Fibonacci's Composed Fractions

3 days ago

Fibonacci introduced composed fractions in Liber Abaci to represent mixed radix quantities, using a notation with numerators and denominators in little-endian order, which persisted for around 300 years before decimal fractions became widespread.
The composed fraction notation mirrored real-world mixed radix systems like currency (e.g., librae, solidi, denarii), weights, and time, offering explicit representations of proportions between units.
Arithmetic operations on composed fractions involved algorithms for multiplication, addition, subtraction, and division, often converting to singular fractions for calculations, as inferred from Fibonacci's examples and implemented here in TypeScript.
Adoption of Hindu-Arabic numerals faced resistance due to concerns about fraud and competition with abacus-based calculations, but gradually replaced Roman numerals in practical use by the late 15th century.
The Fibonacci sequence appears in Liber Abaci as a rabbit breeding problem but was not emphasized by Fibonacci; its naming is attributed to 19th-century mathematician Edouard Lucas, and it was not a central focus of the work.

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