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1

A Renaissance mathematician’s art

100%

Mirek R.

ARGUMENT: Biannual Philosophical Journal

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2019

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vol. 9

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issue 1

147-152

EN

Piero della Francesca is best known as a painter but he was also a mathematician. His treatise De prospectiva pingendi is a superb example of a union between the fne arts and mathemati‑ cal sciences of arithmetic and geometry. In this paper, I explain some reasons why his paint‑ ing is considered as a part of perspective and, therefore, can be identifed with a branch of geometry.

2

Geometrical perspective on rotation and data structure diagnosis in factor analysis

94%

Tarka P.

Econometrics. Ekonometria. Advances in Applied Data Analytics

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2013

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issue 1(39)

198-209

EN

Geometry has always contributed to a great extent and played a significant role in the development of many of the principles of the factor models. While factor-analytic principles and procedures have been generally developed by the heavy emphasis on matrix algebra, there is still a grave importance and need towards a geometrical approach and its application in the factor analysis. In this article the author provides, on selected issues, a description in reference to factor models from a geometric viewpoint with a discussion running through its advantages and disadvantages. Finally, at the end of the paper, conclusions in reference to good conditions of factors rotation are given. This article explains to what extent a geometrical approach brings specific value and offers an extra insight into factor analysis. As proved, geometry still provides an alternative framework which may be helpful for better understanding and data structure diagnosis.

3

Anaximandrova geometrie

83%

Kočandrle R.

Filosofický časopis (Philosophical Journal)

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2013

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vol. 61

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issue 2

163-180

EN

According to tradition Thales brought geometry to Greece from Miletus. Although discussion of the nature of Thales’ geometry has not arrived at a consensus, it seems that the theorems formulated were retrospectively applied in his concrete measurements. So far, however, we have no information about the geometry of Thales’ pupil and successor, Anaximander of Miletus. An exception is presented in the lexicon Suda which claims that Anaximander “in general showed the basics of geometry”. This lexicon at the same time states the points at which the employment of the geometry can be discerned. Most importantly, we have the question of the gnomon, with the help of which an order of measurement is realisable. Clear signs of the application of geometry are likewise shown by Anaximander’s whole conception of cosmology: the shape of the earth and its position at the centre of the universe, and the very description of the heavenly bodies. In addition one can discern geometry involved in the map of the world and the sphere. Thus, although Anaximander is not explicitly connected with geometry, extant texts demonstrate that he significantly exploited geometrical knowledge when he connected concrete observation with the geometrical organisation of the universe as a whole.

CS

Podle tradice přenesl geometrii do Řecka Thalés z Mílétu. Ačkoli v diskusích o povaze Thalétovy geometrie nepanuje konsensus, zdá se, že zformulované teorémy byly až dodatečně uplatněny na jeho konkrétní měření. Již o Thalétově „žákovi a nástupci“, Anaximandrovi z Mílétu, však nemáme žádné zprávy, které by se týkaly geometrie. Výjimku představuje lexikon Súda, který uvádí, že Anaximandros „vůbec ukázal základy geometrie“. Lexikon zároveň vyjmenovává momenty, v nichž může být užití geometrie spatřeno. V prvé řadě se jedná o gnómón, s jehož pomocí mohla být realizována řada měření. Zřejmé znaky uplatnění geometrie vykazuje též celá Anaximandrova koncepce kosmologie: tvar Země a její umístění ve středu univerza, i samotný popis nebeských těles. Podobně lze uplatnění geometrie spatřovat za mapou světa a sférou. Ačkoli tedy Anaximandros není explicitně s geometrií spojován, dochované texty ukazují, že její poznatky významně využil, když propojil konkrétní pozorování s geometrickým uspořádáním celého univerza.

4

A dialéctica do continuum: da análise matemática à filosofia

83%

Borges De Meneses R. D.

Społeczeństwo i Edukacja. Międzynarodowe Studia Humanistyczne

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2015

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issue 4(19)

21-41

EN

There are so many possibilities to the metric continuum from the Geometry to the Mathematical Analysis, with by the way the historical formulation from Pythagoras to Cantor or Dedekind to make up a new continuum’s theory. On this article I refer the possibilities to carry out where is a philosophical foundation to continuum that is a metric property of number, and the geometric space. Meanwhile, finally I propose to determine the philosophical foundations, gnoseological, and ontological to the continuum.

5

The Designation of Geometry Teaching Tools for Visually-Impaired Students Using Plastic Geoboards Created by 3D Printing

83%

Junthong N., Netpradit S., Boonlue S.

The New Educational Review

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2020

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vol. 59

87-102

EN

In the present study, plastic geoboards and accessories were created as geometry teaching tools for visually-impaired students, using 3D printing. Lines, shapes, and angles were illustrated by stretching rubber bands around rivet heads on a geoboard with square edge of 10 x 10 grid array and circular edge of 4-quadrant graph. The coordinate points of 2D geometry were explored by blind touch on braille scales and raised grid lines, while z-axis pillars were used for 3D geometry by connecting rubber bands to the plane. The experimental group revealed significantly more learning achievement than did the control group, and all participants agreed that the new geoboards enhanced the mental imagery and understanding of geometry.

6

Władysław Kretkowski (1840 –1910)

71%

Ciesielska D.

Kwartalnik Historii Nauki i Techniki

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2014

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vol. 59

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issue 4

17–53

EN

Władysław Kretkowski was a mathematician and an engineer. He graduated École Imperiale des Ponts et Chauseés in Paris and also Sorbonne. He obtained PhD from the Jagiellonian University in Kraków, he was a private docent at the Polytechnic and University in Lvov. The first chapter of the paper contains a short biography of Kretkowski, including information about his education and interests. The participation of Kretkowski in the January Uprising is described here as well. In the main Chapter, i.e. Chapter 2, mathematical achievements of Kretkowski in the theory of determinants and their applications in mathematical analysis and geometry is presented. The history of his academic career is also presented in this chapter. The last chapters are devoted to the mathematical contests announced by Kretkowski (especially the most famous one on the problem which is nowadays known as the Third Hilbert Problem from 1900) and to the Dr Władysław Kretkowski Fundation

7

ПРОФЕСІЙНО СПРЯМОВАНІ ЗАДАЧІ В КУРСІ МАТЕМАТИКИ ПТНЗ

71%

Яна Ч.

Педагогічні науки: теорія, історія, інноваційні технології

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2016

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issue 9(63)

201-210

EN

The article indicates the essense of a concept “motivation” and emphasizes importance of highlighting a motivation stage in the structure of each lesson. The author mentions that demonstration of application of knowledge and skills perfected during a lesson in the future professional activity is an effective method of motivation enhancement. The purpose of the article is to consider the ways for enhancement of motivation of students in the process of studying in vocational schools through application of professionally-oriented problems in the mathematics course in vocational schools. Research methods. The author has applied general scientific methods (analysis and synthesis of psychological and pedagogical, scientific and reference literature) and empirical methods (observing an educational process). The article describes methods for enhancement of motivation of the educational activity of students of vocational schools through application of professionally-oriented problems during mathematics lessons. The author notes that a lecturer should select tasks and problems, situations of which contain professionally significant material for pupils, who learn different professions. Currently, students of vocational schools study mathematics with the use of Standard Level student’s books for schools providing general education. None of such books contains a sufficient amount of professionally-oriented problems for different professions, which are studied in vocational schools. Therefore, a lecturer faces a matter of selection of such problems for each specialty learned by pupils. The author substantiates the necessity of development of collections of professionally-oriented problems in mathematics for professions learned by present students of vocational schools. The author highlights that the economic condition change influences the change of a list of professions learned by students of vocational schools. The author describes opportunities of application of professionally-oriented problems at each stage of a lesson. To select such problems, a lecturer should deep in the context of each specialty learned by pupils. It is important to collaborate with lecturers of special disciplines and masters of vocational training. The article presents examples of such problems for specialties “Tailor and cutter” and “Wireman in repair and servicing electrical equipment”.

8

Mathematics and Liberature: Fajfer’s Ten Letters

71%

Matuszyk Ł.

Journal of Language and Cultural Education

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2016

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vol. 4

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issue 2

153-166

EN

The article discusses liberature in the context of its mathematical qualities. In this trend which inextricably connects the textual and physical layer of the work, each element in the book is expected to be created according to a certain formula which should bring a holistic piece of literature. After 1999, a great number of mathematically-oriented works have appeared which are strictly liberary. In the presentation, I base on the theoretical idea behind liberature when discussing Zenon Fajfer’s liberary work Ten Letters (Pol. Dwadzieścia jeden liter). This innovative piece is analysed mainly from the point of view of geometry and play with numbers, which is visible already in the title: the ten-letter phrase “ten letters.” Mathematical qualities are indicated on various layers of the piece: the physical, the textual, and the visual, but especially in its form. The game of numbers is found not only where it is obviously visible and essential to understand the message, but also in places which might not have been intended. Liberature is analysed as literature but at the same time, it is shown not to be literature, and in this respect, to be mathematical at the core.

9

Przestrzeń, filozofia i Wszechświat

71%

Krzanowski R.

Zagadnienia Filozoficzne w Nauce

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2017

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issue 63

249-252

EN

Book review of: M. Heller, Przestrzenie Wszechświata. Od geometrii do kosmologii, Copernicus Center Press, Kraków 2017, ss. 284.

PL

Recenzja książki: Michal Heller. Przestrzenie Wszechświata. Od geometrii do kosmologii, Copernicus Center Press, Kraków 2017, ss. 284.

10

Matematyka nie opisuje świata, lecz wychodzi mu naprzeciw

67%

Mioduszewski J.

Zagadnienia Filozoficzne w Nauce

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2015

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issue 58

7-43

EN

In everyday experience mathematics rarely appears to us as a whole, and certainly never as a system in the sense of David Hilbert’s considerations from early 20th Century. Mathematical disciplines seem to be independent and autonomous. We do not see that specific deduction goes beyond particular convention applicable in given discipline. In the late 19th Century this view was shared by Felix Klein and Richard Dedekind. The latter’s work “What are numbers and what should they be?” (Was Was sind und was sollen die Zahlen?) was the inspiration for writing this article. This essay is an attempt to see mathematics not as a building, but as a living organism seeking its explanation.

11

Some remarks on the first image of a black hole

62%

Szybka S. J.

Zagadnienia Filozoficzne w Nauce

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2020

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issue 68

281-294

EN

On the 10th of April, 2019 the Event Horizon Telescope Collaboration presented the first image of the black hole. The image was obtained with a planet-scale array of eight ground-based radio telescopes. The observation relied on a technique called very long base interferometry which synchronises telescope facilities around the world. The image of a black hole together with the recent detections of gravitational waves confirms one of the most intriguing predictions of Einstein’s gravity theory, namely, the existence of black holes. I will provide more details on this remarkable observation and explore its consequences for our understanding of nature. The physical reality of black holes is strongly supported by recent advances of astronomy. I claim that this fact is the key to understanding the relation between our world and the world of mathematics.

12

Determinanty twórczego podejścia nauczyciela w budowaniu pojęć geometrycznych przez dzieci w wieku przedszkolnym i wczesnoszkolnym

48%

Malina A.

Edukacja Elementarna w Teorii i Praktyce

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2012

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issue 4(26)

PL

Odpowiednie wprowadzanie małego dziecka w świat pojęć geometrycznych nie jest łatwym zadaniem dla nauczyciela. Wymaga odpowiedniego przygotowania od strony matematycznej oraz psychologicznej. Niezbędnymi czynnikami w tym procesie są: ugruntowana wiedza nauczyciela w zakresie pojęć i umiejętności geometrycznych a także znajomość kolejno następujących po sobie poziomów rozwoju myślenia geometrycznego dziecka. Wypełnienie tych kryteriów przez nauczyciela daje mu możliwość twórczego działania w procesie budowania w umyśle dziecka prawidłowych pojęć i umiejętności geometrycznych. Ponadto wiedza odnośnie tych dwóch wymienionych czynników determinuje możliwe sposoby, drogi wybierane prze z nauczyciela do kształtowania pojęć i umiejętności matematycznych. Pozwala na wykorzystanie kreatywności dzieci w poznawaniu otaczającego świata i tworzenie właściwych sytuacji edukacyjnych. Twórcze podejście nauczyciela nie może być jedynie intuicyjnym działaniem, ale powinno opierać się na wiedzy, umiejętnościach, posiadanym doświadczeniu, obserwacji dzieci oraz głębokiej refleksji.

EN

Taking students in the world of geometric concepts is not an easy task for a teacher. It requires preparation in both these areas: mathematical and psychological. In this process essential factors are: deep knowledge of a teacher about geometric concepts and skills as well as awareness of sequence of levels of geometric thinking. Once the teacher meets these two requirements, he or she is able to create correct abstract geometric concepts and skills in a child's mind. What is more, knowledge about these factors allows the teacher to choose possible ways that lead to the development of mathematical concepts and skills. A teacher can use creativity of children for gaining knowledge about the world around them and building appropriate learning situations. A creative approach of a teacher cannot rely only on intuition. Instead, it should be based on knowledge, skills, previous experience, observation of children and deep reflection.

13

Wartość gnozeologiczna i dydaktyczna metody wykresograficznej w teologii

36%

Krukowski K.

Roczniki Teologii Dogmatycznej

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2013

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vol. 5

167-180

EN

In the contemporary postmodernist culture that more and more becomes the “culture of the picture”, the demand of visualization should also be addressed to theology that is inclined to use the traditional forms of verbal message. In the light of the principle of accommodation accepted by the Vaticanum II the imperative expressed there should be considered “urgent” for the present moment. Among the new propositions promoting graphical-pictorial approaches in theology a new method called chart-graphic or geometrical method worked out by Rev. Prof. Franciszek Drączkowski deserves a special attention. The starting point of the chart-graphic method is the figure of the circle in which an equilateral triangle has been inscribed that is a symbolic image of the triune God. The value of geometry in cognition and comprehension of truth was seen in the past by many outstanding scholars, who considered the use of geometry, logic and algebra to be necessary in the process of cognition of the universe (Descartes, Pascal, Clement of Alexandria). Geometry also for Rev. Drączkowski becomes something that is indeed necessary in the process of cognition of the eternal Truth and of transmitting this knowledge to others. He accepts the ancillary role of geometry, transferring it to the ground of theology.

Refine search results

A Renaissance mathematician’s art

Geometrical perspective on rotation and data structure diagnosis in factor analysis

Anaximandrova geometrie

A dialéctica do continuum: da análise matemática à filosofia

The Designation of Geometry Teaching Tools for Visually-Impaired Students Using Plastic Geoboards Created by 3D Printing

Władysław Kretkowski (1840 –1910)

ПРОФЕСІЙНО СПРЯМОВАНІ ЗАДАЧІ В КУРСІ МАТЕМАТИКИ ПТНЗ

Mathematics and Liberature: Fajfer’s Ten Letters

Przestrzeń, filozofia i Wszechświat

Matematyka nie opisuje świata, lecz wychodzi mu naprzeciw

Some remarks on the first image of a black hole

Determinanty twórczego podejścia nauczyciela w budowaniu pojęć geometrycznych przez dzieci w wieku przedszkolnym i wczesnoszkolnym

Wartość gnozeologiczna i dydaktyczna metody wykresograficznej w teologii