历史与综述
Dirichlet proves the general convergence of Fourier series, after pointing out errors in an earlier attempt by Cauchy. We transcribed from Crelle's Journal (1829) with numerous typographical corrections, and added a completed bibliography.…
Lecture given before the Royal Academy Vienna that summarizes the state of knowledge about the mathematics of the ancient Egyptians, up to 1884. Contains all relevant references to classical Greek texts, and the 'latest' archeology results.…
Translated from the Latin original "Novae demonstrationes circa resolutionem numerorum in quadrata" (1774). E445 in the Enestrom index. See Chapter III, section XI of Weil's "Number theory: an approach through history". Also, a very clear…
Maybe the first inverse problem presented in the history of the occidental thought is described in the book Republic, written by Plato. The problem is posed in the Book VII in a text known as the Allegory of the Cave. That text motivated us…
Limit can be defined by two axioms: 1. Strict inequality between limits implies, ultimately, strict inequality between functions. 2. For constant functions limit is trivial. How can basic results on convergence be derived from these axioms?…
In this article we present a new recurrence formula for a finite sum involving the Fibonacci sequence. Furthermore, we state an algorithm to compute the sum of a power series related to Fibonacci series, without the use of term-by-term…
E26 in the Enestrom index. Translated from the Latin original, "Observationes de theoremate quodam Fermatiano aliisque ad numeros primos spectantibus" (1732). In this paper Euler gives a counterexample to Fermat's claim that all numbers of…
E661 in the Enestrom index. This was originally published as "Variae considerationes circa series hypergeometricas" (1776). In this paper Euler is looking at the asymptotic behavior of infinite products that are similar to the Gamma…
This paper derives Touchard's theorem from Euler's form for odd perfect numbers. It also fine-tunes Euler's form.
Points out the errors in the paper "J.G. Chen, S.D. Kominers, and R.W. Sinnott. Walk versus wait: The lazy mathematician wins. arXiv.org Mathematics 2008. arXiv:0801.0297"
A recent paper proposing a model of the limiting speed of the domino effect is discussed with reference to its need and the need of models in general for validation against experimental data. It is shown that the proposed model diverges…
We illustrate the concept of mathematical proof.
This is an article on mathematical publishing during the German occupation of France. Looking at the cases of four of them and especially at the case of Jacques Feldbau (one of the founders of the theory of fibre bundles), we investigate…
Contribution of Indian Mathematics since Vedic Period has been recognised by the Historians. Pingala (200 BC) in his book on 'Chandashaastra', a text related to the description and analysis of meters in poetic work, describes algorithms…
This mathematical recreation extends the analysis of a recent paper, asking when a traveller at a bus stop and not knowing the time of the next bus is best advised to wait or to start walking toward the destination. A detailed analysis and…
In this series of seven papers, predominantly by means of elementary analysis, we establish a number of identities related to the Riemann zeta function. Whilst this paper is mainly expository, some of the formulae reported in it are…
In this series of seven papers, predominantly by means of elementary analysis, we establish a number of identities related to the Riemann zeta function. Whilst this paper is mainly expository, some of the formulae reported in it are…
In this series of seven papers, predominantly by means of elementary analysis, we establish a number of identities related to the Riemann zeta function. Whilst this paper is mainly expository, some of the formulae reported in it are…
In this series of seven papers, predominantly by means of elementary analysis, we establish a number of identities related to the Riemann zeta function. Whilst this paper is mainly expository, some of the formulae reported in it are…
In this series of seven papers, predominantly by means of elementary analysis, we establish a number of identities related to the Riemann zeta function. Whilst this paper is mainly expository, some of the formulae reported in it are…