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At least 325 records · Page 18Linked to original sources
arXiv2014

The Moravian crossroads. Mathematics and mathematicians in Brno between German traditions and Czech hopes

In the paper, we study the situation of the mathematical community in Brno, the maintown of Moravia, between 1900 and 1930. During this time, the First World War and, as one of its consequences, the creation of the new independent Czechoslovakia, created a major perturbation and was the occasion of a reorganization of the community. Its German and Czech sides were in particular constantly looking for a renewed cohabitation which proved difficult to establish along the sliding of political power from the Germans to the Czechs . We try to illustrate how before the war the main place for mathematics in Brno was the German Technical University whereas after the war it became the newly created Masaryk university.

math.HO↗
arXiv2010

Digital Era: Magic Squares and 8th May 2010 (08.05.2010)

In this short note we have produced different kind of magic squares using digital letter having only the algorisms: 0, 1, 2, 5, and 8. The interesting fact in considering these five digits is that the day 8th May 2010 also have these ones (08.05.2010). Moreover, the magic squares presented have some interesting properties, such as: they remains the same if we rotate them by 180 degree, or see in the mirror, or see on the other side of the paper, etc. Two palindrome semi-magic squares of order 3x3 are also given. Still, we have considered other dates having four digits.

math.HO↗
arXiv2014

On a Relation Between the Integral Image Algorithm and Calculus

The Integral Image algorithm is often applied in tasks that require efficient integration over images, such as object detection. In this paper we discuss theoretical aspects of the algorithm's continuous version. We suggest to define the coefficients at the formulation of the algorithm by applying a novel kind of discrete derivative. Based on that operator we build a novel integration method over curves in the plane, and apply it in a theorem that extends the algorithm to general continuous domains.

cs.DM↗
arXiv2010

Odd One Out

This article covers my second talk at the Gathering for Gardner in March, 2010. It is about an Odd One Out puzzle I invented, after having been inspired by Martin Gardner. I do not like Odd One Out questions; that is why I invented one.

math.HO↗
arXiv2010

New Wallis- and Catalan-Type Infinite Products for $π, e$, and $\sqrt{2+\sqrt2}$

We generalize Wallis's 1655 infinite product for $π/2$ to one for $(π/K)\csc(π/K)$, as well as give new Wallis-type products for $π/4, 2, \sqrt{2+\sqrt2}, 2π/3\sqrt3,$ and other constants. The proofs use a classical infinite product formula involving the gamma function. We also extend Catalan's 1873 infinite product of radicals for $e$ to Catalan-type products for $e/4,\sqrt{e}$, and $e^{3/2}/2$. Here the proofs use Stirling's formula. Finally, we find an analog for $e^{2/3}/\sqrt3$ of Pippenger's 1980 infinite product for $e/2$, and we conjecture that they can be generalized to a product for a power of $e^{1/K}$.

math.NT↗
arXiv2010

Proofs, proofs, proofs, and proofs

In logic there is a clear concept of what constitutes a proof and what not. A proof is essentially defined as a finite sequence of formulae which are either axioms or derived by proof rules from formulae earlier in the sequence. Sociologically, however, it is more difficult to say what should constitute a proof and what not. In this paper we will look at different forms of proofs and try to clarify the concept of proof in the wider meaning of the term. This has implications on how proofs should be represented formally.

cs.AI↗
arXiv2011

SIAM 2020

Some observations are made about how the Society for Industrial and Applied Mathematics (SIAM) might be better oriented to serve the industrial and interdisciplinary mathematics community in the future.

math.HO↗
arXiv2010

A different way to read off the time - A new idea for a binary clock

A new idea for a binary clock is presented. It displays the time using a triangular array of 15 bits. It is shown that such a geometric, triangular arrangement is only possible because our system of time divisions is based on a sexagesimal system in which the number of minutes in 12 hours equals the factorial of a natural number (720=6!).

math.HO↗
arXiv2012

Eratosthenes and Pliny, Greek geometry and Roman follies

Supportive attitudes can bring to a blossoming science, while neglect can quickly make science absent from everyday life and provide a very primitive view of the world. We compare one important Greek achievement, the computation of the Earth meridian by Eratosthenes, to its later interpretation by the Roman historian of science Pliny.

math.HO↗
arXiv2010

When is the (co)sine of a rational angle equal to a rational number?

If the cosine of a rational multiple of $π$ is a rational number then it is an integral multiple of $\frac12$. For this fact, we give a proof accessible to an interested school student. We then discuss which quadratic and cubic irrationalities are values of cosine at ratinal multiples of $π$.

math.HO↗
arXiv2014

A pedagogical history of compactness

This paper traces the history of compactness from the original motivating questions, through the development of the definition, to a generalization of sequential compactness in terms of nets and filters.

math.HO↗
arXiv2010

Euler and the Ordinary Differential Equations

The following notes are intended to make a small digression on the topics mentioned in the title of the same, since these were not addressed in the past tribute by the Institute of Physics of the UdeA. We believe more than platitude try to justify the importance and effectiveness in the development of mathematics and physics during the eighteenth century and present such issues, therefore a brief description of the methods and problems attacked by Euler and his contemporaries using the heuristics. Note in advance that they constitute a strong impoverished attempt to honor the memory of who is considered the Shakespeare of Mathematics: Universal, rich in detail and inexhaustible.

math.HO↗
arXiv2010

Gravity, an essential property of matter?

The aim of this short note is to realize that the main reason for non-mechanistic explanation of Newton's gravitational attraction, is explicitly encapsulated in his famous General Scholium of the second Edition of Principia Mathematica (1713).

math.HO↗
arXiv2012

Review of Wüst's 'Mathematik für Physiker und Mathematiker'

This paper has been withdrawn by the author. In this article I review Wüst's recent handbook on mathematical physics from a philosophical standpoint. It emerges a structural approach to mathematics which evidences the utility of logic in the expression of the main concepts of this discipline.

math.HO↗
arXiv2010

Teaching Resources and teachers professional development: toward a documentational approach of didactics

We propose in this paper a theoretical approach of teachers' professional development, focusing on teachers' interactions with resources, digital resources in particular. Documents, entailing resources and schemes of utilization of these resources, are developed throughout documentational geneses occurring along teachers' documentation work (selecting resources, adapting, combining, refining them). The study of teachers' documentation systems permits to seize the changes brought by digital resources; it also constitutes a way to embrace teachers' professional change.

math.HO↗
arXiv2010

Introduction to Working Group 7

Technologies in mathematical education has been a theme present at CERME from the first edition. The available technologies have evolved a lot during these years. At CERME 5 conference, the conclusions of the technology Working Group (Kynigos et al. 2007), as well as Artigue's and Ruthven's interventions (Artigue 2007, Ruthven 2007), signal perspective evolutions towards more comprehensive studies, in several respects. Drawing on these previous works, CERME 6 WG7 intended to go further in the directions they have indicated.

math.HO↗