History Of Mathematics Research Articles

The Archimedean Origin of Modern Positional Number Systems

A symbolic analysis of Archimedes’s periodical number system is developed, from which a natural link emerges with the modern positional number systems with zero. After the publication of Fibonacci’s Liber Abaci, the decimal Indo-Arabic positional system was the basis of the algorithmic and algebraic trend of modern mathematics, but even if zero plays a crucial role in algebra and mathematical analysis, zeroless positional systems show the same capability of producing efficient arithmetical algorithms based on operation tables over digits. The crucial role of digits is assessed, by considering a representation of numbers based on strings in lexicographic order. A new algorithm for the determination of decimal periods is presented by remarking on the cruciality of this topic in number theory. Periods of ordinal numbers and enumerations of recursive enumerability are shortly recalled. Concluding remarks are formulated about the deep relationship between numbers and information, which shed new light on a red line passing through the whole history of mathematics.

Sejarah Peradaban Islam Dalam Perkembangan Matematika

Mathematics is central to our daily lives and is taught from an early age. As a result, mathematics is used in various areas of life. The history of mathematics is very important to know and study because through it we can know and understand the truth and essence of math. Besides, the history of mathematics shows its connection with many other fields of science. In the history of Islamic civilization, the development of mathematics has begun since the descent of the Quran as a sacred book for the Muslims. Through the Quran, Allah comprehensively invites His creatures to study mathematical science, which can help them to do many things, especially in worship. In this journal, the author also uses methods of literature study with qualitative research to find out how the development of mathematics through Islamic civilization. Therefore, in the journal this time, the author will try to review the evolution of mathematics through the history of Islamic civilization

The development of P-adic numbers theoretically and their use in number theory

Stemming from the need to formalize the divisibility of rational numbers, p-adics provide a unique mathematical perspective rooted in prime number theory. This article provides a comprehensive discussion of p-adic numbers, including their research background, definition, properties, theory, and extensions. This study first elucidates the historical background and significance of p-adic numbers, emphasizing their key role in number theory and its applications. At the heart of this research is a deep dive into the precise definition of p-radical numbers, revealing their unique, often counterintuitive, distance measure. We look at their fundamental characteristics, demonstrate their illogical characteristics, and discuss how they affect transcendental number theory, Diophantine equations, and algebraic number theory. Furthermore, this article explores the theoretical foundations of p-radical numbers and their extensions, emphasizing their integral role in advanced mathematical structures such as p-radical analysis and p-radical geometry. By covering these aspects, this study aims to highlight the lasting impact of p-adic on modern mathematics, reshape our understanding of divisibility, and advance mathematical inquiry into new and uncharted territory.

Briefly Recalling Moments in Mathematics Education History:

Arithmetic was the first mathematical subject to enter the school curriculum in the United States in a formalized manner. Until the first quarter of the nineteenth century, the prevailing pedegogy of this subject revolved around the tenets of mental discipline theory and the rules method of teaching, which valued memorization and repetivive drill of procedures. This continued until pedegogical alternatives to this approach were offered by innovative textbook writers, most notably William Colburn and his 1825 text First Lessons in Arithmetic on the Plan of Pestalozzi. In this article, the teaching of arithemtic in the early United States and the influence of Colburn's text is discussed and is later contextualized through their influence on modern mathematics education practice.

Stylistic Approach to the Brachistochrone Problem

The notion of style is frequently used, and in some instances, without the necessary rigor. Authors such as Crombie, Hacking, Bueno and Granger consider presenting a general concept to be essential and sufficient to grasp the notion of style. They found a possibility to apply a strict concept of style even to science and mathematics. Here, using a fundamental criterion raised by Bueno (2012), I test the possibility to characterize a mathematical local style from a particular event in the history of mathematics: the Brachistochrone problem. Because this problem has different solutions, which allows them to be analyzed to verify an occurrence of style on their mathematical development. Moreover, Bueno offers a criterion that establishes a minimal unity of structure to a notion of style, even in mathematics. There are two problems that any concept of style should face: (i) the impregnation problem posed by Bueno and (ii) the cognitive relevance proposed by Mancosu. The former presents a serious implication in supporting a proper style in mathematics because any mathematical object needs a preceding mathematical theory that characterizes it, and if it is not possible to constitute a style in mathematics, then recognizing its cognitive relevance could also be compromised.

TO THE 85TH ANNIVERSARY OF THE ACADEMICIAN OF THE NATIONAL ACADEMY OF SCIENCES OF UKRAINE ANATOLY MYKHAILOVYCH SAMOILENKO

The article reviews the outstanding scientific achievements of Anatoly Mykhailovych Samoilenko, an Academician of the National Academy of Sciences of Ukraine, whose name will forever remain in the world history of mathematics.

Ethno Mathematics at the Traditional House of Mbaru Niang Wae Rebo, Manggarai

Objective: This study aims to identify ethno mathematics in the Mbaru Niang traditional house of the Wae Rebo community, describe related mathematics concepts, and develop learning tools and learning trajectory for mathematics concepts contained in the culture of the Mbaru Niang traditional house. Theoretical framework: Ethno mathematics is all forms of mathematical activities that are culturally based and varied and can be done every day as needed (Rosa, 2011). Ethno mathematics is a group of ideas about the history of mathematics, the cultural roots of mathematics, the mathematics implicit in everyday rules, and the learning of mathematics (Weldeana, 2016). Ethno mathematics is defined as special ways used by a certain cultural group or society in mathematical activities (Sarwoedi, 2018). Ethno mathematics is mathematics applied by a particular cultural group and studies the relationship between mathematics (mathematics education) and the corresponding social and cultural background, i.e. how mathematics is produced, transferred, disseminated, and specialized in diverse cultural systems (Gerdes, 1994; Zhang & Zhang, 2010). Ethnomathematics is a learning approach that is carried out by teaching mathematics by linking mathematics with the nation's own cultural works and also involving the needs and lives of its people (Zaenuri, et al., 2018). Method: The research method used is descriptive qualitative research with an ethnographic approach. The researcher is the main instrument, and data is collected through observation, interviews, and documentation, data validity using source triangulation techniques. Furthermore, the data were analyzed to describe the research findings. Results and Conclusions: The results showed that there were mathematical activities in the construction of the Mbaru Niang traditional house. These activities include measuring activities with the concept of standard and non-standard units and designing activities related to the concept of geometry. Thus, the mathematical concepts contained in the construction of the Mbaru Niang traditional house can be developed by designing learning tools and learning trajectories that are in accordance with school mathematics. The culture of the Mbaru Niang traditional house is a source of learning mathematics that can be presented according to various contexts in learning mathematics. The study's findings contained several mathematical aspects of the culture of the Mbaru Niang traditional house. These aspects were the concept of geometry (in the form of a conical shape) and the concept of measurement (using non-standard measurements). The measurement concept can be applied to elementary school students, and cone geometry can be applied to junior high school. Thus, identifying and exploring Ethno mathematics in the Mbaru Niang. Implications of the research: Mathematics learning strategies that are oriented towards increasing student success in learning, respecting culture, enhancing cooperation and protecting the natural environment. This is done with the "ethno math" approach through learning in schools. Difficult math concepts can be unraveled with ethno math that is real around students and supported by teacher commitment in implementing learning in the classroom. Originality/value: The novelty of this research is the formation of an ethnomathematics model of mbaru niang that can be integrated in learning mathematics at school in order to provide advice for decision makers in this case teachers and government or education observers to be more pro-active in implementing learning in accordance with the culture around the student.

Exploring Polygonal Number Sieves through Computational Triangulation

The paper deals with the exploration of subsequences of polygonal numbers of different sides derived through step-by-step elimination of terms of the original sequences. Eliminations are based on special rules similarly to how the classic sieve of Eratosthenes was developed through the elimination of multiples of primes. These elementary number theory activities, appropriate for technology-enhanced secondary mathematics education courses, are supported by a spreadsheet, Wolfram Alpha, Maple, and the Online Encyclopedia of Integer Sequences. General formulas for subsequences of polygonal numbers referred to in the paper as polygonal number sieves of order k, that include base-two exponential functions of k, have been developed. Different problem-solving approaches to the derivation of such and other sieves based on the technology-immune/technology-enabled framework have been used. The accuracy of computations and mathematical reasoning is confirmed through the technique of computational triangulation enabled by using more than one digital tool. A few relevant excerpts from the history of mathematics are briefly featured.

Konsep Islamisasi Sains Matematika dalam Pemikiran Al-Khawarizmi: Sebuah Kajian Teoritis

The progress of Western civilization's hegemony cannot be separated from the role of Muslim scientists in developing knowledge and science. But on the other hand, when Western scholars develop and apply the theories of Muslim scientists, they reject the Islamic values ​​contained therein. Therefore, this research aims to examine the concept of Islamization developed by al-Khwarizmi, a Muslim scientist who played an important role in the development of modern mathematics. The Islamic values ​​developed by Al-Khwarizmi can be seen in his discoveries, especially in the fields of algebra, arithmetic, algorithms, geography and others. This research uses library research by collecting data through books and journals, using descriptive methods and a systematic approach. The results of the research found that the Islamization values ​​developed by Al-Khwarizmi were the result of his tadabbur and tafakkur on the verses of the Koran. an which talks about roseits, determining days and months, and understanding the Qudsi hadith which talks about nothingness and contributed to determining the latitude and longitude of areas conquered by Islam during the Abbasid era under the Al-Makmun caliphate.

ANALYSIS OF THE EDUCATIONAL POSSIBILITIES OF THE THEME OF BLACK WOMEN IN MATHEMATICS

This article examines the experience of carrying out an educational presentation of scientific dissemination on the participation of black women throughout the history of mathematics, for high school students who visited the Campus of Caraguatatuba of the Federal Institute of São Paulo (IFSP), in May 29, 2023. Therefore, this work articulates research, teaching and extension, in an interdisciplinary way, with the aim of examining the pedagogical possibilities of the thematic axis of black women in mathematics. To support the investigation, a theoretical review was carried out on this subject, through the search for academic works on the subject, using, for this, the “Google Scholar” tool. A questionnaire, which was designed to ascertain the views of those present on the topics covered, was answered by 15 high school students who attended the presentation. The results of this research point to the importance of the concept of intersectionality that takes into account gender, race and class identities when investigating the trajectories of black women who are professionally dedicated to mathematics, as researchers and educators.

Algebraic Structures on Smooth Vector Fields

The aim of this work is to investigate some algebraic structures of objects which are defined and related to a manifold. Consider L to be a smooth manifold and Γ∞(TL) to be the module of smooth vector fields over the ring of smooth functions C∞(L). We prove that the module Γ∞(TL) is projective and finitely generated, but it is not semisimple. Therefore, it has a proper socle and nonzero Jacobson radical. Furthermore, we prove that this module is reflexive by showing that it is isomorphic to its bidual. Additionally, we investigate the structure of the Lie algebra of smooth vector fields. We give some questions and open problems at the end of the paper. We believe that our results are important because they link two different disciplines in modern pure mathematics.

Tikaram and Chandrakala Dhananjaya: A collaborative couple in mathematics from Nepal

Within the history of mathematics and mathematics education in Nepal, Tikaram and Chandrakala Dhananjaya are relatively well-known figures for their two books Śiśubodha Taraṅgiṇī and Līlāvatī. This is despite there being almost no archival or manuscript materials offering a window into their lives: we have no letters, notebooks, diaries, or school records. Rather than focusing on either individual in isolation, in this article we present an argument for considering the Dhananjayas as an analytically indivisible collaborative couple in mathematics. Of the two aforementioned books, one is attributed to Chandrakala and the other to Tikaram; but in fact, both are translations of the same Sanskrit source text, Līlāvatī, into Nepali. By comparing the mathematical contents of these two works, which were published within a few years of each other, we explore what it means to be an author or translator of a mathematical text and propose different models of spousal collaboration which could plausibly have been adopted by the Dhananjayas. In the absence of documentary evidence, the impossibility of delineating each individual’s contributions removes the temptation to focus exclusively on apportioning credit. Instead, we offer the alternative perspective of considering what labour must have been undertaken to bring their books to publication.

Bringing the history of mathematics home: Entangled practices of domesticity, gender, and mathematical work

Although much scholarship on nineteenth and twentieth century mathematics has focused on processes of professionalization, historical mathematicians themselves rarely experienced their lives as neatly divisible into the professional and the private. Taking marriage as a focal point, this introduction brings the fruitful historiography of gender, collaborative couples, and domesticity in science into a broader conversation with the history of mathematics. By historicizing marriage and its relationship to mathematical careers, we lay the groundwork for the special issue which uncovers the myriad ways in which spousal collaboration and support have been central to mathematical work.

Pierre Gassendi: Humanism, Science, and the Birth of Modern Philosophy

Pierre Gassendi: Humanism, Science, and the Birth of Modern Philosophy

학교수학에서 무리수 도입으로 인한 담론 변화 분석

This study examined the method of discovering incommensurable quantities, the origin of irrational numbers, and the changes in Greek mathematics resulting from the discovery of these quantities from Sfard's commognitive perspective. In addition, in light of the history of mathematics, this study looked into changes in the discourse of school mathematics due to the introduction of irrational numbers. As a result of the analysis, the discovery of incommensurable quantities in the history of mathematics was an opportunity to change from empirical mathematics to formal and theoretical mathematics, and was an event that brought about changes in various mathematical concepts, proportion theory and roles of mathematical tools. In other words, the discovery of incommensurable magnitude transformed Greek mathematics into an incommensurable discourse. These changes in the history of mathematics appear similarly in the changes in the discourse of school mathematics due to the introduction of irrational numbers. The introduction of irrational numbers into school mathematics resulted in the application of formal definitions of numbers, changed the concepts of number and area, and led to the emergence of narratives that seemed to contradict previous discourses. It is understood that the introduction of irrational numbers has changed the discourse of school mathematics into a discourse that is incommensurable with the previous one. The analysis of this study could be basic data for the design of teaching and learning methods for students facing the task of transitioning to the incommensurable discourse of irrational number learning.

수학 스토리텔링 자료 활용이 수학적 창의성 및 태도에 미치는 효과

Objectives In this study, mathematical storytelling materials were developed using situations or mathematical history that students could easily experience with the aim of enhancing mathematical creativity and mathematical attitudes. In this way, the purpose of this study was to investigate the effect on the improvement of students' mathematical creativity and mathematical attitudes after conducting learning activities.
 Methods This study was conducted on 56 students in two classes in the second grade of 00 High School in the humanities of 00 metropolitan city. Based on the midterm exam results of the first semester of the second grade, two classes with similar averages were selected, one class was divided into experimental classes and the other class was divided into comparative classes, and 13 classes were conducted for about two months from May 3 to July 4, 2020. The experimental group (28 students) conducted classes using mathematical storytelling materials developed by the researcher, and the comparative group (28 students) conducted traditional classes centered on textbooks and teacher guidance.
 Results The results were obtained as follows by analyzing the effect of classes using mathematical storytelling materials on students' mathematical creativity and mathematical attitudes. First, mathematical creativity and mathematical attitude could be enhanced by classes using mathematical storytelling materials. Second, the mathematical creativity of each group of experimental and comparative classes was analyzed. Classes using mathematical storytelling materials were more effective in mathematical creativity and mathematical attitudes compared to traditional classes centered on textbooks and teacher guides for students in the upper, middle, and lower grades. Third, classes using math storytelling materials changed students' interest. However, students in the lower group tended to bring inferiority within the team. Therefore, in classes using math storytelling materials, it should be guided that lower-class students should learn in cooperation with other students without feeling inferior.
 Conclusions In conclusion, the experimental class that used mathematical storytelling data was more effective in mathematical creativity and mathematical attitudes than the comparative class.

Note on Leonardo’s Combinatorial Approach

The purpose of this research is to carry out a study of Leonardo's combinatorial approach so that it is possible to visualize these numbers through combinatorial interpretation. Thus, research is being developed regarding methods and approaches to linear and recurring sequences, based on the combinatorial study of the Fibonacci sequence. In fact, the Fibonacci sPquence is related to other sequences, one of which is the Leonardo sequence, which has similarities with the Fibonacci numbers according to some researchers in the field. Given this scenario, the present research addresses the combinatorial interpretation of Leonardo's sequence, allowing the definition of Leonardo's combinatorial model, considering the notion of board and bracelets in Lucas' sequence. As research results, the study deals with the integration of sequence content with the area of Combinatorial Analysis, allowing a mathematical advancement of Leonardo's sequence. Furthermore, you can visualize the sequence numbers in front of the tiles. The aspects studied in this research are linked to the teaching of sequences in the History of Mathematics, allowing the teaching of Mathematics.

The Construction of Definitions Through Padovan’s Combinatorial Model: An Investigation With Didactic Engineering in an Initial Education Course for Mathematics Teachers

Background: Given the oversight of specific topics in the history of mathematics books, this research was motivated by the extensive coverage of the Fibonacci sequence. In addition, the existence of the Padovan sequence, which is considered a Fibonacci cousin, stands out. Objectives: Investigating the Padovan sequence, building its definition through a combinatorial model using manipulative materials based on the theory of didactical situations in the initial mathematics teacher education course context. Design: The research methodological design follows didactic engineering, and a didactic teaching situation is created to investigate the Padovan sequence. Thus, manipulative material was developed to facilitate the teaching process and the construction of the sequence definition. Settings and participants: The interventions were done in the mathematics degree course of a higher education institution in Fortaleza. Five students enrolled in the component of History of Mathematics participated in the study. Data collection and analysis: Data were collected during classes, recorded through photos and audio recordings, based on didactic engineering and the theory of didactical situations. Results: The most relevant result of this study is constructing the definition of the Padovan sequence through the manipulative material. Conclusions: We concluded that the research allowed an investigation of the Padovan sequence, enabling the visualisation of its terms and their integration with other mathematical contents, contributing to teaching these numbers.

The Story of Proof: Logic and the History of Mathematics by John Stillwell

The Story of Proof: Logic and the History of Mathematics by John Stillwell

Fundamentals of e-learning in mathematics teaching: future perspectives

Technology in education has changed math instruction, with e-learning being one of the biggest changes. This article examines the origins of e-learning in mathematics education and its future applications. In recent years, e-learning has become a key part of modern mathematics education, helping pupils study, focus, and become proficient. Recently, e-learning has become vital to mathematical education. By giving students interactive mathematical material, educators may make the classroom more engaging. This enables educators to accommodate different learning styles and make the classroom more entertaining for everyone. Thus, employing a range of e-learning tools in mathematics classes may boost student learning. Future math education in regular classrooms is likely to utilize more e-learning. Artificial intelligence, virtual reality, and student analytics may improve math instruction and personalize it. Hybrid and online learning methods like remote education may also make mathematics education more accessible. Math education has changed significantly due to e-learning technologies and technological advances. These improvements caused these modifications. E-learning's importance as a way to make mathematics instruction more productive and enjoyable has expanded in recent years. Artificial intelligence, virtual reality, and student analytics will likely play a larger role in spreading mathematical knowledge in the near future. Thus, pupils' mathematical skills will increase and their teaching will be more personalized. Due to online and hybrid teaching methods, more individuals can learn arithmetic. Future mathematics instruction will be more effective and efficient owing to modern technology.