- Fibonacci numbers are based upon the Fibonacci sequence discovered by Leonardo de Fibonacci de Pisa (b.1170-d.1240). His most famous work, the Liber Abaci (Book of the Abacus), was one of the earliest Latin accounts of the Hindu-Arabic number system. In this work, he developed the Fibonacci number sequence, which is historically the earliest recursive series known to date.
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- The sequence of the Fibonacci numbers is as follows:
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0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89,144, 233, 377 ...... up to infinity |
- Starting with zero and adding one begins the series. The calculation takes the sum of the two numbers and adds it to the second number in the addition. The sequence requires a minimum of eight calculations.
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| 0+1=1)...(1=1=2)...(1+2=3)...(2+3=5)...(3+5=8)... |
| (5+8=13).(8+13=21).(13+21=34) |
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- After the eighth sequence of calculations, there are constant relationships that can be derived from the series. For example, if you divide the former number by the latter, it yields .618.
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34/55 = 0.618181 ~ .618 |
55/89 = 0.618181 ~ 0.618 |
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And, if you divide the latter number by the former, it yields 1.618. |
144/89 = 1.617977 ~ 1.618 |
233/144 = 1.618055 ~ 1.618 |
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- The 0.618 and the 1.618 are two of the four Fibonacci-related numbers that are essential to remember. The other two numbers that are derived from the series, the 0.786 and 1.27, are the square root of the 0.618 and the 1.618, respectively.
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- Fibonacci's additive series is based upon the equation:
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Phi + 1 = Phi squared |
Base = 2.00 |
Half Base = 1.00 |
Height = .618 |
Slope = 1.618 |
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