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arXiv · 2502.05607

On the examples of Egyptian fractions in Liber Abaci

Trond Steihaug·Milo Gardner
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Abstract

The focus of this note is to formulate the algorithms and give the examples used by Fibonacci in Liber Abaci to expand any fraction into a sum of unit fractions. The description in Liber Abaci is all verbal and the examples are numbers which may lead to different algorithmic descriptions with the same input and results. An additional complication is that the manuscripts that exist are copies of an older manuscript and in the process new errors are introduced. Additional errors may also be introduced in the transcript and the translation. Fibonacci introduces seven categories each with several numerical examples. We give a precise description of the computational procedure using standard mathematical notation.

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Trond Steihaug, Milo Gardner. 2025-02-08. On the examples of Egyptian fractions in Liber Abaci. https://arxiv.org/abs/2502.05607

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