scholarly journals A Comparative Study on Three Pioneer Methods for the Square Roots

2021 ◽  
Vol 2 (2) ◽  
pp. 89-96
Author(s):  
Krishna Kanta Parajuli
Keyword(s):  
South Asian ◽  
Analytical Study ◽  
History Of Mathematics ◽  
Square Roots ◽  
Mathematical Ideas ◽  
Wide Range ◽  
Fertile Ground ◽  
Famous Book ◽  
History Of ◽  
Mathematical Treatise

During the classical period, the South Asian region had an illustrious history of mathematics, and it was regarded as fertile ground for the birth of pioneer mathematicians that produced a wide range of mathematical ideas and creations that made significant contributions. Among them, three creative personalities Bhaskaracarya, Gopal Pande and Bharati Krishna Tirthaji and their specific methods to find square roots are focused on this study. The analytical study of their methods is expressing in comparison with similarities, variety and simplicity. Each of the three mathematical treatise has its own formula for calculating the square roots. The Lilavati seems to have some effect upon the Vedic and Pande’s systems. In spite of having influenced by Lilavati, Gopal Pande disagreed on the problems regarding square roots and cube roots. To prove his point, Gopal Pande used the unitary method against the method described in Bhaskaracarya's famous book Lilavati. In the case of practicality and simplicity, the Vedic method is more practical, interesting and simpler to understand for the mathematics learners in comparison to the other two methods.

Three Classical Methods to find the Cube Roots: A Connective Perspective on Lilavati, Vedic and Pande's Procedures

2021 ◽  
Vol 4 (1) ◽  
pp. 23-32
Author(s):  
Krishna Kanta Parajuli
Keyword(s):  
Comparative Study ◽  
South Asian ◽  
History Of Mathematics ◽  
The Other ◽  
Cube Root ◽  
Mathematical Ideas ◽  
Famous Book ◽  
History Of ◽  
The Comparative Study ◽  
South Asian Region

South Asian region has made a glorious history of mathematics. This area is considered as fer- tile land for the birth of pioneer mathematicians who developed various mathematical ideas and creations. Among them, three innovative personalities are Bhaskaracarya, Gopal Pande and Bharati Krishna Tirthaji and their specific methods to find cube root are mainly focused on this study. The article is trying to explore the comparative study among the procedures they adopt. Gopal Pande disagrees with the Bhaskaracarya's verse. He used the unitary method against that method mentioned in Bhaskaracarya's famous book Lilavati to prove his procedures. However, the Vedic method by Tirthaji was not influenced by the other two except for minor cases. In the case of practicality and simplicity, the Vedic method is more practical and simpler to understand for all mathematical learners and teachers in comparison to the other two methods.

Transcultural Networks and Connectivities: The Circulation of Mathematical Ideas between India and England in the Nineteenth Century

2021 ◽  
pp. 097318492110645
Author(s):  
Dhruv Raina
Keyword(s):  
Nineteenth Century ◽  
Mathematics Teaching ◽  
First Generation ◽  
History Of Mathematics ◽  
East India Company ◽  
Institutional Autonomy ◽  
Mathematical Research ◽  
Mathematical Ideas ◽  
History Of ◽  
And Mathematics

The nineteenth century has been characterised as a period in which mathematics proper acquired a disciplinary and institutional autonomy. This article explores the intertwining of three intersecting worlds of the history of mathematics inasmuch as it engages with historicising the pursuit of novel mathematics, the history of disciplines and, more specifically, that of the British Indological writings on Indian mathematics, and finally, the history of mathematics education in nineteenth century India. But, more importantly, the article is concerned with a class of science and mathematics teaching problems that are taken up by researchers—in other words, science and mathematics teaching problems that lead to scientific and mathematical research. The article argues that over a period of 50 years, a network of scholars crystallised around a discussion on mathematics proper, the history of mathematics and education. This discussion spanned not just nineteenth-century England but India as well, involving scholars from both worlds. This network included Scottish mathematicians, East India Company officials and administrators who went on to constitute the first generation of British Indologists, a group of mathematicians in England referred to as the Analytics, and traditional Indian scholars and mathematics teachers. The focus will be on the concerns and genealogies of investigation that forged this network and sustained it for over half a century.

The Representational Value of Hats

2008 ◽  
Vol 14 (1) ◽  
pp. 4-10
Author(s):  
Jane M. Watson ◽  
Noleine E. Fitzallen ◽  
Karen G. Wilson ◽  
Julie F. Creed
Keyword(s):  
Middle School ◽  
Middle School Students ◽  
History Of Mathematics ◽  
Graphical Representations ◽  
Data Sets ◽  
School Students ◽  
Mathematical Ideas ◽  
History Of ◽  
The Way

The literature that is available on the topic of representations in mathematics is vast. One commonly discussed item is graphical representations. From the history of mathematics to modern uses of technology, a variety of graphical forms are available for middle school students to use to represent mathematical ideas. The ideas range from algebraic relationships to summaries of data sets. Traditionally, textbooks delineate the rules to be followed in creating conventional graphical forms, and software offers alternatives for attractive presentations. Is there anything new to introduce in the way of graphical representations for middle school students?

The role of diagram materiality in mathematics

2018 ◽  
Vol 9 (2) ◽  
pp. 183-201 ◽  
Author(s):  
Anna Kiel Steensen ◽  
Mikkel Willum Johansen
Keyword(s):  
History Of Mathematics ◽  
Diagrammatic Reasoning ◽  
Mathematical Ideas ◽  
History Of ◽  
Physical Features

Abstract Based on semiotic analyses of examples from the history of mathematics, we claim that the influence of the material aspects of diagram tokens is anything but trivial. We offer an interpretation of examples of diagrammatic reasoning processes in mathematics according to which the mathematical ideas, arguments, and concepts in question are shaped by the physical features of the chosen diagram tokens.

Historically Speaking—: Identification of Napier's Inequalities

1970 ◽  
Vol 63 (1) ◽  
pp. 67-71
Author(s):  
Sidney G. Hacker
Keyword(s):  
Mathematical Knowledge ◽  
History Of Mathematics ◽  
Real Variable ◽  
Numerical Resolution ◽  
Wide Range ◽  
History Of

The discovery of logarithms by John Napier (1550-1617) is a well known facet in the history of mathematics. His singular accomplishment in defining the logarith mic function of a real variable by providing a numerical description of it, over a wide range of its argument, at small intervals and to several (decimal) places, antedated by many yeara the development of funda mental concepts which the modern stu dent regards as necessary to achieve even the same limited goals. Napier success fully bridged, solely in regard to this function, these lacunae in the mathematical knowledge of bis day. It has long been of interest to identify the concepts which he intuitively invoked. This is not done, it should be clearly said, with any idea of assigning to him some kind of priority for them, but merely in the interests of a elearer appreciation of the ingenuity he displayed and the power of his methods. Two inequalities that he obtained are the key to his numerical resolution of the problem and his consequent table of logarithms. The analytical identification of these inequalities appears to have been overlooked. Before exhibiting this identi-fication we shall speak of the fundamental role that these inequalities played. In the interests of intelligibility we first recollect a few familiar facts regarding Napier's formulation of the problem.

scholarly journals Sīdhu (Śīdhu): the Sugar Cane “Wine” of Ancient and Early Medieval India

2020 ◽  
Vol 8 ◽  
pp. 36-56
Author(s):  
James McHugh
Keyword(s):  
South Asian ◽  
Sugar Cane ◽  
Broad Context ◽  
Early Medieval ◽  
Textual Evidence ◽  
Wide Range ◽  
Drinking Culture ◽  
History Of ◽  
Medieval India

This article considers the nature of one particular drink made from sugar cane called sīdhu (usually m., also śīdhu), exploring the evidence from textual sources. Other drinks were made with sugar cane products, such as āsavas, medicinal ariṣṭas, and the drink called maireya, but I will not consider those here.   As I argue, sīdhu was the basic fermented sugar cane drink, not strongly characterized by additives—“plain” sugar-wine as it were. Though in a manner typical of premodern Indic alcohol culture, even this one drink was a complex and variable affair. Rather than consider this drink in medical sources alone—important as that evidence may be—my methodology here is to examine the history of this drink in the light of a wide range of textual evidence, placing this drink in the broad context of pre-modern South Asian drinking culture.

Review: Mathematics, Culture, and Power

1998 ◽  
Vol 29 (3) ◽  
pp. 357-363
Author(s):  
Richard S. Kitchen ◽  
Joanne Rossi Becker
Keyword(s):  
Mathematical Knowledge ◽  
Cultural Anthropology ◽  
History Of Mathematics ◽  
Mathematical Community ◽  
Cultural Groups ◽  
Mathematical Ideas ◽  
Tribal Societies ◽  
History Of ◽  
P 16 ◽  
Definition Of

Arthur B. Powell and Marilyn Frankenstein's new book, Ethnomathematics: Challenging Eurocentrism in Mathematics Education, illuminates for our consideration a body of very practical mathematical knowledge largely discounted in the traditional mathematical community when compared with the abstract, theoretical mathematical knowledge typically valued highly by mathematicians. Ethnomathematics has caused us to call into question which mathematical knowledge really counts and thus has come to signify more than just “the study of mathematical ideas of nonliterate peoples” (a definition first offered by Marcia and Robert Ascher in the early 1980s in their paper, “Ethnomathematics,” reprinted as chapter 2 of this volume, p. 26). Editors Powell and Frankenstein use, instead, the broader definition of ethnomathematics provided in the book's opening chapter, “Ethnomathematics and Its Place in the History and Pedagogy of Mathematics,” by Ubiratan D'Ambrosio, a Brazilian mathematics educator whom many consider the intellectual progenitor of ethnomathematics. D'Ambrosio defines ethnomathematics as the mathematics that all cultural groups engage in, including “national tribal societies, labor groups, children of a certain age bracket, professional classes, and so on” (p. 16). Each group, including mathematicians, has its own mathematics. From D'Ambrosio's perspective, ethnomathematics exists at the confluence of the history of mathematics and cultural anthropology, overcoming the Egyptian/Greek differentiation between practical and academic mathematics.

Teaching Mathematics through the Art of Kolam

2007 ◽  
Vol 12 (8) ◽  
pp. 422-428
Author(s):  
Syamala Chenulu
Keyword(s):  
Mathematics Instruction ◽  
History Of Mathematics ◽  
Vital Role ◽  
Global Perspective ◽  
Teaching Mathematics ◽  
Mathematical Ideas ◽  
Mathematics Educators ◽  
History Of ◽  
K 12 ◽  
Multicultural Perspective

One goal of the NCTM's connections Standard is that mathematics instruction pre- K–12 should “enable all students to recognize and apply mathematics in contexts outside of mathematics” (NCTM 2000, p. 64). Art of all kinds provides opportunities to address this goal. Moreover, many mathematics educators, including myself, believe that it is important and beneficial to provide a multicultural perspective in our classrooms. “Knowledge of the ideas of others can enlarge our view of what is mathematical and, in particular, add a more humanistic and global perspective to the history of mathematics. This enlarged view, in which mathematical ideas are seen to play a vital role in diverse human endeavors, provides us with a richer and fuller picture of mathematics” (Ascher 2002, p. 200).

scholarly journals Disseminação do estudo de Análise Matemática e a Repercussão de Instituzioni Analitiche de Maria Gaetana Agnesi

2021 ◽  
Vol 23 (1) ◽  
pp. 810-832
Author(s):  
Roseli Alves De Moura ◽  
Fumikazu Saito
Keyword(s):  
Mathematics Education ◽  
Mathematical Analysis ◽  
Methodological Approach ◽  
History Of Mathematics ◽  
Mathematical Work ◽  
Documentary Analysis ◽  
History Of ◽  
Mathematical Treatise

ResumoNeste artigo apresentamos alguns desdobramentos relativos à divulgação e repercussão da obra Instituzioni Analitiche ad uso dela giuveniu italiana, por ocasião de sua publicação em Milão, em 1748, e nos cinquenta anos posteriores, sobretudo em função do direcionamento dado por Maria Gaetana Agnesi (1718-1799) ao seu tratado matemático. Para compreender o lugar ocupado pela estudiosa e sua obra na história da matemática, é essencial situá-la em malhas contextuais mais amplas, de modo a abarcar parte do processo de circulação dos discursos e da divulgação da álgebra e do cálculo, naquele contexto. Mediante este enfoque, a abordagem metodológica adotada neste trabalho se baseou em uma análise documental, a partir da articulação das esferas epistemológica, historiográfica e contextual, na concepção de Alfonso-Goldfarb e Ferraz. Considerando que uma interligação entre tais esferas constituí uma empreitada não trivial, nosso corpus é composto pela obra matemática Instituzioni Analitiche, as correspondencias de Agnesi com seus contemporâneos, além de alguns trabalhos de estudiosos que se debruçaram sobre a vida e obra da estudiosa, como forma de trazer à luz indícios de que houve interesse e comprometimento de Agnesi em divulgar seu tratado para além do solo milanês, e à vista disso, este teve ampla repercussão, a despeito de ter sido esquecido, em sua maioria, sob muitos aspectos, pelos historiadores da matemática.Palavras-chave: História da matemática, Educação matemática, Maria Gaetana Agnesi, Análise matemática, História das ciências.AbstractIn this article, we present some developments related to the dissemination and repercussion of the work Instituzioni Analitiche ad usage della giuveniu Italiana, on its publication in Milan, in 1748, and the following fifty years, mainly due to the direction given by Maria Gaetana Agnesi (1718- 1799) to her mathematical treatise. To understand the place occupied by the scholar and her work in the history of mathematics, it is essential to place it in broader contextual networks, to cover part of the process of circulation of discourses and the dissemination of algebra and calculus in that context. From this perspective, the methodological approach adopted in this work was based on a documentary analysis, from the articulation of the epistemological, historiographical, and contextual spheres, in Alfonso-Goldfarb and Ferraz’s conception. Considering that an interconnection between such spheres constitutes a non-trivial endeavour, our corpus is composed of the mathematical work Instituzioni Analitiche, Agnesi’s correspondence with contemporaries, and some studies based on her life and work, bringing to light evidence that she was interested in and committed to having her treaty publicised beyond Milanese lands, which gave it extensive repercussion. However, despite her importance, Agnesi has been forgotten, in many aspects, by the historians of mathematics.Keywords: History of mathematics, Mathematics education, Maria Gaetana Agnesi, Mathematical analysis, History of sciences.ResumenEn este artículo presentamos algunos desarrollos relacionados con la difusión y repercusión de la obra Instituzioni Analitiche ad use della giuveniu Italiana, en el marco de su publicación en Milán, en 1748, y los siguientes cincuenta años, principalmente debido a la dirección que Maria Gaetana Agnesi (1718-1799) dió a su tratado matemático. Para comprender el lugar que ocupa la académica y su obra en la historia de las matemáticas, es fundamental ubicarla en redes contextuales más amplias, para abarcar parte del proceso de circulación de los discursos y la difusión del álgebra y el cálculo en ese contexto. Desde esta perspectiva, el enfoque metodológico adoptado en este trabajo se basó en un análisis documental, a partir de la articulación de los ámbitos epistemológico, historiográfico y contextual, en la concepción de Alfonso-Goldfarb y Ferraz. Considerando que la interconexión entre tales esferas constituye un esfuerzo no trivial, nuestro corpus está compuesto por el trabajo matemático Instituzioni Analitiche, la correspondencia de Agnesi con sus contemporáneos, y algunos estudios basados en su vida y obra, sacando a la luz evidencias de su interés y comprometimiento a que su tratado se publicitara más allá de las tierras milanesas, lo que le dio una amplia repercusión. Sin embargo, a pesar de su importancia, Agnesi ha sido olvidada, en muchos aspectos, por los historiadores de las matemáticas.Palabras clave: Historia de las matemáticas, Educación matemática, Maria Gaetana Agnesi, Análisis matemático, Historia de las Ciencias.

Afterword

2016 ◽  
pp. 237-240
Author(s):  
Susan Ash
Keyword(s):  
Mass Media ◽  
Identity Construction ◽  
Institutional Identity ◽  
Victorian Era ◽  
Wide Range ◽  
Fertile Ground ◽  
History Of ◽  
Christian Family ◽  
Public Meanings ◽  
As If

The Afterword reiterates how Barnardo orchestrated metaphors, narratives and spectacles to circulate his desired public meanings on a grand scale in the Victorian era. This section speculates that Barnardo used a form of identity construction normally associated with the 20th century, synthetic personalization, which Norman Fairclough argues works to create social spaces that link separate individuals who aren’t present, but nevertheless appear to communicate, simulating the bonds of friendship, loyalty and family. That is, Barnardo used mass media to constitute and perform his identity as the ‘Father’ of the world’s largest and most Christian ‘family’, creating the context for his supporters to feel as if each were individually a significant, contributing member of the Barnardo family. Thus, by using the technologies available to him as a Victorian, Barnardo converted the chaotic work of reform and charity into the perception of a unified, institutional identity and community. His use of metaphor, narrative and spectacle offers fertile ground for further scholarly investigation into a wide range of studies, including the history of marketing and production as well as philanthropy and child reform.

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