the hAnDbook oF teChnICAl AnAlysIs10.1.1 the Fibonacci series
A simple mathematical expression that describes a Fibonacci series is given as
follows:
F F Fnnn+ 1 =+ − 1where Fn represents the current number, Fn−1 the previous number, and Fn+1 the
next number in the Fibonacci series. Alternatively, due to the iterative nature of
the mathematical expression, it may also be expressed as:
F F Fnnn=+−− 1 2where Fn−1 and Fn−2 represent the immediately previous two numbers of the sequence.
Regardless of the way it is mathematically expressed, every number in the
Fibonacci sequence is the sum of its last two previous whole numbers.
Therefore, starting with Fn−1 = 0 as the previous number and Fn =1 as the cur-
rent number in the series, we obtain Fn+1, the next number in the Fibonacci series,
by repeating or iterating the process for each new Fn:
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377,...where we see that: 1+ 0 = 1, 1+ 1 = 2, 2+ 1 = 3, 3+ 2 = 5, 5+ 3 = 8, and so on, ad
infinitum.
10.1.2 the French Connection: the Lucas series
A variant of this iterative series may be constructed by changing the initial two
numbers of the series, that is, by starting with Fn−1 = 2 and Fn = 1 instead of
Fn−1 = 0 and Fn−1 = 1. This new series is popularly referred to as the Lucas Series,
after Edouard Lucas, a French mathematician. Similarly, by iteration via the Fibo-
nacci sequence, we obtain:
2, 1, 3, 4, 7, 11, 18, 29, 47, 76, 123, 199, 322,...
where we see that: 2+ 1 = 3, 3+ 1 = 4, 4+ 3 = 7, 7+ 4 =11, 11+ 7 = 18, and so on, ad
infinitum.
Letting Ln be the current number in a Lucas series, the relationship between
the Lucas and Fibonacci number series is given by the mathematical relationship:
L F Fnnn=+ (^2) − 1
Let us examine this formulaic relationship a little more closely. As we have
seen, the tenth Fibonacci number in the sequence given above is 34. Hence, via this
mathematical expression, the corresponding tenth Lucas number should be L 10 =
F 10 + 2F 9 = 34 + 2(21) = 34 + 42 = 76, which turns out to be the expected answer.
As we shall see later, Fibonacci (as well as Lucas) number counts are extremely
popular technical tools commonly used to forecast potential top and bottom re-
versals in the markets, especially when they are used in conjunction with other