Engel Expansions, Continued Fractions, and Fibonacci
Kraaikamp and Wu (2004) observe that an Engel expansion can also be written as an ascending variant of a continued fraction:
They claim that ascending continued fractions such as this have been studied as early as Fibonacci's Liber Abaci (1202). This claim appears to refer to Fibonacci's compound fraction notation in which a sequence of numerators and denominators sharing the same fraction bar represents an ascending continued fraction:
If such a notation has all numerators 0 or 1, as occurs in several instances in Liber Abaci, the result is an Engel expansion. However, Engel expansion as a general technique does not seem to be described by Fibonacci.
Read more about this topic: Engel Expansion
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