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
DOI: https://doi.org/10.32381/GB
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.
ProQuest
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Mathematical Review
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Editor UM-DAE Centre for Excellence in Basic Sciences Ramjas College Meltra-A23 Muzammil Manzil Compound R-20, Ras Bahar Colony Department of Mathematics Encyclopedia Islamic Foundation Science & Engg. Research Institute Islamic Studies Department of Mathematics University of Utrecht Höhenstr. 28 Universita degli Studi di Milano Roskilde University REHSEIS-CNRS and Dept. of Computer Sc. University of Tokyo The Graduate Centre University of the D.C. Prof. K.V. Sarma Research Foundation Department of Computer Science Academy of Mathematics & Systems Science The Hellenic Open Unversity Department of Computer Science Academy of Mathematics & Systems Science The Hellenic Open Unversity Dipartimento di Matematica Société mathématique du Luxembourg Department of Mathematics
S.G. Dani
Vidyanagari Campus of University of Mumbai
Kalina, Mumbai 400098, India
Managing Editor
Ruchika Verma
University of Delhi
Delhi-110007, India
Assistant Editor
V. M. Mallayya
T. C. 25/1974(2)
Deshabhimani Road
Trivandrum 695001, India
Members
S.M.S. Ansari
Dodhpur Road
Aligarh 202002, India.
R. C. Gupta
P. O. Lahar Gird,
Jhansi-284003, India
Kim Plofker
Union College
Schenectady, NY 12308
USA
Mohammad Bagheri
PO Box 13145-1785
Tehran
Iran
Takao Hayashi
Doshisha University
Kyotanabe Kyoto 610-0394
Japan
F. Jamil Ragep
McGill University
Morrice Hall, 3485 McTavish Street
Montreal, Quebec,
Canada H3A 1Y1
S. C. Bhatnagar
University of Nevada
Las Vegas
USA
Jan P. Hogendljk
P.O. Box 80010
3508 TA Utrecht
The Netherlands
S. R. Sarma
40227 Düsseldorf
Germany
Umberto Botttazzni
Dipartimento di Matematica
Federigo Enriques Via Saldini 50
20133, Milano
Italy
Jens Hoyrup
Section for Philosophy and Science Studies
Denmark
Karine Chemla
University Paris7, 75019,
Paris, France
Subhash Kak
MSCS 219
Oklahoma State University
Stillwater, OK 74078, USA
Chikara Sasaki
3-8-1 Komaba,
Meguro-Ru,
Tokyo 153-8902
Japan
J. W. Dauben
CUNY, 33, West 42nd Street
New York, NY 10036
U.S.A.
Victor J. Katz
4200 Connecticut Ave.
N.W.Washington, D.C 20008
USA
M. S. Sriram
Venkatarathnam Nagar
Adyar, Chennai - 600020
Nachum Dershowitz
Tel Aviv University,
Tel Aviv
Israel
Wenlin Li
Chinese Academy of Science,
No. 55, Zhongguancun East Road,
Haidan District, Beijing, 100190,
China
Ioannis M. Vandoulakis
School of Humanities
23, Syngrou Avenue,
GR-11743, Athens, Greece.
Nachum Dershowitz
Tel Aviv University,
Tel Aviv
Israel
Wenlin Li
Chinese Academy of Science,
No. 55, Zhongguancun East Road,
Haidan District, Beijing, 100190,
China
Ioannis M. Vandoulakis
School of Humanities
23, Syngrou Avenue,
GR-11743, Athens, Greece.
Enrico Giusti
Viale Morgagni, 67/A
I-50134 Firenze, Italy
Jean-Paul Pier
117 rue Jean-Pierre Michels
L-4243 Esch-sur-Alzette
Luxembourg
D. E. Zitarelli
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
Abstract
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.
DOI : https://doi.org/10.32381/GB.2021.43.2.1
Price: 251
Meanings of savarnana in Indian Arithmetic
By: Taro Tokutake
Page No : 121-149
Abstract
In Indian mathematical texts the term savarnana
DOI : https://doi.org/10.32381/GB.2021.43.2.2
Price: 251
Aryabhatiya 2.19 in a Commentary on Two Examples from Sridhara
By: Taro Tokutake , Takanori Kusuba
Page No : 151-165
Abstract
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.
DOI : https://doi.org/10.32381/GB.2021.43.2.3
Price: 251
Al-Biruni
By: Yue Pan
Page No : 167-176
Abstract
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.
DOI : https://doi.org/10.32381/GB.2021.43.2.4
Price: 251
Several Algebraic Unknowns
By: Jens Hoyrup
Page No : 177-198
Abstract
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
DOI : https://doi.org/10.32381/GB.2021.43.2.5
Price: 251
News : Professor R. C. Gupta honored with Padma Shri
By: No author
Page No : 199
Price: 251
Jan-2021 to Jun-2021
Peeping into Fibonacci
By: Jens Hoyrup
Page No : 1-70
Abstract:
The following collects observations I made during the reading of Fibonacci
DOI : https://doi.org/10.32381/GB.2021.43.1.1
Price: 251
Treatment of
By: Dionisy I. Pronin
Page No : 71-86
Abstract
The paper is dedicated to signs meaning
DOI : https://doi.org/10.32381/GB.2021.43.1.2
Price: 251
Some Recent Publications in History of Mathematics
By: No author
Page No : 87-92
Price: 251
Jan-2020 to Dec-2020
The Central Role of Incommensurability in Pre-Euclidean Greek Mathematics and Philosophy
By: Stelios Negrepontis , Vassiliki Farmaki , Marina Brokou
Page No : 1-34
Abstract
In this paper we outline the tremendous impact that the Pythagorean discovery of incommensurability had on pre-Euclidean Greek Mathematics and Philosophy. This will be a consequence of our findings that the Pythagorean method of proof of incommensurability is anthyphairetic, namely depends on Proposition X.2 of the Elements, according to which if the anthyphairesis of two line segments is infinite, then they are incommensurable.
Our fundamental finding is that the main entity of Plato
DOI : https://doi.org/10.32381/GB.2020.42.1-2.1
Price: 251
Some Magic and Latin Squares and the Bhuvane
By: R. C. Gupta
Page No : 35-54
Abstract
The nine Indian planetary magic squares of order 3 are attributed to Garga, who is said to belong to the hoary past. Formation of magic squares of order 9 from those of order 3, as bimagic squares, is found both in India and China. Bhuvane
DOI : https://doi.org/10.32381/GB.2020.42.1-2.2
Price: 251
Fifteenth-century Italian symbolic algebraic calculation with four and five unknowns
By: Jens Hoyrup
Page No : 55-86
Abstract
The present article continues an earlier analysis of occurrences of two algebraic unknowns in the writings of Fibonacci, Antonio de
DOI : https://doi.org/10.32381/GB.2020.42.1-2.3
Price: 251
Clairaut, Euler and the Figure of the Earth
By: Athanase Papadopoulos
Page No : 87-127
Abstract
The sphericity of the form of the Earth was questioned around the year 1687, primarily, by Isaac Newton who deduced from his theory of universal gravitation that the Earth has the form of a spheroid flattened at the poles and elongated at the equator. In France, some preeminent geographers were not convinced by Newton
DOI : https://doi.org/10.32381/GB.2020.42.1-2.4
Price: 251
Apodictic discourse and the Cauchy-Bunyakovsky-Schwarz inequality
By: Satyanad Kichenassamy
Page No : 129-147
Abstract
Bunyakovsky
DOI : https://doi.org/10.32381/GB.2020.42.1-2.5
Price: 251
Department of Mathematics at Banaras Hindu University: A history, circa 1916-1950
By: Ritesh Gupta
Page No : 149-173
Abstract
A historical study of Science Colleges and their constituting departments and disciplines, viz. Mathematics, Physics, Chemistry, Zoology, Botany, et cetera established in early universities could bring to light new facts and values to the history of science in modern India. However, not much scholarship has catered to the institutional histories of Science Colleges established in the late nineteenth and early twentieth centuries. Survey and scrutiny of institutionalization of modern sciences and mathematics in Indian universities have remained rather neglected. Therefore, the present paper explores the early history of the Banaras Hindu University
DOI : https://doi.org/10.32381/GB.2020.42.1-2.6
Price: 251
Book Reviews
By: M.S. Sriram
Page No : 175-181
Ganitagannadi, (Mirror of Mathematics)
Price: 251
Book Reviews
By: Avinash Sathaye
Page No : 182-186
A Primer to Bharatiya Ganitam; Bharatiya-Ganita-Pravesa by M.D. Srinivas (Editor), and Authors: V. Ramakalyani, M.V. Mohana, R.S. Venkatakrishna and N. Kartika
Reviewed by
Avinash Sathaye
Department of Mathematics, University of Kentucky, Lexington KY, U.S.A.
Price: 251
Some recent publications in History of Mathematics
By: No author
Page No : 187-196
Price: 251
Jan-2019 to Dec-2019
Brahmagupta
By: Satyanad Kichenassamy
Page No : 1-21
Abstract
DOI : https://doi.org/10.32381/GB.2019.41.1-2.1
Price: 251
Reinventing or Borrowing Hot Water? Early Latin and Tuscan Algebraic Operations with Two Unknowns
By: Jens Hoyrup
Page No : 23-67
Abstract
In mature symbolic algebra, from Vi
DOI : https://doi.org/10.32381/GB.2019.41.1-2.2
Price: 251
Nearest-Integer Continued Fractions in Drkkarana
By: Venketeswara Pai R. , M. S. Sriram
Page No : 69-89
Abstract
The Kara
DOI : https://doi.org/10.32381/GB.2019.41.1-2.3
Price: 251
Mathematics and Map Drawing in the Eighteenth Century
By: Athanase Papadopoulos
Page No : 91-126
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.
DOI : https://doi.org/10.32381/GB.2019.41.1-2.4
Price: 101
On the Contribution of Anders Johan Lexell in Spherical Geometry
By: A. Zhukova
Page No : 127-149
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
Price: 251
Magic Squares and Other Numerical Diagrams on the Chittagong Plaster Replicas in the David Eugene Smith Collection
By: Takao Hayashi
Page No : 151-180
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
Price: 251
Book Reviews
By: ..
Page No : 181-196
Price: 251
-2018 to Jun-2018
T.A. Sarasvati Amma: A Centennial Tribute
By: P. P. Divakaran
Page No : 1-16
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
DOI : https://doi.org/10.32381/GB.2018.40.01.1
Price: 251
The Seminal Contribution of K. S. Shukla to our Understanding of Indian Astronomy and Mathematics
By: M. D. Srinivas
Page No : 17-51
Abstract
DOI : https://doi.org/10.32381/GB.2018.40.01.2
Price: 251
On Old Babylonian Mathematical Terminology and its Transformations in the Mathematics of Later Periods
By: Jens Hoyrup
Page No : 53-99
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
DOI : https://doi.org/10.32381/GB.2018.40.01.3
Price: 251
Jul-2018 to Dec-2018
Katyayana Sulvasutra
By: S. G. Dani
Page No : 101-114
Abstract
The K
Price: 251
Essay Review: On the Interpretations of the History of Diophantine Analysis: A Comparative Study of Alternate Perspectives
By: Ioannis Vandoulakis
Page No : 115-152
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 Arithm
Price: 251
Nasir al-Din al-Tusi Treatise on the Quadrilateral: The Art of Being Exhaustive
By: Athanase Papadopoulos
Page No : 153-180
Abstract
We comment on some combinatorial aspects of Nasir al-Din al-Tusi
Price: 251
Book Reviews
By: ..
Page No : 191-198
The Mathematics of India : Concepts, Methods, Connections by P. P. Divakaran
Reviewed by Satyanad Kichenassamy
Price: 251
Book Reviews
By: ..
Page No : 191-198
Karanaapaddhati 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
Price: 251
Jan-2017 to Jun-2017
Archimedes
By: Jens Hoyrup
Page No : 1-21
Abstract
With Apuleius and Augustine as the only partial exceptions, Latin Antiquity did not know Archimedes as a mathematician but only as an ingenious engineer and astronomer, serving his city and killed by fatal distraction when in the end it was taken by ruse. The Latin Middle Ages forgot even much of that, and when Archimedean mathematics was translated in the 12th and 13th centuries, almost no integration with the traditional image of the person took place. Petrarca knew the civically useful engineer and the astrologer (!); no other fourteenth-century Humanist seems to know about Archimedes in any role. In the 15th century, however,
Price: 251
On the History of Nested Intervals: From Archimedes to Cantor
By: G. I. Sinkevich
Page No : 23-45
Abstract
The idea of the principle of nested intervals, or the concept of convergent sequences which is equivalent to this idea, dates back to the ancient world. Archimedes calculated the unknown in excess and deficiency, approximating with two sets of values: ambient and nested values. J. Buridan came up with a concept of a point lying within a sequence of nested intervals. P. Fermat, D. Gregory, I. Newton, C. MacLaurin, C. Gauss, and J.-B. Fourier used to search for an unknown value with the help of approximation in excess and deficiency. In the 19th century, in the works of B. Bolzano, A.-L. Cauchy, J.P.G. Lejeune Dirichlet, K. Weierstrass, and G. Cantor, this logical construction turned into the analysis argumentation method. The concept of a real number was elaborated in the 1870s in works of Ch. M
Price: 251
Explanation of the Vakyasodhana procedure for the Candravakyas
By: M. S. Sriram
Page No : 47-53
Abstract
The Candrav
Price: 251
Madhyahnakalalagna in Karanapaddhati of Putumana Somayaji
By: Venketeswara Pai R. , M. S. Sriram
Page No : 55-74
Abstract
Madhyahnakalalagna is the time interval between the rise of the equinox and the instant when a star with a non zero latitude is on the meridian. Algorithms for finding the Madhyahnakalalagna are given in the text Kara
Price: 251
Vedic Mathematics and Science in the Vedas (in Kannada) by S. Balachandra rao
Reviewed by Surabhi Saccidananda
By: ..
Page No : 75-77
Price: 251
Some Recent Publications in History of Mathematics
By: ..
Page No : 79-90
Price: 251
News
By: ..
Page No : 91-92
Price: 251
Obituary
By: ..
Page No : 93-94
Price: 251
Jul-2017 to Dec-2017
An Indian Version of al-Kashi
By: Kim Plofker
Page No : 95-106
Abstract
The well-known
Price: 251
Nilakantha's Critique on Aryabhata's Verses on Squaring and Square-roots
By: N. K. Sundareswaran
Page No : 107-124
Abstract
N
Price: 251
Sign and Reference in Greek Mathematics
By: Ioannis Vandoulakis
Page No : 125-145
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.
Price: 251
On the History of Analysis -The Formation of Concepts
By: G. Sinkevich
Page No : 147-162
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
Price: 251
Book Reviews
By: ..
Page No : 163-173
Price: 251
News
By: ..
Page No : 195-197
Price: 251
Jan-2016 to Jun-2016
Embedding: Multipurpose Device for Understanding Mathematics and its Development, or Empty Generalization?
By: Jens Hoyrup
Page No : 1-29
Abstract
Price: 251
Rolle
By: G. Sinkevich
Page No : 31-53
Abstract
We discuss the history of the famous Rolle
Price: 251
Book Reviews
By: ..
Page No : 55-72
Price: 251
Some Recent Publications in History of Mathematics
By: ..
Page No : 73-84
Price: 251
Annual Conference of ISHM - 2015 : A Report
By: ..
Page No : 85-89
Price: 251
Announcement
By: ..
Page No : 91-92
Price: 251
Jul-2016 to Dec-2016
Siddhanta-karana conversion: Some algorithms in the Grahaganitadhyaya of Bhaskara
By: Kim Plofker
Page No : 93-110
Abstract
Price: 251
The Candravakyas of Madhava
By: M. S. Sriram , M. D. Srinivas , K. Ramasubramanian ,
Page No : 111-139
Price: 251
The poetic features in the gol
By: K. Ramasubramanian , Anuj Misra , Clemency Montelle
Page No : 141-156
Abstract
Many astronomical works in India, like those in other intellectual disciplines, were composed in beautiful verses. While most studies focus on the technical contents of these verses, very few have examined the poetic features, here known as ala
Price: 251
Roshdi Rashed, Historian of Greek and Arabic Mathematics
By: Athanase Papadopoulos
Page No : 157-182
Abstract
We survey the work of Roshdi Rashed, the Egyptian-French historian of mathematics. Surveying Rashed
Price: 251
A tribute to Syamadas Mukhopadhyaya
By: S. G. Dani
Page No : 183-194
Price: 251
Annual Conference of ISHM - 2016 : A Report
By: ..
Page No : 195-197
Price: 251
Jan-2015 to Dec-2015
Bhaskaracarya
By: M. S. Sriram
Page No : 1-38
Abstract
Price: 251
Some Aspects of Patadhikara in Siddhantasiromani
By: Venketeswara Pai R. , M. S. Sriram , Sita Sundar Ram
Page No : 39-68
Abstract
Vyatipata and Vaidhrta occur when the magnitudes of the declinations of the Sun and the Moon are equal, and one of them is increasing, while the other is decreasing. In this paper, we discuss the calculations associated with them in the patadhikara in the Grahaganita part of Siddhantsiromani. Some of these are similar to the computations in Brahmasphutasiddhanta and Sisyaddhidatantra, but the computation of the golasandhi appears here for the first time. We also compare Bhaskara
Price: 251
The Phenomena of Retrograde Motion and Visibility of Interior Planets in Bhaskara
By: Shailaja M , Vanaja V , S. Balachandra Rao
Page No : 69-82
Abstract
In this paper we present the interesting phenomena of the retrograde motion of taragrahas as also the visibility of Budha (Mercury) and Sukra (Venus) in the eastern and western horizons.
Bhaskaracarya in his astronomical works has dwelt at length on these phenomena and provided the relevant critical and stationary points. WE work out the details in the case of the two interior planets and compare the results with modern ones.
Price: 251
True Positions of Planets According to Karanakutuhala
By: Shailaja M , Vanaja V , S. Balachandra Rao
Page No : 83-96
Abstract
We will be presenting briefly the procedure of determining the mean and true positions of the Sun, the Moon and the t
Price: 251
The Influence of Bhaskaracarya
By: Kim Plofker
Page No : 97-109
Abstract
The well-known treatises of Bhaskara II or Bhaskaracarya (b.1114) are unanimously recognized as canonical in Sanskrit mathematics and mathematical astronomy, but the specific details of their influence on later works remain largely unexplored (partly because most of those later works themselves still await comprehensive study). This article examines a few texts from the sixteenth to eighteenth centuries whose authors were familiar with some aspects of Greco-Islamic astronomy and mathematics, and discusses their continued use of Bh
Price: 251
Bhaskaracarya
By: Avinash Sathaye
Page No : 111-123
Abstract
Bhaskaracarya
Price: 251
Issues in Indian Metrology, from Harappa to Bhaskaracharya
By: Michel Danino
Page No : 125-143
Abstract
Numerous systems of units were developed in India for lengths, angles, areas, volumes, time or weights. They exhibit common features and a continuity sometimes running from Harappa to Bh
Price: 251
Indian Records of Historical Eclipses and their Significance
By: K. Ramasubramanian , Aditya Kolachana
Page No : 145-162
Abstract
Among the various techniques that are employed in determining the variation in the length of day (LOD), the recorded observations of ancient eclipses play a crucial role, particularly for estimating variations in the remote past. Scholarly investigations of these records preserved in different cultures around the world, for the above purpose, have completely ignored the Indian record of historical eclipses on the presumption that
Price: 251
Medieval Eclipse Prediction: A Parallel Bias in Indian and Chinese Astronomy
By: Jayant Shah
Page No : 163-178
Abstract
Since lunar and solar parallax play a crucial role in predicting solar eclipses, the focus of this paper is on the computation of parallax. A brief history of parallax computation in India and China is traced. Predictions of solar eclipses based on N
Price: 251
Jan-2014 to Jun-2014
Mathematical Models and Data in the Bra
By: Kim Plofker
Page No : 1-12
Abstract
While many of the innovative mathematical techniques developed by medieval Indian astronomers have been studied extensively, much less is known about how they chose to select and apply specific mathematical models to physical phenomena. This paper focuses on the paks.a or astronomical school associated with Brahmagupta (628 CE) and investigates what some of its characteristic features may tell us about the evolution of Indian mathematical astronomy.
Price: 251
From Verses in Text to Numerical Table
By: Clemency Montelle
Page No : 13-25
Abstract
A twelfth century set of astronomical tables, the Brahmatulyasa-ran. , poses some interesting challenges for the modern historian. While these tables exhibit a range of standard issues that numerical data typically present, their circumstances and mathematical structure are further complicated by the fact that they are purported to be a recasting of another work by Bhaskara II that was originally composed in verse, the Karan.akutu- hala (epoch 1183 CE). We explore this relationship by considering the tables for solar declination and lunar latitude and comparing them to their textual counterparts.
Price: 251
Instantaneous Motion(ta-tka-likagati) and the
By: M. S. Sriram
Page No : 37-52
Abstract
It was well known even before Bha-skara-ca -rya that the daily motion of a planet would vary from day to day. In his Siddha-nta
Price: 251
On the Works of Euler and his Followers on Spherical Geometry
By: Athanase Papadopoulos
Page No : 53-108
Abstract
We review and comment on some works of Euler and his followers on spherical geometry. We start by presenting some memoirs of Euler on spherical trigonometry. We comment on Euler
Price: 251
Sawai Jai Singh
By: Virendra N Sharma
Page No : 109-125
Abstract
The paper reviews Sawai Jai Singh
Price: 251
Obituary
By: ..
Page No : 127
Price: 251
Jul-2014 to Dec-2014
Hyperbolic Geometry in the Work of J. H. Lambert
By: Athanase Papadopoulos , Guillaume Théret
Page No : 129-155
Abstract
The memoir Theorie der Parallellinien (1766)* by Johann Heinrich Lambert is one of the founding texts of hyperbolic geometry, even though its author
Price: 251
On the Legacy of Ibn Al-Haytham: An Exposition Based on the Work of Roshdi Rashed
By: Athanase Papadopoulos
Page No : 157-177
Abstract
We report on the work of Ibn al-Haytham, an Arabic scholar who had settled in Cairo in the eleventh century, and worked in several fields, including mathematics, physics and philosophy. We review some of his work on optics, astronomy, number theory and especially spherical geometry. Our report is mostly based on the books published by Roshdi Rashed, a specialist on Ibn alHaytham and the world expert on Arabic and Greek mathematics and their interaction. We also provide a report on the life of Ibn al-Haytham, his influence, and the general background in which he flourished. The year 2015 has been declared by the UNESCO the
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Otto H
By: R. Sridharan
Page No : 179-191
Abstract
Otto H
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Some Identities and Series Involving Arithmetic and Geometric Progressions in P
By: Shriram M. Chauthaiwale
Page No : 193-204
Abstract
The celebrity Indian mathematician trio
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Book Reviews
By: ..
Page No : 205-218
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Some Recent Publications in History of Mathematics
By: ..
Page No : 219-226
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Report on the Annual Conference of ISHM - 2014 Dedicated to
By: ..
Page No : 227-230
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News
By: ..
Page No : 231-233
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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”.