The Book of Squares

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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] Fibonacci's identity, establishing that the set of all sums of two squares is closed under multiplication, appears in it. The book anticipated the works of later mathematicians like Fermat and Euler.[3] 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 ${\displaystyle n}$ odd integers is ${\displaystyle n^{2}}$, and the solution to the congruum problem.[4]

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. ^ 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
4. ^ McClenon, R. B., "Leonardo of Pisa and his Liber Quadratorum", American Mathematical Monthly, Vol. 26, No. 1, January 1919, pp. 1–8.