Zobrazeno 1 - 10
of 175
pro vyhledávání: '"01A50"'
Autor:
Holtz, Olga
Publikováno v:
Notices Amer. Math. Soc. 71 (2024), no. 6, 725-731
This short note for non-experts means to demystify the tasks of evaluating the Riemann Zeta Function at non-positive integers and at even natural numbers, both initially performed by Leonhard Euler. Treading in the footsteps of G. H. Hardy and others
Externí odkaz:
http://arxiv.org/abs/2308.11637
Autor:
Morrison, Amie, Falconer, Isobel
Publikováno v:
British Journal for the History of Mathematics 37 (2022) 2-23
The eighteenth century saw a flourishing of scientific and philosophical thought throughout Scotland, known as the Scottish Enlightenment. The accomplishments of prominent male figures of this period have been well documented in all disciplines. Howe
Externí odkaz:
http://arxiv.org/abs/2306.06390
Autor:
Hassler, Uwe, Hosseinkouchack, Mehdi
The number $\frac{\pi ^{2}}{6}$ is involved in the variance of several distributions in statistics. At the same time it holds $\sum\nolimits_{k=1}^{\infty }k^{-2}= \frac{\pi ^{2}}{6}$, which solves the famous Basel problem. We first provide a histori
Externí odkaz:
http://arxiv.org/abs/2103.13249
Autor:
Katz, Mikhail G.
Publikováno v:
Journal of Humanistic Mathematics 10 (2020), no. 1, 475-515
We compare several approaches to the history of mathematics recently proposed by Blasjo, Fraser--Schroter, Fried, and others. We argue that tools from both mathematics and history are essential for a meaningful history of the discipline. In an extens
Externí odkaz:
http://arxiv.org/abs/2002.00249
Autor:
Pengelley, David J.
Publikováno v:
In Euler at 300: An Appreciation (editors Robert E. Bradley, Lawrence A. D'Antonio, C. Edward Sandifer), Mathematical Association of America, 2007, pp. 169-190
Leonhard Euler likely developed his summation formula in 1732, and soon used it to estimate the sum of the reciprocal squares to 14 digits --- a value mathematicians had been competing to determine since Leibniz's astonishing discovery that the alter
Externí odkaz:
http://arxiv.org/abs/1912.03527
Autor:
Di Biase, Fausto
We correct a common (but mistaken) attribution of the evaluation of the probability integral, usually attributed to Poisson, Gauss, or Laplace.
Externí odkaz:
http://arxiv.org/abs/1910.08791
Autor:
Milici, Pietro
In La G\'eom\'etrie, Descartes proposed a balance between geometric constructions and symbolic manipulation with the introduction of suitable ideal machines. In modern terms, that is a balance between analog and symbolic computation. Descartes' geome
Externí odkaz:
http://arxiv.org/abs/1904.03094
Autor:
Karjanto, N.
Publikováno v:
Teaching Mathematics and Its Applications 30: 70--74, 2011
Trigonometry is one of the topics in mathematics that the students in both high school and pre-undergraduate levels need to learn. Generally, the topic covers trigonometric functions, trigonometric equations, trigonometric identities and solving obli
Externí odkaz:
http://arxiv.org/abs/1808.08049
Autor:
Basu, Soham, Velleman, Daniel J.
Carl Friedrich Gauss is often given credit for providing the first correct proof of the fundamental theorem of algebra in his 1799 doctoral dissertation. However, Gauss's proof contained a significant gap. In this paper, we give an elementary way of
Externí odkaz:
http://arxiv.org/abs/1704.06585
Autor:
Rubinstein-Salzedo, Simon
In this article, we investigate how Euler might have been led to conjecture the Prime Number Theorem, based on what he knew. We also speculate on why he did not do so.
Comment: To appear in Mathematics Magazine
Comment: To appear in Mathematics Magazine
Externí odkaz:
http://arxiv.org/abs/1701.04718