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Elliott's study of the mathematical properties of waves and patterns led him to conclude that the Fibonacci summation series is the basis of the wave principle. Numbers from the Fibonacci sequence repeatedly occur in Elliott wave structures, including motive waves (1, 3, 5), a single full cycle (5 up, 3 down = 8 waves), and the completed motive (89 waves) and corrective (55 waves) patterns. Elliott developed his model before he realized that it bears resemblance to the Fibonacci sequence.
The Fibonacci sequence is also related to the ratio known as the Golden Mean (ca 1.618). Technical Analysts commonly use this ratio to establish support and resistance levels for market waves, specifically the price points which help define the parameters of a trend.
By definition, the first two Fibonacci numbers are 0 and 1, and each remaining number is the sum of the previous two. Some sources omit the initial 0, instead beginning the sequence with two 1s. The Fibonacci sequence is used in many ways including Fibonacci Retracement Levels, Fibonacci Arc, and Fibonacci Fan lines. Key Fibonacci ratios include 23.6%, 38.2%, 50%, 61.8% and 100%.