Ganita Bharati

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

Current Volume: 43 (2021 )

ISSN: 0970-0307

Periodicity: Half-Yearly

Month(s) of Publication: June & December

Subject: Mathematics


Online Access is Free for Life Member


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.

Zentralblatt Math
Mathematical Review


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

T. C. 25/1974(2)
Deshabhimani Road
Trivandrum 695001, India

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

Mohammad Bagheri

Encyclopedia Islamic Foundation
PO Box 13145-1785

Takao Hayashi

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

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

Jan P. Hogendljk

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

S. R. Sarma

Höhenstr. 28
40227 Düsseldorf

Umberto Botttazzni

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

Jens Hoyrup

Roskilde University
Section for Philosophy and Science Studies

Karine Chemla

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,
Tokyo 153-8902

J. W. Dauben

The Graduate Centre
CUNY, 33, West 42nd Street
New York, NY 10036

Victor J. Katz

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

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

Wenlin Li

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

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

Wenlin Li

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

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

D. E. Zitarelli

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

Volume 43 Issue 2 , (Jul-2021 to Dec-2021)

Further Examples of Apodictic Discourse, I

By: Satyanad Kichenassamy

Page No : 93-120

The analysis of problematic mathematical texts, particularly from India, has required the introduction of a new category of rigorous discourse, apodictic discourse. We briefly recall why this introduction was necessary. We then show that this form of discourse is widespread among scholars, even in contemporary Mathematics, in India and elsewhere. It is in India a natural outgrowth of the emphasis on non-written communication, combined with the need for freedom of thought. New results in this first part include the following: (i) ?ryabha?a proposed a geometric derivation of a basic algebraic identity; (ii) Brahmagupta proposed an original argument for the irrationality of quadratic surds on the basis of his results on the varga-prak?ti problem, thereby justifying his change in the definition of the word karani.


Price: 251

Meanings of savarnana in Indian Arithmetic

By: Taro Tokutake

Page No : 121-149

In Indian mathematical texts the term savarnana


Price: 251

Aryabhatiya 2.19 in a Commentary on Two Examples from Sridhara

By: Taro Tokutake , Takanori Kusuba

Page No : 151-165

In a commentary on example verse 112 for rule verses 97-98 in the mathematical series of the Patiganita, various solutions of a problem are described. After solving the problem according to the given rule, the commentator shows alternative methods: Aryabhatiya 2.19, linear equations, and rule verses 99-101. Also in the commentary on example verse 113 for rule verses 99-101, he again employs Aryabhatiya 2.19. The present paper has a threefold objective. First, we fully investigate the ways of solving which the commentary exhibits for the two examples. Secondly, we point out particularly where Aryabhatiya 2.19 is applied, although neither the author Aryabhatiya nor the title of his work is cited in the commentary. And thirdly, we study excerpts of rules concerning the bijaganita quoted there.


Price: 251


By: Yue Pan

Page No : 167-176

As a Medieval Muslim polymath, al-Biruni had also been an observer of Indian astronomy. He gave some opinions on Indian theory of precession in his Tahqiq ma li-l-Hind. Al- Biruni adhered to Ptolemaic theory of the movement of the sphere of the fixed stars, which is opposite to medieval Indian theory of precession. It was such a contradiction that made al- Biruni misjudge medieval Indian theory of precession. This case reveals a particular aspect, both of the difference between pre-Ptolemaic Greco-Indian astronomy and Ptolemaic Greek one, and of the influence of Greek thought on Muslim scholars including al- Biruni.


Price: 251

Several Algebraic Unknowns

By: Jens Hoyrup

Page No : 177-198

At the Annual conference of the Indian Society for History of Mathematics in 2020 I spoke about the scattered use of several algebraic unknowns in Italian algebra from Fibonacci to Pacioli, and in 2021 about Benedetto da Firenze


Price: 251

News : Professor R. C. Gupta honored with Padma Shri

By: No author

Page No : 199

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”.

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