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

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.

2021 ◽  
Vol 2 (2) ◽  
pp. 89-96
Author(s):  
Krishna Kanta Parajuli

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.


Author(s):  
Marko Geslani

The introduction reviews the historiographic problem of the relation between fire sacrifice (yajña) and image worship (pūjā), which have traditionally been seen as opposing ritual structures serving to undergird the distinction of “Vedic” and “Hindu.” Against such an icono- and theocentric approach, it proposes a history of the priesthood in relation to royal power, centering on the relationship between the royal chaplain (purohita) and astrologer (sāṃvatsara) as a crucial, unexplored development in early Indian religion. In order to capture these historical developments, it outlines a method for the comparative study of ritual forms over time.


2017 ◽  
Vol 21 (3) ◽  
pp. 208-223
Author(s):  
Byung Mun Lee

Purpose The purpose of this paper is to describe and analyze the rules on the formation of contracts under Korean law and the Contracts for the International Sale of Goods (CISG) in a comparative way and introduce the relevant proposed rules under the Amendment Draft of the Korean Civil Code (KCC). In addition, it attempts to compare and evaluate them in light of the discipline of comparative law. Design/methodology/approach In order to achieve the purposes of the study, it executes a comparative study of the rules as to the formation of contracts of the CISG, Korean law and the Amendment Draft of the KCC. The basic question for this comparative study is placed on whether a solution from one jurisdiction is more logical than the others and to what extent each jurisdiction has responded to protect the reasonable expectations of the parties in the rules as to the formation of contracts. Findings The comparative study finds that most of the rules under the CISG are quite plausible and logical and they are more or less well reflected in the proposals advanced by the KCC amendment committee. On the other hand, the other rules under the CISG which have brought criticisms in terms of their complexity and inconsistent case law invite us their revision or consistent interpretation. The drawbacks of the CISG have also been well responded in the Amendment Draft of the KCC. Nevertheless, it is quite unfortunate that the Amendment Draft of the KCC still has a rule that regards any purported performance with non-material alteration of the terms of an offer as an acceptance. Originality/value This study may provide legal and practical advice to both the seller and the buyer when they enter into a contract for international sales of goods. In addition, it may render us an insight into newly developed or developing rules in this area and show us how they interact with each other. Furthermore, it may be particularly useful in Korea where there is an ongoing discussion for revision of the KCC.


1989 ◽  
Vol 111 ◽  
pp. 205-213 ◽  
Author(s):  
M.W. Feast

The Mira variables make important contributions to four of the main problems under discussion at this meeting, (1) stellar pulsation, (2) stellar evolution, (3) the morphology and history of the Galaxy, (4) the comparative study of different galaxies. The Miras also show how these rather different fields of study overlap, so that it is no longer possible to deal with any one field in isolation.


Africa ◽  
1928 ◽  
Vol 1 (4) ◽  
pp. 413-428 ◽  
Author(s):  
Werner Eiselen

The several forms of preferential mating, such as cross-cousin marriage, sororate and levirate, are well known and have been reported from all the ethnographic provinces of the world. Lately Lowie and Rivers have devoted special chapters in their books on social organization to the comparative study of these important institutions. Lowie has pointed out that there is strong evidence for the correlation of sororate and levirate. The later publication of Rivers hardly serves to make these matters any clearer than Lowie's work. Although the latter scholar, with Tylor and others, recognized the close connexion existing between sororate and levirate, the evidence at his disposal did not allow him to arrive at a similar conclusion with regard to the other forms of preferential marriage. Accordingly he had to treat them, for the time being, as institutions of independent origin.


2010 ◽  
Vol 53 (3) ◽  
pp. 747-770 ◽  
Author(s):  
RICHARD BOURKE

ABSTRACTThis article recovers the rationale behind the project to found a ‘new’ British history undertaken by J. G. A. Pocock in the early 1970s, and contrasts this with the approach adopted in the subsequent historiography. The article argues that British history as conceived by Pocock was intended to transcend the parochialism of national history whilst also rehabilitating the writing of imperial history without succumbing to the temptations of metropolitan whiggism. Pocock's perspective was constructed against the backdrop of a British withdrawal from empire and led him to a neo-Seeleyan interest in the dynamics of imperial expansion and retrenchment. While this process is best understood through the comparative study of empires, any such undertaking raises complex questions about the ultimate subject of historical inquiry and the nature of historical explanation. In addressing these questions, this article distinguishes the ambition to write the history of a polity from the aim of writing histories of ‘party’ as originally formulated by the historians of the Scottish enlightenment whose work has been among Pocock's abiding subjects of investigation.


1896 ◽  
Vol 59 (353-358) ◽  
pp. 137-141 ◽  

In a paper published in the ‘Philosophical Transactions’ (Series B, 1894), the comparative study of the spore-bearing members of the Lycopodineæ, including the Psilotaceæ, has led to the conclusion that there is reasonable probability that septation of sporangia originally simple, to form synangia, has taken place; that a septate body (synangium) may be homologous with a non-septate body (simple sporangium); and that there is no essential difference between tissue which will form septa or trabeculæ, and that which will form spores, since the tissues can mutually undergo conversion one into the other. But the considerations there brought forward do not amount to an actual demonstration that septation has occurred.


2018 ◽  
Vol 18 (1) ◽  
pp. 42-67
Author(s):  
Markéta Křížová

Abstract The present article represents a partial outcome of a larger project that focuses on the history of the beginnings of anthropology as an organized science at the end of the nineteenth and the beginning of the twentieth centuries, in the broader socio-political context of Central Europe. Attention is focused especially on the nationalist and social competitions that had an important impact upon intellectual developments, but in turn were influenced by the activities of scholars and their public activities. The case study of Vojtěch (Alberto) Frič, traveler and amateur anthropologist, who in the first two decades of the twentieth century presented to European scientific circles and the general public in the Czech Lands his magnanimous vision of the comparative study of religions, serves as a starting point for considerations concerning the general debates on the purpose, methods, and ethical dimensions of ethnology as these were resonating in Central European academia of the period under study.


AMERTA ◽  
2020 ◽  
Vol 38 (2) ◽  
pp. 129-144
Author(s):  
Erlin Novita Idje Djami

Abstract. Megalithic Of Gunung Srobu In Melanesian Cultural Context. Megalithic is one of the cultural elements that is discovered worldwide, and it is often used as evidence for cultural hyperdiffusion theory. Such a cultural element is also present in the Melanesian region. However, there is still debate among scholars as to where it comes from and when it was introduced to this area. In this context, the recently excavated megalithic site in Gunung Srobu in Youtefa Bay, Jayapura, Papua may shed light on this matter. This paper is intended to describe the megalithic findings of Gunung Srobu and then compare them with other megalithic findings in several sites in the Melanesian region. The comparative study aims to find out the similarities and differences between Gunung Srobu megalithic and the other Melanesian megalithic as well as to know the position of Gunung Srobu in the Melanesian regional. The method used includes surveys, excavations, and literature studies. The result shows that Gunung Srobu is a very complex megalithic site in the region with very varied shapes and types. The date from around the 4th Century AD put Gunung Srobu as the oldest megalithic site in the region which is likely to occupy a central position in the megalithic distribution in the Melanesian Region. Abstrak. Megalitik merupakan salah satu unsur budaya yang ditemukan sangat luas di dunia dan sering menjadi bukti bagi teori hiperdifusi. Unsur budaya megalitik juga ditemukan di kawasan Melanesia. Namun, banyak ahli masih memperdebatkan asal-usul dan waktu persebarannya. Dalam konteks ini, temuan megalitik yang baru-baru ini ditemukan dalam penggalian di situs Gunung Srobu, Teluk Youtefa, Papua, mungkin dapat menjelaskan masalah ini. Tulisan ini dimaksudkan untuk mendeskripsikan temuan megalitik di Gunung Srobu dan membandingkannya dengan temuan megalitik di beberapa situs lainnya di kawasan Melanesia. Tujuannya adalah untuk mengetahui persamaan dan perbedaan unsur megalitik antara yang ada di Gunung Srobu dan di situs Melanesia lainnya, serta mengetahui kedudukan megalitik Gunung Srobu di kawasan Melanesia. Metode yang digunakan mencakup survei, ekskavasi, dan studi pustaka. Hasilnya menunjukkan bahwa Gunung Srobu merupakan situs megalitik yang sangat kompleks di kawasan itu dengan bentuk dan jenis yang sangat bervariasi. Pertanggalan yang berasal dari sekitar abad ke-4 M menempatkannya sebagai megalitik tertua yang kemungkinan menempati posisi sentral dalam persebaran megalitik di kawasan Melanesia.


2021 ◽  
pp. 130-139
Author(s):  
Т.В. ГОВЕНЬКО

В статье анализируются методологические взгляды на миф выдающегося русского ученого А.Н. Веселовского (1838–1906). Мифологическая проблематика стала для Веселовского одной из центральных еще в молодые годы, когда он работал над дипломной работой, и оставалась таковой навсегда, о чем свидетельствуют его исследования как теоретического, так и сравнительно-исторического характера о международном фольклоре, средневековой словесности и литературе поздних веков. Отказавшись следовать канонам «мифологической школы», ученый поставил перед собой задачу разработать новый метод научного анализа, который позволит изучать эволюцию и генезис художественных форм как с формальной, так и с идейно-содержательной точек зрения. В этой статье мы ставим перед собой задачу собрать в единое целое суждения Веселовского о мифе, оценить их теоретический потенциал и доказать, что диалектика мифа и есть тот самый метод, благодаря которому он создал уникальную верификационную систему объяснения исторических изменений такого феномена как поэзия. Для раскрытия этой темы наиболее важными для нас являются: дипломная работа ученого (1857), статьи-рецензии «Заметки и сомнения о сравнительном изучении средневекового эпоса» (1868), «Сравнительная мифология и ее метод» (1873), теоретические статьи «Из введения в историческую поэтику. Вопросы и ответы» (1894), «Из истории эпитета» (1895), «Психологический параллелизм и его формы в отражении поэтического стиля» (1898), «Синкретизм древнейшей поэзии и начала дифференциации поэтических родов» (1899), в том числе неопубликованные при жизни Веселовского труды: «Поэтика сюжетов» (1913), «Определение поэзии» (1959) и другие. The article analyzes the methodological views on the myth of the outstanding Russian scientist A.N. Veselovsky (1838-1906). Mythological issues became for Veselovsky one of the central in his young years, when he worked on the graduation work, and turned into his lifelong priority. This is evidenced by his research of both theoretical and comparative historical nature about the international folklore, medieval literature and literature of late centuries. By refusing to follow the canons of the "mythological school", the scientist set himself the task of developing a new method of scientific analysis, which allowed to study the evolution and genesis of artistic forms with formal and ideological as well as meaningful points of view. In this article, we set ourselves the task of collecting judgments of Veselovsky about myth, to evaluate their theoretical potential and prove that the dialectic of myth is that very method, thanks to which he created a unique verification system for explaining historical changes to such a phenomenon as poetry. The most important for our topic is the scholar's diploma work (1857), critical reviews «Notes and doubts about the comparative study of the medieval epic» (1868), «Comparative mythology and its method» (1873), theoretical articles «From the introduction to historical poetics. Questions and Answers» (1894), «From the history of the epithet» (1895), «Psychological parallelism and its form in the reflection of the poetic style» (1898), «Syncretism of ancient poetry and the beginning of differentiation of poetic labor» (1899), including works of Veselovsky unpublished during his lifetime: «Excursions in the Fiction» (1913), «Definition of Poetry» (1959) and others.


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