The Fibonacci sequence, named for its discoverer Leonardo Fibonacci, forms the basis for Elliott Wave theory used in trading financial markets. Out of Elliott Wave theory comes Fibonacci retracements and Fibonacci arcs discussed below. The Fibonacci sequence is 1,1,2,3,5,8,13,21,,34,55,89… to infinity. The sum of two consecutive numbers equals the next number. The ratio of any number to its next highest number approaches .618. The ratio of alternating numbers approaches .382. Also, 1 – .618 = .382. The midpoint of .382 and .618 is .50. This is why .382, .50, and .618 are used.
Following an uptrend, Fibonacci arcs use a line that connects the low and high of the trend – but the line is drawn from high to low (not low to high as in retracements). Three curves that intersect the trendline (drawn from high to low) at the retracement levels of 38.2%, 50% and 61.8% are the Fibonacci arcs. The arcs are also estimations for support.