Фибоначчидің 1202 жылғы «Есеп кітабы»

Mathematics book written in 1202 by Fibonacci

The Liber Abaci or Liber Abbaci (Latin for "The Book of Calculation") was a 1202 Latin work on arithmetic by Leonardo of Pisa, posthumously known as Fibonacci. It is primarily famous for helping popularize Arabic numerals in Europe.

Liber Abaci was among the first Western books to describe the Hindu–Arabic numeral system and to use symbols resembling modern "Arabic numerals". By addressing the applications of both commercial tradesmen and mathematicians, it promoted the superiority of the system, and the use of these glyphs. Although the book's title is sometimes translated as "The Book of the Abacus", notes that it is an error to read this as referring to calculating devices called "abacus". Rather, the word "abacus" was used at the time to refer to calculation in any form; the spelling "abbacus" with two "b"s (which is how Leonardo spelled it in the original Latin manuscript) was, and still is in Italy, used to refer to calculation using Hindu Arabic numerals, which can avoid confusion. The book describes methods of doing calculations without aid of an abacus, and as confirms, for centuries after its publication the algorismists (followers of the style of calculation demonstrated in Liber Abaci) remained in conflict with the abacists (traditionalists who continued to use the abacus in conjunction with Roman numerals). The historian of mathematics Carl Boyer emphasizes in his History of Mathematics that although "Liber abaci is not on the abacus" per se, nevertheless " it is a very thorough treatise on algebraic methods and problems in which the use of the Hindu Arabic numerals is strongly advocated."

The first section introduces the Hindu–Arabic numeral system, including methods for converting between different representation systems. This section also includes the first known description of trial division for testing whether a number is composite and, if so, factoring it. The second section presents examples from commerce, such as conversions of currency and measurements, and calculations of profit and interest. The third section discusses a number of mathematical problems; for instance, it includes (ch. II.12) the Chinese remainder theorem, perfect numbers and Mersenne primes as well as formulas for arithmetic series and for square pyramidal numbers. Another example in this chapter involves the growth of a population of rabbits, where the solution requires generating a numerical sequence. Although the problem dates back long before Leonardo, its inclusion in his book is why the Fibonacci sequence is named after him today. The fourth section derives approximations, both numerical and geometrical, of irrational numbers such as square roots. The book also includes proofs in Euclidean geometry. Fibonacci's method of solving algebraic equations shows the influence of the early 10th century Egyptian mathematician Abū Kāmil Shujāʿ ibn Aslam.

The first appearance of the manuscript was in 1202. No copies of this version are known. A revised version of Liber Abaci, dedicated to Michael Scot, appeared in 1227 CE. There are at least nineteen manuscripts extant containing parts of this text. There are three complete versions of this manuscript from the thirteenth and fourteenth centuries. There are a further nine incomplete copies known between the thirteenth and fifteenth centuries, and there may be more not yet identified. There was no known printed version of Liber Abaci until Boncompagni's Italian translation of 1857. The first complete English translation was Sigler's text of 2002.