Historia Mathematica最新文献

This article presents evidence of the transmission and reception of Petrus Ramus's mathematical pedagogy, as witnessed in a multi-volume Sammelband constructed and used in late sixteenth-century Germany. It considers how the methodological influence of Ramus was transmitted to students by the mathematical work of Thomas Fincke, before suggesting that idiosyncratic users of the Sammelband tangled with authoritative interpretations of Euclid by incorporating their own reading and notational practices. Whilst Fincke's work was aimed toward students familiar with Ramist teaching, marginalia found within the Sammelband reinterpret these intentions, demonstrating the pedagogical relationships shared between Fincke, his predecessors, and the later readers of the volume.

During the first half of the 20th century the Danish geometer Johannes Hjelmslev developed what he called a geometry of reality. It was presented as an alternative to the idealized Euclidean paradigm that had recently been completed by Hilbert. Hjelmslev argued that his geometry of reality was superior to the Euclidean geometry both didactically, scientifically and in practice: Didactically, because it was closer to experience and intuition, in practice because it was in accordance with the real geometrical drawing practice of the engineer, and scientifically because it was based on a smaller axiomatic basis than Hilbertian Euclidean geometry but still included the important theorems of ordinary geometry. In this paper, I shall primarily analyze the scientific aspect of Hjelmslev's new approach to geometry that gave rise to the so-called Hjelmslev (incidence) geometry or ring geometry.

Carlini's career was mainly dedicated to astronomy, but he was also a particularly skilled mathematician. In this article we collect and analyse his mathematical contributions in detail. In particular, in his important Memoir of the year 1817 devoted to Kepler's equation he introduced an innovative idea to solve ordinary differential equations with singular perturbations by means of asymptotic expansions. In the same Memoir also appeared, five years before Laplace's contributions, what is usually called the Laplace limit constant. Furthermore, Carlini published other mathematical Memoirs anticipating, 70 years in advance, the importance of complex branches of the Lambert's special function.

The Italian mathematician Antonio Bordoni is mainly known for his adherence to the Lagrangian approach to the foundations of calculus and for his role in creating an important school of mathematics. In this paper, I consider his less known work on the application of probability to design exams and analyze their outcomes. Within this framework, he obtained in 1837, as Mondésir and Poisson, the result that would lead Catalan to formulate his “new principle” of probability (Jongmans and Seneta, 1994). Moreover, in 1843, Bordoni also gave an early complete proof of the finite rule of succession.

As a new statistician, W.F. Sheppard wrote a series of letters to the leading statistician of the day, Karl Pearson, for his advice. Written a century ago and spanning three decades, the letters provide a glimpse into the development of two significant contributions to statistics: the normal probability tables, and the corrections of moment estimates. Sheppard's normal probability tables were the first set of modern tables for the standard normal distribution and have been widely used since the twentieth century. We provide an examination of the statistical research carried out by Sheppard and Pearson in the context of their correspondence.

The history of Liouville's identities is of remarkable interest especially as far as the methods used to prove them are concerned. In Liouville's opinion, the identities had to be proved by merely arithmetic considerations. Some mathematicians, such as Uspensky, developed Liouville's approach and used elementary methods. However, other mathematicians (among them Nazimoff and Bell) followed Hermite's suggestions of deriving Liouville's identities from the theory of elliptic functions: most of them thought that analytic methods were preferable since they allowed one to discover new identities (and not only to prove known ones).

One of the most fundamental results in combinatorial optimization is the polynomial-time 3/2-approximation algorithm for the metric traveling salesman problem. It was presented by Christofides in 1976 and is well known as “the Christofides algorithm”. Recently, some authors started calling it “Christofides-Serdyukov algorithm”, pointing out that it was published independently in the USSR in 1978. We provide some historic background on Serdyukov's findings and a translation of his article from Russian into English.