The Book of Squares

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The Book of Squares, (Liber Quadratorum[1] in the original Latin) is a book on algebra by Leonardo Fibonacci, published in 1225. 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,[4] 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.


  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"". 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.

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