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.,
โโLeonardo 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. 19rโ39v.[4] During the 19th century, the work was 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
edit- ^ Fibonacci, Leonardo Pisano, The Book of Squares (Liber Quadratorum). An annotated translation into modern English by L. E. Sigler (1987) Orlando, FL: Academic Press. ISBNย 978-0-12-643130-8
- ^ "Full text of "Leonardo of Pisa and his Liber Quadratorum"". archive.org. January 1919. Retrieved 2016-10-04.
- ^ The Book of Squares (Liber Quadratorum). An annotated translation into modern English by L. E. Sigler (1987) Orlando, FL: Academic Press.
- ^ E. Picutti, Il ยซLibro dei Quadratiยป di Leonardo Pisano, in ยซPhysis. Rivista Internazionale di Storia della Scienzaยป XXI, 1979, pp. 195โ339
- ^ 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. 253โ283.
- ^ Berlinghoff, William P. and Fernando Q. Gouvรชa (2004). Math through the ages: a gentle history for teachers and others. MAA, p. 34. ISBNย 0-88385-736-7
- ^ McClenon, R. B., "Leonardo of Pisa and his Liber Quadratorum", American Mathematical Monthly, Vol. 26, No. 1, January 1919, pp. 1โ8.
Further reading
edit- B. 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 1862, pp.ย 253โ283
- P. Ver Eecke, Lรฉonard de Pise. Le livre des nombres carrรฉs. Traduit pour la premiรจre fois du Latin Mรฉdiรฉval en Franรงais, Paris, Blanchard-Desclรฉe โ Bruges 1952.
- G. Arrighi, La fortuna di Leonardo Pisano alla corte di Federico II, in Dante e la cultura sveva. Atti del Convegno di Studi, Melfi, 2โ5 novembre 1969, Firenze 1970, pp.ย 17โ31.
- E. Picutti, Il Libro dei quadrati di Leonardo Pisano e i problemi di analisi indeterminata nel Codice Palatino 557 della Biblioteca Nazionale di Firenze, in ยซPhysis. Rivista Internazionale di Storia della Scienzaยป XXI, 1979, pp.ย 195โ339.
- L.E. Sigler, Leonardo Pisano Fibonacci, the book of squares. An annotated translation into modern English, Boston 1987.
- M. Moyon, Algรจbre & Practica geometriรฆ en Occident mรฉdiรฉval latin: Abลซ Bakr, Fibonacci et Jean de Murs, in Pluralitรฉ de lโalgรจbre ร la Renaissance, a cura di S. Rommevaux, M. Spiesser, M.R. Massa Esteve, Paris 2012, pp.ย 33โ65.
External links
edit- Fibonacci and Square Numbers at "Fibonacci and Square Numbers โ Introduction | Mathematical Association of America". maa.org. Retrieved 2023-09-10.
