Liber quadratorum

work by Fibonacci

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June 30, 2026

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The Liber quadratorum, written by Fibonacci in 1225, is considered his masterpiece and a significant contribution to number theory. This work is dedicated to Holy Roman Emperor Frederick II and focuses entirely on Diophantine equations of the second degree, which involve squares.1

Fibonacci, an Italian mathematician, introduced Hindu-Arabic numerals to Europe through his earlier work, the Liber abaci. The Liber quadratorum delves into complex problems, many of which Fibonacci developed himself, using his own proofs to find general solutions. It explores concepts like congruent numbers and the properties of square numbers, making it a foundational text between the time of Diophantus and later mathematicians like Pierre de Fermat.12

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Fibonacci
Contributions to number theory
He dedicated his Liber quadratorum (1225; “Book of Square Numbers”) to Frederick. Devoted entirely to Diophantine equations of the second degree (i.e., containing squares), the Liber quadratorum is considered Fibonacci’s masterpiece. It is a systematically arranged collection of theorems, many invented by the author, who used his own…
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He dedicated his Liber quadratorum (1225; “Book of Square Numbers”) to Frederick. Devoted entirely to Diophantine equations of the second degree (i.e., containing squares), the Liber quadratorum is considered Fibonacci’s masterpiece. It is a systematically arranged collection of theorems, many invented by the author, who used his own…
Read More