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.

中文翻译：

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从斐波那契到 Farkas 的线性规划

在 13 世纪初，斐波那契描述了使用印度-阿拉伯算术系统制作各种混合物的规则。他的工作在早期印刷的算术书籍中得到了重复，其中许多都包含关于“鳄鱼”的章节，因为这个主题被人们所熟知。但规则是用文字表达的，所以这个主题往往显得很困难，有时也很神秘。当 Thomas Harriot 在 1600 年左右引入现代形式的代数符号时，一些清晰度开始出现，几乎可以肯定，他是第一个用代数术语表达鳄鱼基本规则的人。因此，与 17 世纪约翰·佩尔 (John Pell) 和约翰·克西 (John Kersey) 等数学家对丢番图问题的研究建立了联系。约瑟夫·傅立叶' 他在力学方面的工作使他提出了一种基于逻辑和代数组合处理线性不等式的程序；他还介绍了以几何方式描述可行解集的想法。1898 年，受傅立叶工作的启发，Gyula Farkas 证明了一个关于线性不等式系统的基本定理。这个主题最终找到了许多应用，它被称为线性规划。Farkas 定理在博弈论中也扮演着重要的角色。