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- Ganita Bharati : Bulletin of The Indian Society for History of Mathematics

# Ganita Bharati : Bulletin of The Indian Society for History of Mathematics

**ISSN:**0970-0307

**e-ISSN:********

**Subject:**Mathematics

**Periodicity:**Half Yearly

**DOI:**10.32381/GB.

**Month(s) of Publication:**June & December

**Current Volume:**41 (2019)

- About the Journal
- Indexing & Abstracting
- Editors
- Current Issue
- Previous Issue(s)
- Instructions to Authors
- Ethics Policy
- Call For Papers
- Copyright

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.

**Sites are:**

ProQuest

EBSCO

Zentralblatt MATH,

Mathematical Review,

Genamics(JournalSeek) etc.

### Editor-In-Chief

- Shrikrishna G. Dani, Department of Mathematics, Indian Institute of Technology Mumbai, Powai, Mumbai-400078, Email: ganitabharati@gmail.com

### International Advisory Board

- Virender Dalal, Ramjas College, University of Delhi, Delhi - 110007

### Assistant Editor

- V.M. Mallayya, MELTRA-A23, T.C.25/1974(2), Deshabhimani Road, Trivandrum-695001

### Members

- S.M.S.Ansari
- Mohammad Bagheri
- S. C. Bhatnagar
- Umberto Bottazzini
- Karine Chemla
- J.W.Dauben
- Nachum Dershowitz
- Enrico Guisti
- R.C.Gupta
- Takao Hayashi
- Jan P.Hogendijik
- Subhash Kak
- Victor J.Katz
- Wenlin Li
- J.C.Martzloff
- Jean-Paul Pier
- Kim Plofker
- F.Jamil Ragep
- S.R.Sharma
- Chikara Sasaki
- M.S.Sriram
- A.M.Vadiya
- Ioannis M Vandoulakis
- D.E.Zitarelli

### Volume 41 (2019) Issue 1-2 , (January-2019 to December-2019)

January-December

**Brahmagupta’s Apodictic Discourse**
* by Satyanad Kichenassamy *

**Abstract:**We continue our analysis of Brahmagupta’s Brahmasphutasiddhanta (India, 628), that had shown that each of his sequences of propositions should be read as an apodictic discourse: a connected discourse that develops the natural consequences of explicitly stated assumptions, within a particular conceptual framework. As a consequence, we established that Brahmagupta did provide a derivation of his results on the cyclic quadrilateral. We analyze here, on the basis of the same principles, further problematic passages in Brahmagupta’s magnum opus, regarding number theory and algebra. They make no sense as sets of rules. They become clear as soon as one reads them as an apodictic discourse, so carefully composed that they leave little room for interpretation. In particular, we show that (i) Brahmagupta indicated the principle of the derivation of the solution of linear congruences (the kuttaka) at the end of chapter 12 and (ii) his algebra in several variables is the result of the extension of operations on numbers to new types of quantities – negative numbers, surds and “non-manifest” variables. AMS classification (MSC 2010): 01A32, 01A35, 11-03, 11A05, 51-03.

DOI -https://doi.org/10.32381/GB.2019.41.1-2.1

** Reinventing or Borrowing Hot Water? Early Latin and Tuscan Algebraic Operations with Two Unknowns**
* by Jens Hoyrup *

**Abstract:**In mature symbolic algebra, from Viète onward, the handling of several algebraic unknowns was routine. Before Luca Pacioli, on the other hand, the simultaneous manipulation of three algebraic unknowns was absent from European algebra and the use of two unknowns so infrequent that it has rarely been observed and never analyzed. The present paper analyzes the five occurrences of two algebraic unknowns in Fibonacci’s writings; the gradual unfolding of the idea in Antonio de’ Mazzinghi’s Fioretti; the distorted use in an anonymous Florentine algebra from ca 1400; the regular appearance in the treatises of Benedetto da Firenze; and finally what little we find in Pacioli’s Perugia manuscript and in his Summa. It asks which of these appearances of the technique can be counted as independent rediscoveries of an idea present since long in Sanskrit and Arabic mathematics – metaphorically, to which extent they represent reinvention of the hot water already available on the cooker in the neighbour’s kitchen; and it raises the question why the technique once it had been discovered was not cultivated – pointing to the line diagrams used by Fibonacci as a technique that was as efficient as rhetorical algebra handling two unknowns and much less cumbersome, at least until symbolic algebra developed, and as long as the most demanding problems with which algebra was confronted remained the traditional recreational challenges. AMS classification (MSC 2010): 01A32, 01A35, 11-03, 11A05, 51-03.

DOI -https://doi.org/10.32381/GB.2019.41.1-2.2

**Nearest-Integer Continued Fractions in Drkkaraoa
**

*by Venketeswara Pai R. and M. S. Sriram*

**Abstract:**The Karaõa texts of Indian astronomy give simplified expressions for the mean rates of motion of planets. The Kerala text Karaõapaddhati (c. 1532-1566 CE) expresses these rates which involve ratios of large numerators or multipliers (guõakras) and large demominators or divisors (hÀrakas), as ratios of smaller numbers using essentially the method of simple continued fraction expansion. A modified version of this method is described in a slightly later Malayalam text named DÃkkaraõa (c. 1608 CE), also. A very interesting feature of the DÃkkaraõa algorithm is that a nearest-integer continued fraction expansion with the minimal length is implicit in it. We discuss this algorithm in this paper.

DOI -https://doi.org/10.32381/GB.2019.41.1-2.3

**Mathematics and Map Drawing in the Eighteenth Century**
* by Athanase Papadopoulos *

**Abstract:**We consider the mathematical theory of geographical maps, with an emphasis on the eighteenth century works of Euler, Lagrange and Delisle. This period is characterized by the frequent use of maps that are no more obtained by the stereographic projection or its variations, but by much more general maps from the sphere to the plane. More especially, the characteristics of the desired geographical maps were formulated in terms of an appropriate choice of the images of the parallels and meridians, and the mathematical properties required by the map concern the distortion of the maps restricted to these lines. The paper also contains some notes on the general use of mathematical methods in cartography in Greek Antiquity, and on the mutual influence of the two fields, mathematics and geography. AMS Mathematics Subject Classiflcation: 01A55, 30C20, 53A05, 53A30, 91D20.

DOI -https://doi.org/10.32381/GB.2019.41.1-2.4

**On the Contribution of Anders Johan Lexell in Spherical Geometry**
* by A. Zhukova *

**Abstract:**In this paper, we discuss results in spherical geometry that were obtained by a remarkable mathematician of the XVIIIth century, Anders Johan Lexell. We also present a short note on the place of these results in the history of this field as well as a short biography of Lexell.

DOI -https://doi.org/10.32381/GB.2019.41.1-2.5

**Magic Squares and Other Numerical Diagrams on the Chittagong Plaster Replicas in the David Eugene Smith Collection**
* by Takao Hayashi *

**Abstract:**The Rare Book and Manuscript Library of Columbia University has a set of 20 plaster replicas that D. E. Smith brought from Chittagong in 1907 CE. They are twin replicas of 10 stone slabs. Most of the replicas show one or a few numerical diagrams including magic squares. In this paper I analyze them and discuss their construction methods.

DOI -https://doi.org/10.32381/GB.2019.41.1-2.6

**Book Reviews
Scholars and Scholarship in Late Babylonian Uruk by Christine Proust and John M. Steel Reviewed by Jens Hoyrup**

**Vedic Mathematics and Science in the Vedas by S Balachandra Rao Reviewed by Shailaja D. Sharma**

### Volume 40 (2018)

#### Volume 40 (2018) Issue 2 , (July-2018 to December-2018)

Jul-Dec. 2018

**Katyayana Sulvasutra : Some Observations**
* by S. G. Dani *

**Abstract:**The Katyayana SulvasÂtra has been much less studied or discussed from a modern perspective, even though the first English translation of two adhyayas (chapters) from it, by Thibaut, appeared as far back as 1882. Part of the reason for this seems to be that the general approach to the Sulvasatra studies has been focussed on “the mathematical knowledge found in them (as a totality)”; as the other earlier Sulvasatras, especially of Baudhayana and Apastamba substantially cover the ground in this respect, the other two Sulvasatras, Manava and Katyayana, received much less attention, the latter especially so. On the other hand the broader purpose of historical mathematical studies extends far beyond cataloguing what was known in various cultures, rather to understand the ethos of the respective times from a mathematical point of view, in their own setting, in order to evolve a more complete picture of the mathematical developments, ups as well as downs, over history. Viewed from this angle, a closer look at Katyayana Sulvasatra assumes significance. Coming at the tail-end of the Sulvasatras period, after which the Sulvasatras tradition died down due to various historical reasons that are really only partly understood, makes it special in certain ways. What it omits to mention from the body of knowledge found in the earlier Sulvasatras would also be of relevance to analyse in this context, as much as what it chooses to record. Other aspects such as the difference in language, style, would also reflect on the context. It is the purpose here to explore this direction of inquiry.

DOI-https://doi.org/10.32381/GB.2018.40.02.1

**Essay Review: On the Interpretations of the History of Diophantine Analysis: A Comparative Study of Alternate Perspectives
**

*by Ioannis Vandoulakis*

**Abstract:**This is a review of the following two books, in particular comparing them with relevant works of I.G.Bashmakova on the topic. Les Arithmétiques de Diophante : Lecture historique et mathématique, par Roshdi Rashed en collaboration avec Christian Houzel, Berlin, New York : Walter de Gruyter, 2013, IX-629 p. Histoire de l’analyse diophantienne classique : D’Abu Kamil à Fermat, par Roshdi Rashed, Berlin, New York : Walter de Gruyter, 2013, X-349 p.

DOI-https://doi.org/10.32381/GB.2018.40.02.2

**Nasir al-Din al-Tusi’s Treatise on the Quadrilateral: The Art of Being Exhaustive**
* by Athanase Papadopoulos *

**Abstract:**We comment on some combinatorial aspects of Nasir al-Din al-Tusi’s Treatise on the Quadrilateral, a 13th century work on spherical trigonometry. AMS classification: 01A20, 01A30, 01A35.

DOI-https://doi.org/10.32381/GB.2018.40.02.3

**Book Reviews
The Mathematics of India : Concepts, Methods, Connections by P. P. Divakaran
Reviewed by Satyanad Kichenassamy
Karaõapaddhati of Putumana Somayaji with translation and explanatory notes by Venketeswara Pai, K. Ramasubramanian, M.S. Sriram and M.D. Srinivas
Reviewed by S.G. Dani and Clemency Montelle**

#### Volume 40 (2018) Issue 1 , (January-2018 to June-2018)

January-June

**T. A. Sarasvati Amma: A Centennial Tribute**
* by P. P. Divakaran *

**Abstract:**Sarasvati Amma published very few research papers. All her insights into the Indian mathematical (specifically, geometric) tradition are to be found in her book “Geometry in Ancient and Medieval India”, published in 1979 but prepared as her thesis in the University of Madras 20 years earlier. The present article is, consequently, an evaluation of the mathematics described in the book and of the historiographic significance of its interpretation by her. The book pays specific attention to certain themes: e.g., the key ideas of the geometry of the Vedic period, cyclic quadrilaterals, geometric algebra etc. and, especially, the infinitesimal trigonometry of MÀdhava, all in a style designed to bring out the continuity in their evolution. The case is made in this article that Sarasvati Amma’s work, along with the earlier book of B. Datta and A. N. Singh, marks the founding of an autonomous discipline of scholarship into India’s mathematical past.

DOI-https://doi.org/10.32381/GB.2018.40.01.1

**The Seminal Contribution of K. S. Shukla to our Understanding of Indian Astronomy and Mathematics**
* by M. D. Srinivas *

**Abstract:**In this article we shall highlight some of the important contributions to the study of Indian astronomy and mathematics made by Prof. Kripa Shankar Shukla (1918 - 2007), on the occasion of his birth centenary. Shukla was a student of Prof. A. N. Singh (1905 - 1954) at Lucknow University and was also fortunate to have come in close contact with Prof. Singh’s renowned collaborator Bibhutibhusan Datta (1888-1958). Dr. Shukla became the worthy successor of Prof. Singh to lead the research programme on Indian astronomy and mathematics at Lucknow University. Prof. Shukla brought out landmark editions of twelve important source-works of Indian astronomy and mathematics. A remarkable feature of many of these editions is that they also include lucid English translations and detailed explanatory notes. This is indeed one of the greatest contributions of Prof. Shukla since, till the 1960s, there had been very few editions of the classical source-works of Indian astronomy which also included a translation as well as explanatory notes. The editions of Shukla have become standard textbooks for the study of development of Indian astronomy during the classical SiddhÀntic period from °ryabhaÇa to OErÁpati. Prof. Shukla also wrote over forty important research articles, which have ushered in an entirely new perspective on the historiography of Indian astronomy and mathematics. We shall discuss in some detail the following seminal contributions of Prof. Shukla: (i) Correct explanation of the manda-saÉskÀra (equation of centre) in Indian astronomy, including the computation of the avioeiÈÇa-mandakarõa (iterated manda-hypotenuse) and its significance. (ii) Correction of the faulty readings and translations of some of the crucial verses giving the number of civil days and other parameters of a yuga, as presented in the 1978 edition of YavanajÀtaka by David Pingree. (iii) Publication of a revised and updated version of Part III of the ‘History of Hindu Mathematics’ by B. B. Datta and A. N. Singh.

DOI-https://doi.org/10.32381/GB.2018.40.01.2

**On Old Babylonian Mathematical Terminology and its Transformations in the Mathematics of Later Periods**
* by Jens HØyrup *

**Abstract:**Third-millennium (BCE) Mesopotamian mathematics seems to have possessed a very restricted technical terminology. However, with the sudden flourishing of supra-utilitarian mathematics during the Old Babylonian period, in particular its second half (1800–1600 BCE) a rich terminology unfolds. This mostly concerns terms for operations and for definition of a problem format, but names for mathematical objects, for tools, and for methods or tricks can also be identified. In particular the terms for operations and the way to structure problems turn out to allow distinction between single localities or even schools. After the end of the Old Babylonian period, the richness of the terminology is strongly reduced, as is the number of known mathematical texts, but it presents us with survival as well as innovations. Apart from analyzing the terminology synchronically and diachronically, the article looks at two long-lived non-linguistic mathematical practices that can be identified through the varying ways they are spoken about: the use of some kind of calculating board, and a way to construct the perimeter of a circle without calculating it – the former at least in use from the 26th to the 5th century BCE, the later from no later than Old Babylonian times and surviving until the European 15th century CE.

DOI-https://doi.org/10.32381/GB.2018.40.01.3

### Volume 39 (2017)

#### Volume 39 (2017) Issue 2 , (July-2017 to December-2017)

Jul-Dec

**An Indian Version of al-Kashi’s Method of Iterative Approximation of sin 1°**
* by Kim Plofker *

**Abstract:**The well-known “feedback loop” of trigonometry of sines, from its origin in Indian astronomy to the Islamic world in the first millennium CE and back to India in the mid-second, includes many interesting and under-studied developments. This paper examines a Sanskrit adaptation and refinement of a medieval method foRsine approximation, apparently from the court of Jai Singh in the early 18th century.

**Nilakantha Critique on Aryabhata’s Verses on Squaring and Square-roots 107-124**
* by N. K. Sundareswaran *

**Abstract:**Nilakantha commentary on Aryabhata's is well known for clarity and simplicity of language and for its expository nature. He goes on clarifying all the possible doubts. The way in which he formulates and interconnects ideas is simply beautiful. At times his commentary on a particular point runs into pages. But it would be a pleasure to read it, for, the language and style of argument are the same as in a polemical text of philosophy. This paper makes a close study of the commentary on the fourth verse of Ganitapada, wherein Nilakantha explains the method for finding the square root of a number, focusing on the development of ideas and the thought process. Here Nilakantha deals, at length, with many of the rationales and the concepts involved. The explanation given by Nilakantha for Baudhayana’s approximation of is unique. It is a fine specimen of geometrical demonstration of arithmetical ideas, a significant trend of medieval school of Kerala mathematics.

**Sign and Reference in Greek Mathematics**
* by Ioannis M. Vadoulakis *

**Abstract:**In this paper, we will examine some modes of reference to mathematical entities used in Greek mathematical texts. In particular, we examine mathematical texts from the Early Greek period, the Euclidean, Neo-Pythagorean, and Diophantine traditions.

**On the History of Analysis -The Formation of Concepts**
* by G. Sinkevich *

**Abstract:**Mathematical analysis was conceived in XVII century in the works of Newton and Leibniz. The issue of logical rigor in definitions was however first considered by Arnauld and Nicole in ‘’Logique ou l’art de penser’’. They were the first to distinguish between the bulk of the concept and its structure. They created a tradition which was strong in mathematics till XIX century, especially in France. The definitions were in binomial nomenclature mostly, but another type of definition appears in Cantor theory – it was the descriptive definition. As it used to be in humanities, first the object had only one characteristic, then as research continued it got enriched with new characteristics leading to a fledged concept. In this way mathematics acquired its own creativity. In 1915 Luzin laid down a new principle of the descriptive theory: a structural characteristic is done, the analytical form had to be found. New schools of descriptive set theory appeared in Moscow in the first half of the 20th century.

**Book Reviews :
Mathematics in Ancient Egypt: A Contextual History by Annette Imhausen Reviewed by Jens Hoyrup
The Siddhhantasundara of Jnanaraja by Toke Lindegaard Knudsen Reviewed by Surabhi Saccidananda
**

**News**
* *

#### Volume 39 (2017) Issue 1 , (January-2017 to June-2017)

Jan-Jun

**Archimedes – Knowledge and Lore from Latin Antiquity to the Outgoing European Renaissance**
* by Jens Hoyrup *

**On the History of Nested Intervals: From Archimedes to Cantor**
* by G. I. Sinkevich *

**Explanation of the Vakyasodhana procedure for the Candravakyas**
* by M. S. Sriram *

**Madhyahnakalalagna in Karanapaddhati of Putumana Somayaji**
* by Venketeswara Pai R. & M.S. Sriram *

**Vedic Mathematics and Science in the Vedas (in Kannada) by S. Balachandra rao,
Reviewed by Surabhi Saccidananda
**

**Some Recent Publications in History of Mathematics**
* *

**News **
* *

**Obituary**
* *

### Volume 38 (2016)

#### Volume 38 (2016) Issue 2 , (July-2016 to December-2016)

July-December

**Siddhanta-karana conversion: Some algorithms in the Grahaganitadhyaya of Bhaskara’s Siddhantasiromani and in his Karanakutuhala**
* by Kim Plofker *

**The Candravakyas of Madhava**
* by R. Venketeswara Pai, K. Ramasubramanian, M. D. Srinivas and M. S. Sriram *

**The poetic features in the goladhyaya of Nityananda’s Sarvasiddhantaraja**
* by Anuj Misra, Clemency Montelle and K. Ramasubramanian *

**Roshdi Rashed, Historian of Greek and Arabic Mathematics
**

*by Athanase Papadopoulos*

**A tribute to Syamadas Mukhopadhyaya; On the occasion of his 150th birth anniversary**
* by S. G. Dani *

**Annual Conference of ISHM - 2016 : A Report**
* *

#### Volume 38 (2016) Issue 1 , (January-2016 to June-2016)

June

**Embedding: Multi-purpose Device for Understanding Mathematics and its Development, or Empty Generalization?
**

*by Jens Hoyrup*

**Rolle’s Theorem and Bolzano-Cauchy Theorem : a View from the End of the 17th century until K. Weierstrass’ Epoch
**

*by G.I. Sinkevich*

**Ganitananda: Selected works of Radha Charan Gupta on History of Mathematics, Ed. by K. Ramasubramanian Reviewed by Kim Plofker (Page 55-60)
Aryabhatiyam, translation of the complete text with commentary, in Kannada, by Dr. S. Balachandra Rao Reviewed by B. S. Shylaja (Page 61-63)
Chintamani Ragoonatha Charry and Contemporary Indian Astronomy, by B.S. Shylaja
Reviewed by Surabhi Saccidananda (Page 64-67)
Pangeometry by Nikolai Lobachevsky Edited and Translated, by Athanase Papadopoulos Reviewed by Tali Pinsky (Page 67-72)**

**Some Recent Publications in History of Mathematics **
* *

**Annual Conference of ISHM - 2015 : A Report **
* *

**Announcement 91-92**
* *

**CONTENTS**
* *

### Volume 37 (2015)

#### Volume 37 (2015) Issue 1-2 , (January-2015 to December-2015)

January to December

**BhaskaracaryaÃ¢â‚¬â„¢s Mathematics and Astronomy: An Overview**
* by M. S. Sriram *

**Some Aspects of Patadhikara in Siddhantasiromani
**

*by Venketeswara Pai R., M. S. Sriram and Sita Sundar Ram*

**The Phenomena of Retrograde Motion and Visibility of Interior Planets in BhÃ„ÂskaraÃ¢â‚¬â„¢s works
**

*by Shailaja M., Vanaja V. and S. Balachandra Rao*

**True Positions of Planets according to KaranakutÃ…Â«hala
**

*by Vanaja V., Shailaja M. and S. Balachandra Rao*

**The inÃ¯Â¬â€šuence of BhÃ„ÂskarÃ„ÂcÃ„ÂryaÃ¢â‚¬â„¢s Works in Ã¢â‚¬Å“WesternizedÃ¢â‚¬Â Sanskrit Mathematical Traditions**
* by Kim Plofker *

**BhÃ„ÂskarÃ„ÂcÃ„ÂryaÃ¢â‚¬â„¢s Treatment of the Concept of Infinity
**

*by Avinash Sathaye*

**Issues in Indian Metrology, from Harappa to BhÃ„ÂskarÃ„ÂchÃ„Ârya**
* by Michel Danino *

**Indian Records of Historical Eclipses and their Significance
**

*by Aditya Kolachana and K. Ramasubramanian*

**Medieval Eclipse Prediction A Parallel Bias In Indian And Chinese Astronomy
**

*by Jayant Shah*

**PREFACE**
* *

### Volume 36 (2014)

#### Volume 36 (2014) Issue 2 , (July-2014 to December-2014)

July - December

**Hyperbolic Geometry in the Work of J. H. Lambert **
* *

**On the Legacy of Ibn Al-Haytham: An Exposition Based on the Work of Roshdi Rashed**
* by Athanase Papadopoulos *

**Otto HÃƒÂ¶lder : A Multifaceted Mathematician**
* by R. Sridharan *

**Some Identities and Series Involving Arithmetic and Geometric Progressions in PÃƒâ‚¬Ãƒâ€¡ÃƒÂgaÃƒÂµitam, GaÃƒÂµitasÃƒâ‚¬rasaÃƒÂ´grahaÃƒÂ and GaÃƒÂµitakaumudÃƒÂ**
* by Shriram M. Chauthaiwale *

**Book Reviews:
Indian Astronomy - Concepts and Procedures, by S. Balachandra Rao, Reviewed by Jayant Narlikar
Bhaskaracharya virachita LÃƒÂlavatÃƒÂ (in Kannada), by S. Balachandra Rao, Reviewed by C. S. Aravinda
La ThÃƒÂ©orie des Lignes ParallÃƒÂ¨les de Johann Heinrich Lambert (in French), by A. Papadopoulos and G. ThÃƒÂ©ret, Reviewed by Ravi Raghunathan**

**Some Recent Publications in History of Mathematics**
* *

**Report on the Annual Conference of ISHM - 2014 Dedicated to Bhaskaracarya**
* *

**News**
* *

**Contents**
* *

#### Volume 36 (2014) Issue 1 , (January-2014 to June-2014)

Jan-Dec

**Mathematical Models and Data in the Brahmpaksa School of Indian Astronomy**
* by Kim Plofker *

**From Verses in Text to Numerical Table - The Treatment of Solar Declination and Lunar Latitude in Bhaskara II's Karanakutuhala and the Related Tabular Work, the Brahmatulyasarani**
* by Clemency Montelle *

**Intantaneous Motion (taktalikagati) and the "Derivative" of the Sine Function in Bhaskara - II's Siddhantasiromani **
* by M. S. Sriram *

**On the Works of Euler and His Followers on Spherical Geometry **
* by Athanase Papadopoulos *

**Sawai Jai Singh's Efforts to Revive Astronomy**
* by Virendra N. Sharma *

**Obituriy Note**
* *

### Volume 35 (2013)

#### Volume 35 (2013) Issue 1-2 Comb. , (January-2013 to December-2013)

January-December

**A History of Pingala's Combintorics**
* by Jayant Shah *

**Authenticity of the Verses in the Printed Edition of the Ganitatilaka**
* by Takao Hayashi *

**Some Interesting Addenda to a Manuscript of the Kautukallavati of Ramacandra **
* by Takao Hayashi *

**An Analysis of the MandaphalaTables of Makaranda and Revision of Parameters**
* by Balachandra Rao S, Rupa K and Padmaja Venugopal *

**Proof-Events in History of Mathematics**
* by Ioannis M.Vandoulakis and Petros Stefaneas *

**Pingala's Fountain**
* by R. Sainudiin, R. Sridharan, M.D. Srinivas and K.Yogeeswaran *

**Book Review:
Sri Rajaditya's Vyavaharaganita, Ed. & Tr. by Padmavathamma, Krishnaveni and K.G. Prakash**

*by S. Balachandra Rao*

**Some Recent Publications in History of Mathematics**
* *

### Volume 34 (2012)

#### Volume 34 (2012) Issue 1-2 Comb. , (January-2012 to December-2012)

January-December

* by Jens Hoyrup *

**A hypothetical history of Old Babylonian mathematics: places, passages, stages, development **
* by Jens HÃ¸yrup *

**Mesopotamian zig-zag function of day length from Indian point of view **
* by Yukio Ohashi *

**Eccentric Model of the Solar Orbit in China**
* by Yukio Ohashi *

**Mathematical conceptual changes in Renaissance music **
* by Abdounur, Oscar JoÃ£o *

**Treatises and tables, algorithms and approximations: the role of computation in early modern Sanskrit astronomy **
* by Kim Plofker *

**Fundamentals of arithmetic according to ?a?kara V?riyar (Kerala, 1500-1560) **
* by Pierre-Sylvain Filliozat *

**From Jyasam.varga-nyaya to Jyanayana: A recursive formula for tabular Rsines **
* by Vanishri Bhat and K. Ramasubramanian *

**Use of Continued Fractions in Karanapaddhati **
* by M.S.Sriram and Venketeswara Pai R *

**Muh.ammad Barakat's Commentary on Euclid: An Unintended Mathematics Textbook **
* by Gregg De Young *

**Open issues in the new historiography of European early modern mathematics **
* by NiccolÃ² Guicciardini *

* by Athanase Papadopoulos *

### Volume 33 (2011)

#### Volume 33 (2011) Issue 1-2 Comb. , (January-2011 to December-2011)

January-December

**Absence of Geometric Models in Medieval Chinese Astronomy**
* by Jayant Shah *

**Textual Analysis of Ancient Indian Mathematics**
* by Satyanad Kichenassamy *

* by Konstantinos Nikolantonakis *

**Varasankalita of Narayana Pandita**
* by Shriram M. Chauthaiwale *

**Varasankalita of Narayana Pandita**
* by Shriram M. Chauthaiwale *

* by Christopher Minkowski and Toke Knudsen *

**Seasonal Poetry as Science: The Rtuvarnana in Some Astronomy Treatises**
* by Christopher Minkowski *

**A Partial History of the Indian Statistical Institute**
* by Somesh Chandra Bagchi *

**Book Review Tantrasangraha of Nilakantha Somayaji**
* by K. Ramasubramanian and M. S. Sriram Reviewed by S. R. Sarma *

**Current Bibliography of Radha Charan Gupta**
* by Takao Hayashi *

**Some Recent Publications in History of Mathematics**
* by K. A. C. H. A. Kothalawala, Sanjay Kumar, Y. P. Singh, Mahesh Chander and H.R. Meena *

### Volume 32 (2010)

#### Volume 32 (2010) Issue 1-2 Comb. , (January-2010 to December-2010)

January-December

**Preface**
* *

**Foreword**
* *

**Old Babylonian Ã¢â‚¬Å“AlgebraÃ¢â‚¬Â, and What It Teaches Us about Possible Kinds of Mathematics**
* by Jens Hoyrup *

**The Origin of Decimal Counting: Analysis of Number Names in the R gveda**
* by Bhagyashree Bavare *

**Modes of Creation of a Technical Vocabulary: the Case of Sanskrit Mathematics**
* by Pierre-Sylvain Filliozat *

**A Study of the Operation Called Samkramana and Related Operations**
* by Takanori Kusuba *

**The Resolution of Diophantine Equations According to Bhaskara and a Justification of the Cakravala by Krsnadaivajna**
* by FranÃ§ois Patte *

**Indian Elements in Kushyar's Mathematics and Astronomy**
* by Mohammad Bagheri *

**The Discovery of Madhava Series by Whish: An Episode in Historiography of Science**
* by U. K. V. Sarma, Vanishri Bhat, Venketeswara Pai and K. Ramasubramanian *

**The "Ignominious Fate" of Spherical Trigonometry?**
* by Kim Plofker *

**Translating the Elements into Sanskrit: Jaganna-thaÃ¢â‚¬â„¢sRekha-gan.ita. A Preliminary Assessment**
* by Clemency Montelle *

### Volume 31 (2009)

#### Volume 31 (2009) Issue 1-2 Comb. , (January-2009 to December-2009)

January-December

**On the Rationale of the Maxim Ankanam Vamato Gatih**
* by Sreeramula Rajeswara Sarma *

**Eugene Jacquet and his Pioneering Study of Indian Numerical Notations**
* by JÃ©rÃ´me Petit *

**On the Figurate Numbers from the Bhagavati Sutra**
* by Dipak Jadhav *

**Effects of Moon's Parallax: Lambana and Nati in Indian Astronomy - A Study**
* by S. Balachandra Rao and Padmaja Venugopal *

**The Vakya Method of Finding the Moon's Longitude**
* by Venketeswara Pai, Dinesh Mohan Joshi and K. Ramasubramanian *

**India and the World of Mathematics**
* by M.S. Raghunathan *

**Professor R.C. Gupta Receives the Kenneth O. May Prize**
* by Kim Plofker *

**A Centennial Tribute to Professor L.V. Gurjar**
* by Medha S. Limaye *

**Hermann Minkowski - in Remembrance**
* *

**Review of "Ganitasarakaumudi: The Moonlight of the Essence of Mathematics, by Thakkura Pheru, Edited with Introduction, Translation, and Mathematical Commentary by SaKHYa" **
* by Surabhi Saccidananda *

**Some Recent Publications in History of Mathematics**
* *

**Obituary Note**
* *

### Volume 30 (2008)

#### Volume 30 (2008) Issue 2 , (July-2008 to December-2008)

July - December

**Some Remarks On The History of Solitary Waves
**

*by Wang Lixia*

**Serbian Mathematical School And Karamata's Theory : Historical Background
**

*by Dragan Djurcic, Ljubisa D.R. Kocinac, Malisa R. Zizovic*

**On Raising A Number To Its Own Power In Ancient India**
* by Dipak Jadhav *

**Vedic Mathematics And Work of Aryabhata**
* by Dr.Parmeshwar Jha *

**Indian Perspective On The Ontology of A Theory **
* by K.Mahesh , K.Ramasubramaniam *

**History of Mathematics For Primary School Teachers Training
**

*by Konstantinos Nikolantonakis*

**Analysis of Madhava's Series Method For Determination of Desired Rsines
**

*by V.Madhukar Mallayya*

**Letter To Editor**
* *

#### Volume 30 (2008) Issue 1 , (January-2008 to June-2008)

January-June

**Mathematical Ideas in Bhagavati Sutra(BS)**
* by R. S. Shah *

**Chinese Mathematical Astronomy from ca. 4th Century to ca. 6th Century**
* by Yukio Ohashi *

** RENAISSANCE On Mathematical Immortality**
* by Satish C. Bhatnagar *

**Vojislav G. Avakumovic (1910 - 1990)A Passionate Man of Mathematics**
* by Vojislav Maricâ€š and Aleksandar M. Nikolic *

**Vatesvara's Trigonometric Tables and the Method**
* by V. Madhukar Mallayya *

**ADDENDUM TO "A Concise View of the History of Mathematics in Latin America" Gaita Bh rati, 28(2006) 111-128**
* by Ubiratan D Ambrosio *

**Was India Mathematically Illiterate Until the Fifth Century A.D.?**
* by V. Lakshmikantham *

**Contribution to History of n-Groups**
* by Malisa Zizovi *

**A Complex-Domain Analysis of Actions of A Conscious Human Being**
* by Radhey Shyam Kaushal *

**Ramanujan's First Publication: A Solution To A Problem in The Educational Times**
* by James J. Tattersall and Shawnee L. Mcmurran *

### Volume 29 (2007)

#### Volume 29 (2007) Issue 1-2 , (January-2007 to December-2007)

January - December

**A Tacit Appropriation of Hindu Algebra In Renaissance Practical Aritmetic **

*by Albrecht Heeffer*

**Pride - Worthy Indian Contribution To Morley's Miracle**

*by V.G. Tikekar*

**A Note On Submissions From India To The Mathematics Selections of The Educational Times And The Journal of The Indian Mathematical Society **

*by James J. Tattersall*

**Mathematics of Anuyogadwara - Sutra**

*by R.S. Shah*

**Formulation of Chinese Classical Mathematical Astronomy **

*by Yukio Ohashi*

**Algebraic Models In Paitamaha Siddhanta **

*by G.S. Pandey*

**Letters To The Editor**

**News Cafe**

**Book Review**

The History of Mathematics And Mathematician of India

Reviewed By N.L. Maiti, Venugopal D. Heroor

### Volume 28 (2006)

#### Volume 28 (2006) Issue 1-2 , (January-2006 to December-2006)

January - December

**David Pingree And Indian Mathematics**

*by Kim Plofker*

**Revisiting A Chapter From The Notebooks of Ramanujan On Hypergeometric Series **

*by G. Vanden Berghe, K . Srinivasa Rao*

** On The Algorithmic Spirit of The Ancient Chinese And Indian Mathematics **

*by Wenlin Li*

** Kerala Mathematical Tradition - Some Landmarks **

*by V. Madhukar Mallayya*

** The History of The Chinese Written Zeroes Revisited **

*by Jean-Claude Martzloff*

** The Riemann Hypothesis Reviewed In A Historical Nutshell **

*by B.S. Yadav*

** Ivan Bernoulli Series Universalissima**

*by A.K. Kwasniewski*

**The Great Mathematical Research Centres of The 20th Century And The "Miracle" of Lwow I**

*by N. Schlomiuk*

**A Concise View of The History of Mathematics In Latin America **

*by Ubiratan D Ambrosio*

**Istankapancavimsatika of Tejasimha **

*by Takao Hayashi*

**Ancient And Medieval Astronomers And Mathematicians of India **

*by V. Lakshmikantham, J. Vasundhara Devi, S. Leela*

**An Ancient Egyptian Problem And Its Innovative Arithmetic Solution **

*by Milo Gardner*

**Class Room Notes**

The Interplay Between Numbers And Geometry In The History of Mathematics

*by A.M. Vaidya*

** Renaissance**

Calculus Defines Civilization

*by S.C. Bhatnagar*

**News Cafe **

Meetings

The 2nd International Congress of History of Science

**Obituary **

Irving Kaplansky

*by B.S. Yadav*

**Paul Halmos - Expositor Par Excellence **

*by V S Sunder*

**GB Contents Pages Vol. 1-27 **

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J.W. Dauben. The first international connexions in history of mathematics: The case of the Encyclopadie.
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R.C. Gupta. Sino-Indian interaction and the great Chinese Buddhist astronomer-mathematician I-Hsing.
Ganita Bhāratī, 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
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### Introduction

Ganita Bhāratī, 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. It is our endeavor to be a global vehicle for dissemination of original research on topics in history of mathematics, as well expositions (in a form not currently available in literature) that would facilitate research and/or enhance awareness on
the topic of exposition, or of the subject on a broader scale. Ganita Bhāratī also publishes Book Reviews, Brief introductory comments on recent publications, Notes and News items on matters and current events of interest to the broad community involved with the study of history of mathematics, including scholars, students, as well as general enthusiasts of the subject.

This journal is in 38th year of publication and it is indexed/Abstracted in Zentralblatt MATH, Mathematical Review, Genomics(JournalSeek) etc.

### Topics

History of mathematics of various periods, from ancient to modern

### Subject Covered

Articles on a broad range of topics, all the way from mathematics from the ancient cultures around the world to historical aspects of modern mathematics are welcome.

### Instructions to Authors

### Submit Your Article

ganitabharati@gmail.com

### Frequency

2 issues per year.