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Fibonacci's Liber Abaci: A Translation into Modern English of Leonardo Pisano's Book of Calculation (Sources and Studies in the History of Mathematics and Physical Sciences) by Sigler, Laurence (2003) Paperback
"Though it is now mostly known for introducing the Hindu number system and the algorithms of arithmetic that children now learn in grade school, Liber Abaci is much It is an encyclopaedia of thirteenth-century mathematics, both theoretical and practical. It develops the tools rigorously, establishes them with Euclidean proofs, and then shows how to apply them to all kinds of situation in business and trade, including conversion of measures and currency, allocations of profit, computation of interest, and alloying of currencies. It is rigorous mathematics, well applied, and vividly described." As the first translation into a modern language of the Liber Abaci, this book will be of interest not only to historians of science, but to all mathematicians and mathematics teachers interested in the origins of their methods.
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First published January 1, 1202
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Displaying 1 - 4 of 4 reviews
May 18, 2019
Whew. I am finished. Some very interesting algebraic problems towards the end there. I liked the geometrical solutions, but I did find that some were flawed. As such, I applied Al-Khwarizmi's method to many of them, as he did not, and I found the correct answer to some where he actually had an answer significantly different than the correct solution.
That being said, I will definitely keep this book with me. At times, I realize now how important the two major different options (Almuchabala and proportional substitution) can be because sometimes they can help solve for unknowns where the equation would have 3 or 4 different exponents (and therefore very difficult to solve without a calculator via algebra). Very important to even know about these different methods, as I had applied Algebra to some of these proportional problems and substitution and algebra both gave me different answers.
Beneath the surface of an otherwise perfunctory trading manual lies a treasure trove of philosophy behind mathematics itself. It isn't spoken on the surface, obviously (he leaves that for his Book of Squares), but the problems/equations themselves are Diophantine, and both determinate and indeterminate. Some have only one solution, some have many, some have implications that can make you just put the book down and stare into space. This is a book written by a mathematician for a mathematician. Heavy recommend.
4/5 though because it did drag on and was extremely dry.
That being said, I will definitely keep this book with me. At times, I realize now how important the two major different options (Almuchabala and proportional substitution) can be because sometimes they can help solve for unknowns where the equation would have 3 or 4 different exponents (and therefore very difficult to solve without a calculator via algebra). Very important to even know about these different methods, as I had applied Algebra to some of these proportional problems and substitution and algebra both gave me different answers.
Beneath the surface of an otherwise perfunctory trading manual lies a treasure trove of philosophy behind mathematics itself. It isn't spoken on the surface, obviously (he leaves that for his Book of Squares), but the problems/equations themselves are Diophantine, and both determinate and indeterminate. Some have only one solution, some have many, some have implications that can make you just put the book down and stare into space. This is a book written by a mathematician for a mathematician. Heavy recommend.
4/5 though because it did drag on and was extremely dry.
December 10, 2020
Detailed and time consuming but certainly worth the time. By my reckoning a book that shared wisdom and shared techniques that actually changed the world.
Often people think what we know now is recent knowledge and that we , as current custodians of the world are so clever, and getting cleverer.
Well that maybe, however having read Liber Abaci (as a novice in mathematical historical development), there has clearly been great wisdom right back beyond my reckoning.
We are only able to read about those wise souls that gained such prominence and/or wealth, if their wisdom was able to go to print.
Often people think what we know now is recent knowledge and that we , as current custodians of the world are so clever, and getting cleverer.
Well that maybe, however having read Liber Abaci (as a novice in mathematical historical development), there has clearly been great wisdom right back beyond my reckoning.
We are only able to read about those wise souls that gained such prominence and/or wealth, if their wisdom was able to go to print.
June 18, 2024
I first discovered this book when it was referenced on Khan Academy, in the article 'READ: Overview of New Economic Systems', in Unit 5, in the course 'World History Project - Origins to the Present'. The article states that this book changed the fact that, aside the moral issues around credit and interest, people just didn't really know how to use these technologies - they were used in parts of Asia but had not reached Europe yet. The author had traveled far and wide, gathering mathematical knowledge that had originated in the Middle East and India, and his book introduced Europe to fractions and decimals as well as the Hindu-Arabic numeral system (1,2,3, etc.). This book also contains important ideas that helped to solve the existing economic problems of the time, like putting a price on merchandise, converting currency, calculating profits and interest rates, and predicting investment returns.
Displaying 1 - 4 of 4 reviews