  The Fibonacci numbers are familiar to all of us. They appear unexpectedly
often in mathematics, so much there is an entire journal and a sequence of
conferences dedicated to their study. However, there is also another sequence
of numbers associated with Fibonacci. In The On-Line Encyclopedia of Integer
Sequences, a sequence of numbers which is an approximation to the real root of
the cubic polynomial. Fibonacci gave the first few numbers in the sequence in
the manuscript Flos from around 1215. Fibonacci stated an error in the last
number and based on this error we try, in this paper to reconstruct the method
used by Fibonacci. Fibonacci gave no indication on how he determined the
numbers and the problem of identifying possible methods was raised already the
year after the first transcribed version of the manuscript was published in
1854. There are three possible methods available to Fibonacci to solve the
cubic equation; two of the methods have been shown to give Fibonacci's result.
In this paper we show that also the third method gives the same result, and we
argue that this is the most likely method.
