We owe a debt of gratitude to the Italian mathematician Leonardo Pisano (1170-1250) Best known by his nickname, Fibonacci (he also went by "Bigollo," which may have meant "wandering good-fornothing"), he wrote the famous book, Liber abaci(1202). In it, he introduced to Europe the HinduArabic place-valued decimal system and Arabic. He also discussed mathematical problems that resulted in what we now call the Fibonacci summation sequence and the ratios derived from it. Here's one of the most important problems Pisano posed, and the result. Although the question sounds lighthearted, the answer has produced serious resolutions. "If one places a rabbit couple in an enclosed place, how many rabbits would one obtain after a certain time assuming they reproduce once per month, and that those born can reproduce at the age of a month?" The following infinite progression (now called Fibonacci numbers), results: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, and 144, after each month. You'll notice that Fibonacci numbers run in a sequence. Each successive number equals the sum of the two previous numbers: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, and so forth. The interrelationships between these numbers are intriguing. First, starting with the number five, any of these numbers equals approximately 1.618 times the preceding number. Second, any number equals approximately 0.618 times the subsequent number. Cool, huh? It's remarkable that so many objects formed in Fibonacci proportions occur throughout nature, including butterflies, sea shells, and spiral galaxies. The pentagram, Christian crucifix, and Pythagorean triangles also contain these proportions, as well as the art pieces of Leonardo da Vinci and Michelangelo. The four popular Fibonacci studies used by traders include arcs, fans, retracements, and time zones. Most charting software programs include Fibonacci retracements. Some of the more advanced programs utilize arcs, fans, and time zones. For now, we'll look at retracements.
What you need to know about Fibonacci retracements: Slocks.·often
Fibonacci ratios are gauged at 38.2 percent, 50.0 percent, and 61.8 percent, and are considered a leading indicator (predicting possible future price action).
Your job is to draw an uptrend (or downtrend) line, connecting a major peak and trough. Then, activate your charting software's Fibonacci retracement option. Start at the bottom of the trendline and drag your cursor to the top of the trend. (Fancy charting programs will include a 23.6 percent line.) You'll see five horizontal lines, representing 0.0 percent, then 38.2, 50, 61.8, and 100 percent of the entire move, or trend.
These levels act as support and resistance areas.
Since so many traders use Fibonacci retracement levels for guidance, some support/resistance action may be a self fulfilling prophecy. Still, it's positively uncanny how many times a stock in an uptrend will pull back to a Fibonacci level, then bounce. Or, a stock in a downtrend will rebound to a Fibonacci level, and then begin its fall anew. Some traders use "Fib ratios" by placing their stop-loss points a quarter-point below a stock's 61.8 percent retracement level from the previous high. Remember, though, that no indicator in this world predicts future price movement with absolute accuracy. Just because your stock happens to be heading for a Fibonacci retracement level is no guarantee it's going to halt there and bounce. It could just as easily slice right through it. Indicators-no matter what flavor-are just that. They indicate. Please don't use them as an excuse to stay in a losing position!

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