Article ID: CBB910977328

Linear Programming from Fibonacci to Farkas (2021)

unapi

At the beginning of the 13th century Fibonacci described the rules for making mixtures of all kinds, using the Hindu-Arabic system of arithmetic. His work was repeated in the early printed books of arithmetic, many of which contained chapters on ‘alligation', as the subject became known. But the rules were expressed in words, so the subject often appeared difficult, and occasionally mysterious. Some clarity began to appear when Thomas Harriot introduced a modern form of algebraic notation around 1600, and he was almost certainly the first to express the basic rule of alligation in algebraic terms. Thus a link was forged with the work on Diophantine problems that occupied mathematicians like John Pell and John Kersey in the 17th century. Joseph Fourier's work on mechanics led him to suggest a procedure for handling linear inequalities based on a combination of logic and algebra; he also introduced the idea of describing the set of feasible solutions geometrically. In 1898, inspired by Fourier’s work, Gyula Farkas proved a fundamental theorem about systems of linear inequalities. This topic eventually found many applications, and it became known as Linear Programming. The theorem of Farkas also plays a significant role in Game Theory.

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Authors & Contributors
Hachaichi, Yassine
M. Rosa Massa-Esteve
Hamouda, Leïla
Paola Magrone
Manolova, Divna
Mellado-Romero, Antonio
Concepts
Mathematics
Algebra
Arithmetic
Algorithms
Sequences and series (mathematics)
Logic
Time Periods
Medieval
19th century
18th century
20th century, early
17th century
Prehistory
Places
Germany
France
United Kingdom
Nuremberg (Germany)
Mediterranean region
Byzantium
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