YouTube Video Thumbnail

Ganita Bharati

Published in Association with Bulletin of The Indian Society for History of Mathematics

Current Volume: 44 (2022 )

ISSN: 0970-0307

Periodicity: Half-Yearly

Month(s) of Publication: June & December

Subject: Mathematics

DOI: https://doi.org/10.32381/GB

Online Access is Free for Life Member

250

Ganita Bharati, the Bulletin of the Indian Society for History of Mathematics is devoted to publication of significant original articles in history of Mathematics and related areas. Although English is the official language of the journal, an article of exceptional merit written in French, German, Sanskrit or Hindi will also be considered only as a special case.

The ISHM aims to Promote study, research and education in history of mathematics. It provides a forum for exchange of ideas and experiences regarding various aspects of history of mathematics. In addition to the annual conferences, ISHM aims at organizing seminars/symposia on the works of ancient, medieval and modern mathematics, and has been bringing out the bulletin Ganita Bharati. Scholars, Teachers, Students and all lovers of mathematical sciences are encouraged to join the Society.

ProQuest
EBSCO
Zentralblatt Math
Mathematical Review
Genamics(JournalSeek)

 

Editor
S.G. Dani

UM-DAE Centre for Excellence in Basic Sciences
Vidyanagari Campus of University of Mumbai
Kalina, Mumbai 400098, India


Managing Editor
Ruchika Verma

Ramjas College
University of Delhi
Delhi-110007, India


Assistant Editor
V. M. Mallayya

Meltra-A23, 'Padmasree'
T. C. 25/1974(2)
Near Gandhari Amman Kovil,
Thiruvananthapuram, Kerala,
PIN: 695001, India.


Members
S.M.S. Ansari

Muzammil Manzil Compound
Dodhpur Road
Aligarh 202002, India.


R. C. Gupta

R-20, Ras Bahar Colony
P. O. Lahar Gird,
Jhansi-284003, India


Kim Plofker

Department of Mathematics
Union College
Schenectady, NY 12308
USA


Mohammad Bagheri

Encyclopedia Islamic Foundation
PO Box 13145-1785
Tehran
Iran


Takao Hayashi

Science & Engg. Research Institute
Doshisha University
Kyotanabe Kyoto 610-0394
Japan


F. Jamil Ragep

Islamic Studies
McGill University
Morrice Hall, 3485 McTavish Street
Montreal, Quebec,
Canada H3A 1Y1


S. C. Bhatnagar

Department of Mathematics
University of Nevada
Las Vegas
USA


Jan P. Hogendljk

University of Utrecht
P.O. Box 80010
3508 TA Utrecht
The Netherlands


S. R. Sarma

Höhenstr. 28
40227 Düsseldorf
Germany


Umberto Botttazzni

Universita degli Studi di Milano
Dipartimento di Matematica
Federigo Enriques Via Saldini 50
20133, Milano 
Italy


Jens Hoyrup

Roskilde University
Section for Philosophy and Science Studies
Denmark


Karine Chemla

REHSEIS-CNRS and
University Paris7, 75019,
Paris, France


Subhash Kak

Dept. of Computer Sc.
MSCS 219
Oklahoma State University
Stillwater, OK 74078, USA


Chikara Sasaki

University of Tokyo
3-8-1 Komaba,
Meguro-Ru,
Tokyo 153-8902
Japan


J. W. Dauben

The Graduate Centre
CUNY, 33, West 42nd Street
New York, NY 10036
U.S.A.


Victor J. Katz

University of the D.C.
4200 Connecticut Ave.
N.W.Washington, D.C 20008
USA


M. S. Sriram

Prof. K.V. Sarma Research Foundation
Venkatarathnam Nagar
Adyar, Chennai - 600020

 


Nachum Dershowitz

Department of Computer Science
Tel Aviv University,
Tel Aviv
Israel


Wenlin Li

Academy of Mathematics & Systems Science
Chinese Academy of Science,
No. 55, Zhongguancun East Road,
Haidan District, Beijing, 100190,
China


Ioannis M. Vandoulakis

The Hellenic Open Unversity
School of Humanities
23, Syngrou Avenue,
GR-11743, Athens, Greece.


Nachum Dershowitz

Department of Computer Science
Tel Aviv University,
Tel Aviv
Israel


Wenlin Li

Academy of Mathematics & Systems Science
Chinese Academy of Science,
No. 55, Zhongguancun East Road,
Haidan District, Beijing, 100190,
China


Ioannis M. Vandoulakis

The Hellenic Open Unversity
School of Humanities
23, Syngrou Avenue,
GR-11743, Athens, Greece.


Enrico Giusti

Dipartimento di Matematica
Viale Morgagni, 67/A
I-50134 Firenze, Italy


Jean-Paul Pier

Société mathématique du Luxembourg
117 rue Jean-Pierre Michels
L-4243 Esch-sur-Alzette
Luxembourg


D. E. Zitarelli

Department of Mathematics
Temple University
Philadelphia, PA 19/22, USA.


Volume 44 Issue 2 , (Jul-2022 to Dec-2022)

Pre-Eudoxean Geometric Algebra

By: Stelios Negrepontis , Vasiliki Farmaki , Demetra Kalisperi

Page No : 107-152

Abstract
In the light of our re-interpretation of Plato’s philosophy and of our reconstruction of the proofs of quadratic incommensurabilities by the Pythagoreans, Theodorus, and Theaetetus, in terms of periodic anthyphairesis, we re-examine the Geometric Algebra hypothesis in Greek Mathematics, originally enunciated by Zeuthen and Tannery and supported by van der Waerden and Weil, but challenged by Unguru and several modern historians. Our reconstruction of these proofs employs, for the computation of the anthyphairetic quotient at every step, the solution of a Pythagorean Application of Areas, either in excess or in defect, and is thus qualified as “school algebra” in the spirit of van der Waerden. For the Application of Areas in defect in the Theaetetean Books X and XIII of the Elements, by which the alogoi lines are characterized, the periodic nature of their anthyphairesis is revealed by the Scholia in Eucliden X.135 and 185 and by our re-interpretation of the ill-understood Meno 86e-87b passage. In conclusion, the pre-Eudoxean uses of Applications of Areas fall under the description of “school algebra” solutions of quadratic equations. It is interesting that these early uses stand in sharp contrast to the later uses of more general versions of Application of Areas by Appolonius in his Conic Sections, and which, according to Zeuthen, qualify as Geometric Algebra too, but in the form of pre-Analytic Geometry.
 

Authors:
Stelios Negrepontis : Department of Mathematics, Athens University, Athens 157 84, Greece
Vasiliki Farmaki : Department of Mathematics, Athens University, Athens 157 84, Greece
Demetra Kalisperi : Department of Mathematics, Athens University, Athens 157 84, Greece
 

DOI : https://doi.org/10.32381/GB.2022.44.2.1

Price: 251

The “Hundred Fowls” Problem in the Gaṇitasārasaṅgraha of Mahāvīrācārya and Some New Perspectives on the “Kuṭṭaka”

By: Catherine Morice-Singh

Page No : 153-191

Abstract
Our main goal in this paper is to analyze the two rules for solving “hundred fowls” type of problems described in Mahāvīrācārya’s well-known Gaṇitasārasaṅgraha. This will be done based on two manuscripts that Prof. M. Rangacharya consulted to prepare his edition and translation of the text, in 1912, and which are still available at the Government Oriental Manuscripts Library and Research Centre – Chennai (Madras). One of the manuscripts contains a running commentary in a medieval form of Kannada that is particularly useful for clarifying the steps of the algorithms. It allows us to see how Rangacharya, in an unusual way, deviated for the first example from the solution given in the manuscripts and provided his own solution instead. It will also allow us to appreciate the uniqueness and originality of Mahāvīrācārya’s second rule. We are fortunate that four well-known Sanskrit texts propound independent rules for this type of problems and give as illustration an identical example involving the buying of four species of birds. This is a rare instance that can help us revise previous understandings regarding the meaning of technical terms such as kuṭṭaka and kuṭṭīkāra – usually considered as synonyms and translated as “pulverizers” – and suggest new perspectives.

Author:
Catherine Morice-Singh : c/o Laboratoire SPHERE, 8 Rue Albert Einstein, Bâtiment Olympe de Gouge. Université Paris Cité, F-75013 Paris, France
 

DOI : https://doi.org/10.32381/GB.2022.44.2.2

Price: 251

Indian Solutions for Conjunct Pulverisers (lafÜy"Vdqêd) From Āryabhaṭa II to Devarāja

By: Shriram M Chauthaiwale

Page No : 193-204

Abstract
After canvassing the solutions for indeterminate linear equations (kuṭṭaka), Indian scholars deliberated on the common solution for the two systems of similar equations under the caption “Conjunct Pulverisers (saṃśliṣṭakuṭṭaka).” Āryabhaṭa II, Mahāvīra, Śrīpatī, Bhāskara II, Nārāyaṇa Paṇḍita, Kṛṣṇa Daivajña, and Devarāja is the chain of the Indian scholars who explained similar or different methods for extracting the solutions. B. Datta discussed some of these methods, and T. Hayashi commented on Devarāja’s methods. S. K. Ganguli discovered an alternative method from the manuscript copies of Līlāvatī. This paper provides the juxtaposed mathematical formats of the methods after translating the relevant verses. Later, these methods are compared. Illustrations from the referred texts are quoted with answers.

Author:
Shriram M Chauthaiwale : Lecturer (Rt) in Mathematics, Amolakchand College, Yavatmal (M.H.)
 

DOI : https://doi.org/10.32381/GB.2022.44.2.3

Price: 251

Obituary

By: ..

Page No : 205-208

Price: 251

Instruction to the Author

It is preferred that the article is created in MS Word using 12-point Times New Roman type throughout. Once an article has been accepted the final version may be submitted in TeX / LaTeX also, together with the corresponding PDF file. The title, numbered equations and tables, should be centered. Everything else must be aligned to the left without any indent. A double space above and below all headings is required. If special characters (e.g. Chinese, Cyrillic) other than Latin or Greek alphabets and common mathematical symbols are used, PDF files should be supplied to indicate their placement. In fact a PDF file showing complete article with everything embedded as it should appear in the print, must be supplied.

The main body of the article should be divided by appropriate numbered section and sub-section headings all in upper/lower bold type and aligned to the left. An Acknowledgment section may be included before the list of references. Manuscripts must generally be organized in the following manner:

(i) Title (bold face) followed by author name(s) only [centered], (ii) Abstract and Key Words, (iii) Article Text, (iv) Acknowledgments, (v) References, (vi) Appendices.

The abstract should be followed by three to seven keywords that would be useful in identifying it for reference purposes.

Please avoid using any Footnotes. All references in the text must be cited by author surname and year, like (Smith, 1993) or Smith (1985b). List all the cited references at the end of the article, in alphabetical order of the surnames (writing initials first followed by the surnames), strictly in accordance with the following examples:

J.W. Dauben. The first international connexions in history of mathematics: The case of the Encyclopadie. Historia Mathematica, 26: 343-359, 1999.

R.C. Gupta. Sino-Indian interaction and the great Chinese Buddhist astronomer-mathematician I-Hsing. Ganita Bh?rat?, 11: 38-49, 1989. G.H. Hardy. A Mathematician's Apology . Cambridge Univ. Press: Cambridge, 1988. (Reprinted) E. von Collani. History, State of the Art and Future of the Science of Stochastics. In: Ivor Grattan-Guinness and B.S. Yadav ed. History of The Mathematical Sciences, 171-194. Hindustan Book Agency: New Delhi, 2002.
As a last section, please provide brief information about each contributing author's contact details, including his/her current affiliation(s), email addresses and URL (if any). The corresponding author will receive galley proofs as a PDF file via E-mail, to enable him/her to point out any corrections to be made.

All the manuscripts submitted for the Ganita Bharati should accompany a covering letter giving an undertaking following certain principles under Ethical Policy.

The cover letter should include a written statement from the author(s) that:
1. The manuscript is an original research work and has not been published elsewhere including open access at the internet.

2. The data used in the research has not been manipulated, fabricated, or in any other way misrepresented to support the conclusions.

3. No part of the text of the manuscript has been plagiarised.

4. The manuscript is not under consideration for publication elsewhere.

5. The manuscript will not be submitted elsewhere for review while it is still under consideration for publication in the Ganita Bharati.

The cover letter should also include an ethical statement disclosing any conflict of interest that may directly or indirectly impart bias to the research work. Conflict of interest most commonly arises from the source of funding, and therefore, the name(s) of funding agency must be mentioned in the cover letter. In case of no conflict of interest, please include the statement that “the authors declare that they have no conflict of interest”.

Products related to this item

© All Rights Reserved 2024, Prints Publications Pvt. Ltd.

Powered by : Prints Publications Pvt Ltd