scholarly journals MÉTODO PARA RESOLVER EQUAÇÕES DIOFANTINAS COM COEFICIENTES NO CONJUNTO DOS NÚMEROS RACIONAIS

2015 ◽  
Vol 37 ◽  
pp. 47
Author(s):  
Josias Neubert Savóis ◽  
Daiane Freitas
Keyword(s):  
Diophantine Equations ◽  
Basic Education ◽  
Daily Life ◽  
Rational Numbers ◽  
Greatest Common Divisor ◽  
Practical Application ◽  
Mathematical Concepts ◽  
The Real ◽  
Linear Diophantine Equations ◽  
The Creation

http://dx.doi.org/10.5902/2179460X14529Develop a solid understanding of linear Diophantine equations in two variables facilitates the resolution of many problems of daily life and also the real understanding of some mathematical concepts taught in school but they seem useless and without practical application. Moreover, the relationships that these equations are established with other content that are already inserted into the basic education justify their education and become an important tool for contextualizing and interdisciplinarity. This work also aims to show the importance of teaching of rational numbers and in this context do analysis on a new concept of greatest common divisor,called generalized maximum common divisor, and thus we can use the numberpad as rational coefficients of Diophantine equations, expanding the breadth of problems solved by these equations. The creation of various practical problems of implementation of the theory studied serves to convince us of the importance of this work and to encourage their implementation and creating new problems taking into account the reality of each school and its students.

scholarly journals OS USOS FLEXÍVEIS DO CONCEITO DE VARIÁVEL NA EDUCAÇÃO BÁSICA: UM ESTUDO COM AS EQUAÇÕES DIOFANTINAS LINEARES

2015 ◽  
Vol 37 ◽  
pp. 356
Author(s):  
Wagner Marcelo Pommer
Keyword(s):  
Content Analysis ◽  
Diophantine Equation ◽  
Functional Relationship ◽  
Diophantine Equations ◽  
Basic Education ◽  
Linear Equations ◽  
Linear Diophantine Equation ◽  
Linear Diophantine Equations ◽  
Theoretical Considerations ◽  
Literal Symbols

http://dx.doi.org/10.5902/2179460X14370In many curricular documents for Basic Education the variable concept is briefly quoted, seen as a paramathematics notion, intrinsic to the development of functions, without further references. This article aims to present and discuss the context of Linear Diophantine Equation as a possible theme to explore the flexible uses of the variable concept in algebraic education. The theoretical considerations is based upon Küchemann (1981), Usiskin (1995) and Ursini;Trigueros (2001), researchers who believe that variables can assume different roles: unknown, generalized number and in a functional relationship. In that scenary, the understanding of the variable concept pervades some potential ways. We were inspired at Content Analysis, described in Bardin (2004), as metodological referencial to search contexts that favour such framework. In preanalisys realized we consider the epistemology present on Diophantine Linear Equations theme as a possible way to explore the flexible uses of the variable concept. The analysis revealed that the Linear Diophantine Equations allow the acquisition of the following potentialities, expressed in Ursini and Trigueiros (2001): executing calculations and simple operations with the literal symbols; create a context of integration to the variables flexible uses; allow situating some advantages on the different uses of the variable concept.

Richard Sisson and Leo E. Rose. War and Secession: Pakistan, India and the Creation of Bangladesh. New Delhi: Vistaar Publications. 1990. 338 pp.Price Rs 225.00 (Hardbound).

1991 ◽  
Vol 30 (1) ◽  
pp. 95-99
Author(s):  
Ziaul Haque
Keyword(s):  
Political Polarization ◽  
The Political ◽  
New Delhi ◽  
Historical Events ◽  
National Elections ◽  
The Real ◽  
Global Issues ◽  
Political Processes ◽  
Political Events ◽  
The Creation

After thirteen long years of military dictatorship, national elections on the basis of adult franchise were held in Pakistan in December 1970. The Awami League, led by Sheikh Mujibur Rahman, and the Pakistan Peoples Party, under Zulfiqar Ali Bhutto, emerged as the two majority political parties in East Pakistan and West Pakistan respectively. The political party commanding a majority in one wing of the country had almost no following in the other. This ended in a political and constitutional deadlock, since this split mandate and political exclusiveness gradually led to the parting of ways and political polarization. Power was not transferred to the majority party (that is, the Awami League) within the legally prescribed time; instead, in the wake of the political/ constitutional crisis, a civil war broke out in East Pakistan which soon led to an open war between India and Pakistan in December 1971. This ultimately resulted in the dismemberment of Pakistan, and in the creation of Bangladesh as a sovereign country. The book under review is a political study of the causes and consequences of this crisis and the war, based on a reconstruction of the real facts, historical events, political processes and developments. It candidly recapitulates the respective roles of the political elites (both of India and Pakistan), their leaders and governments, and assesses their perceptions of the real situation. It is an absorbing narrative of almost thirteen months, from 7 December, 1970, when elections were held in Pakistan, to 17 December, 1971 when the war ended after the Pakistani army's surrender to the Indian army in Dhaka (on December 16, 1971). The authors, who are trained political scientists, give fresh interpretations of these historical events and processes and relate them to the broader regional and global issues, thus assessing the crisis in a broader perspective. This change of perspective enhances our understanding of the problems the authors discuss. Their focus on the problems under discussion is sharp, cogent, enlightening, and circumspect, whether or not the reader agrees with their conclusions. The grasp of the source material is masterly; their narration of fast-moving political events is superbly anchored in their scientific methodology and political philosophy.

Holding a Mirror Up to Theatre

2021 ◽  
Vol 65 (1) ◽  
pp. 54-61
Author(s):  
Carol Martin
Keyword(s):  
Daily Life ◽  
The Real ◽  
Suspension Of Disbelief

Swiss director Milo Rau holds a mirror up to theatre to call into question its assumptions, conventions, and relationship to daily life. Rau’s nonfictional story of the murder of Ihsane Jarfi takes place within two overarching narratives with different timeframes—what happens on the stage now, and what happened beyond the stage then. His dramaturgy cautions against both suspension of disbelief and catharsis and against confusing the fictional with the real.

Оксана Кукуруз, Взаимодействие политики и права в процессе общественной трансформации в Украине и Республике Польша

2021 ◽  
pp. 158-162
Author(s):  
Ivanna Kyliushyk
Keyword(s):  
Public Interest ◽  
Book Research ◽  
Social Transformation ◽  
Common Goal ◽  
The Real ◽  
The Public ◽  
The Creation ◽  
The Republic ◽  
Effective Development ◽  
Politics And Law

The author of the book research the interaction of politics and law as two important social regulators that have a common goal the effective development of society. The author defines the real models of interaction between politics and law, which have formed in Ukraine and the Republic of Poland in the process of social transformation, and the creation of an appropriate model, which should be based on the goal of ensuring the public interest.

Geometric Transformations in the Plane: Shapes in Motion.

2021 ◽  
Vol 8 (3) ◽  
pp. 156-175
Author(s):  
Antonio Paulo Muccillo de Medeiros ◽  
Lícia Giesta Ferreira De Medeiros
Keyword(s):  
Historical Perspective ◽  
Basic Education ◽  
Practical Application ◽  
Geometric Transformations

This work intends to analyze the validity of inserting the study of Geometric Transformations in Basic Education. It is based on the analysis, from the historical perspective, of the use of these transformations by man and the development of these concept by mathematicians. It intends to show that this subject can be used as an integrating content between the branches of mathematics in basic education to contextualize teaching of subjects in which students do not easily see a practical application.

Mandelstam: The Realm of Unexpectedness

2021 ◽  
Vol 64 (2) ◽  
pp. 62-83
Author(s):  
Svetlana S. Neretina
Keyword(s):  
Middle Ages ◽  
Speech Act ◽  
Classical Antiquity ◽  
Logical Framework ◽  
Creation Process ◽  
The Real ◽  
Logical Construction ◽  
The World ◽  
The Creation ◽  
The Middle Ages

In the essay “Conversation about Dante,” Mandelstam described logic, which he defined as the “realm of unexpectedness,” which is unlike any everyday logical construction. Based on the analysis of Mandelstam’s text, it is assumed that we are talking about a tropology that arose in the Middle Ages, the principles of which can be derived from studies of St. Augustine’s treatise De Dialectica and Petrus Сomestor’s Historia Scholastica. It is this triple commonwealth (Augustine – Comestor – Dante, read by Mandelstam) that creates the multilayered logical framework of the work. Augustine created a completely different dialectic than in classical antiquity. Augustine considers dialectics as an art of discussion and describes the real steps that contribute to the emergence of speech, which corresponds to Mandelstam’s concept of conversation. According to Augustine, at the basis of any speech, is a trope-turn. In the article, attention is drawn to the sound nature of creation process. This logic, used in explaining the creation of the world according to the logos/word (tropology), assumes that, at the basis of the speech act, there is no the word as a unit of speech, but the sound itself – the sound, which was considered initially equivocal (ambiguous). In the process of pronounciation, the sound could turn into its opposite and could change the meaning of speech if the context has been changed. Dante expressed the meaning of tropology in practice. Mandelstam wrote that he had chosen Dante for the conversation (between poet and poet) “because he is the greatest and indisputable master of reversible and reversing poetic substance.” Mandelstam saw Dante as the Descartes of metaphor.

Coordination sequences and layer-by-layer growth of periodic structures

2019 ◽  
Vol 234 (5) ◽  
pp. 291-299
Author(s):  
Anton Shutov ◽  
Andrey Maleev
Keyword(s):  
Generating Functions ◽  
Diophantine Equations ◽  
Periodic Structures ◽  
Layer Growth ◽  
Layer By Layer ◽  
Explicit Formulas ◽  
New Approach ◽  
Coordination Numbers ◽  
Linear Diophantine Equations ◽  
Recurrent Relations

Abstract A new approach to the problem of coordination sequences of periodic structures is proposed. It is based on the concept of layer-by-layer growth and on the study of geodesics in periodic graphs. We represent coordination numbers as sums of so called sector coordination numbers arising from the growth polygon of the graph. In each sector we obtain a canonical form of the geodesic chains and reduce the calculation of the sector coordination numbers to solution of the linear Diophantine equations. The approach is illustrated by the example of the 2-homogeneous kra graph. We obtain three alternative descriptions of the coordination sequences: explicit formulas, generating functions and recurrent relations.

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