensions at the 127.2 percent and 138.2 percent levels, for example.(more)
Some traders use ratios derived from the Fibonacci sequence—including 61.8 percent, the reciprocal of the golden ratio—as tools in financial technical analysis. Known as Fibonacci retracements and extensions, these methods mark percentage levels on price charts to suggest where prices might slow down, change direction, or continue moving.

Từ khóa » Phi 1 618