The Book of Squares, (Liber Quadratorum in the original Latin) is a book on algebra by Leonardo Fibonacci, published in 1225.[1] It was dedicated to Frederick II, Holy Roman Emperor.[2]

After being brought to Pisa by Master Dominick to the feet of your celestial majesty, most glorious prince, Lord F.,

— Leonardo Fibonacci, Liber quadratorum, epistle (translated by L. E. Sigler[3])

The Liber quadratorum has been passed down by a single 15th-century manuscript, the so-called ms. E 75 Sup. of the Biblioteca Ambrosiana (Milan, Italy), ff. 19r-39v.[4] During the 19th century, the work has been published for the first time in a printed edition by Baldassarre Boncompagni Ludovisi, prince of Piombino.[5]

Appearing in the book is Fibonacci's identity, establishing that the set of all sums of two squares is closed under multiplication. The book anticipated the works of later mathematicians such as Fermat and Euler.[6] The book examines several topics in number theory, among them an inductive method for finding Pythagorean triples based on the sequence of odd integers, the fact that the sum of the first odd integers is , and the solution to the congruum problem.[7]

Notes

  1. ^ Fibonacci, Leonardo Pisano, The Book of Squares (Liber Quadratorum). An annotated translation into modern English by L. E. Sigler (1987) Orlando, FL: Academic Press. ISBN 978-0-12-643130-8
  2. ^ "Full text of "Leonardo of Pisa and his Liber Quadratorum"". archive.org. Retrieved 2016-10-04.
  3. ^ The Book of Squares (Liber Quadratorum). An annotated translation into modern English by L. E. Sigler (1987) Orlando, FL: Academic Press.
  4. ^ E. Picutti, Il «Libro dei Quadrati» di Leonardo Pisano, in «Physis. Rivista Internazionale di Storia della Scienza» XXI, 1979, pp. 195-339
  5. ^ Baldassarre Boncompagni Ludovisi, Opuscoli di Leonardo Pisano secondo un codice della Biblioteca Ambrosiana di Milano contrassegnato E.75. Parte Superiore, in Id., Scritti di Leonardo Pisano matematico del secolo decimoterzo, vol. II, Roma, Tipografia delle scienze matematiche e fisiche, 1862, pp. 253-283.
  6. ^ Berlinghoff, William P. and Fernando Q. Gouvêa (2004). Math through the ages: a gentle history for teachers and others. MAA, p. 34. ISBN 0-88385-736-7
  7. ^ McClenon, R. B., "Leonardo of Pisa and his Liber Quadratorum", American Mathematical Monthly, Vol. 26, No. 1, January 1919, pp. 1–8.

Further reading

External links

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