# Clemency Montelle's research while affiliated with University of Canterbury and other places

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## Publications (42)

Telling time by the length of gnomon shadows is a very ancient practice. Prior to the development of spherical cosmological models and accompanying trigonometric techniques in the last few centuries bce, such computations relied on non-trigonometric algorithms approximately relating shadow lengths to time and geographic location.

Arithmetic and algebra form two fundamental branches of mathematics. While arithmetic deals with mathematical operations, algebra deals with the determination of unknown entities. Hence arithmetic was known as vyakta (manifest) gaṇita and algebra was known as avyakta (unmanifest) gaṇita.

Bhāskara’s Bījagaṇitam (BB) contains 11 chapters consisting of 187 verses pertaining to algebra, 2 introductory verses and 9 verses in the epilogue [BīGa1980, pp. 7–59]. In the second verse of the epilogue Bhāskara admits that this text is compiled by selecting notable ideas from his predecessors like Brahmagupta, Śrīdhara, Padmanābha and others [B...

It is well known that Bhāskara is the first Indian astronomer who mentioned clearly the addition and subtraction formula for the sine and the cosine.

Commendably consolidating the works of his predecessors and brilliantly employing his poetic skills, Bhāskarācārya composed his Līlāvatī (L)—a treatise that deals with arithmetic, algebra and geometry without the knowledge of which one cannot appreciate the later chapters in the Grahagaṇita and Golādhyāya.

The Bhūtasaṅkhyā system is a method of expressing numerals with specific words in Sanskrit.

After the publication of the Common Core State Standards for Mathematics (CCSSM, 2010) in the United States, over forty of the fifty states have adopted them in their school mathematics curriculum.

In this study I use two editions of the Līlāvatī, both of which are accompanied by commentaries. One edition is with the Buddhivilāsinī (1545) by Gaṇeśa Daivajña and a vivaraṇa (1587) by Mahīdhara [Līlā1937]. This also includes the auto-commentary by Bhāskara.

The translation movement of scientific texts initiated during the early Abbasid period (750-950) in West and Central Asian countries during the Islamic Middle Age was naturally transmitted to medieval India during the Sultanate and Mughal periods, when learned scholars seeking patronization thronged to the courts of Indian Sultans, Mughal emperors,...

The doyen of scholars Dr. K. V. Sarma, who completely dedicated himself to unearth, identify and edit seminal works produced by the mathematical tradition of Kerala, has recorded that there are six commentaries written in Malayalam on the Līlāvatī [Līlā1975, p. xiii].

Mensuration with quadrilaterals had received attention in the siddhānta tradition at least since Brahmagupta. However, in Bhāskarācārya’s Līlāvatī we come across some distinctively new features. In this paper an attempt will be made to put the development in historical perspective.

Unlike the writers on other branches of Sanskrit learning about whom we know nothing but their names, authors of works on Jyotiḥśāstra, from Āryabhaṭa onwards, generally mention the years of their birth or epochs that are closer to their own times.

Sanskrit literature is rich in a variety of texts across a wide range of disciplines including mathematics, astronomy, medicine, history, philosophy, drama, mythology and so on. A perusal of literature around the world will show that, while it is common to compose works related to history, literature, mythology etc. in metrical form, scientific lit...

Bhāskarācārya’s grandson Caṅgadeva established a college (maṭha) for the propagation of his grandfather’s works (śrī-bhāskarācārya-nibaddha-śāstravistāra- hetoḥ) and announced this fact in an inscription in 1207.

Bhāskarācārya is basically a paṇḍita of the twelfth century, well-versed in Sanskrit śāstras at the level they had reached in his times. That was a period of great refinement, a summit in all cultural fields, science, literature and arts.

Apart from composing the celebrated textbooks of Indian mathematics and astronomy, viz. Līlāvatī, Bījagaṇita and Siddhāntaśiromaṇi, Bhāskarācārya also wrote the Vāsanābhāṣyas, commentaries which have acquired the status of canonical expository texts as they present detailed explanations and justifications for the results and processes outlined in t...

The Siddhāntaśiromaṇi composed in 1150 ce by Bhāskarācārya is one of the most comprehensive treatises on Indian astronomy. It has two parts, namely, Grahagaṇita and Golādhyāya.

In his most comprehensive and critical history of Bhāratīya Jyotiṣa, the great savant Sankara Balakrishna Dikshit remarks that Bhāskarācārya used his exceptional talents in formulating rationales for the mathematical and astronomical procedures but not in advancing the techniques of observational astronomy [Dik1981, pp. 114–123, esp. 120–121].

One of the important topics of the traditional luni-solar calendar is how to insert intercalary months so that the lunar month, which is dependent on the lunar phase, can be adjusted to the solar month, which is determined by the position of the sun.

Jyotpatti, literally ‘Production of Sines’, is the name given to one of the chapters of Bhāskara’s Siddhāntaśiromaṇi (1150 ce).

This book covers the works of Bhāskara, in particular, his monumental treatise on astronomy, the Siddhāntaśiromaṇi, his astronomical handbook, the Karaṇakutūhala, and his two mathematical treatises, the Līlavatī and the Bījagaṇita, on arithmetic and algebra, respectively. It is a collection of selected papers presented at Bhāskara 900, an internati...

A set of tables devoted to solar and lunar phenomena entitled the Candrārkī was prepared in Sanskrit by the sixteenth-century Indian astronomer Dinakara. Along with the tables, Dinakara composed a short accompanying text which instructed the user how to extract and manipulate the tabular data to construct their own calendar for any desired year and...

A set of tables devoted to the sun and the moon, titled the Candrārkī (“Related to the moon and sun”), was compiled in Sanskrit by Indian astronomer Dinakara along with a short accompanying text, intended to give guidance on how to construct a calendar (pañcāṅga) for any desired year and geographical circumstances. The epoch of this table-text is 9...

This groundbreaking volume provides an up-to-date, accessible guide to Sanskrit astronomical tables and their analysis. It begins with an overview of Indian mathematical astronomy and its literature, including table texts, in the context of history of pre-modern astronomy. It then discusses the primary mathematical astronomy content of table texts...

Hitherto we have discussed the content and structure of Sanskrit astronomical tables abstracted from their physical embodiment in manuscripts. In this chapter we consider the manuscripts themselves: their overall position within the corpus of Sanskrit jyotiṣa and the scribal conventions that characterize them.

In this chapter we broadly outline two different aspects of the genre of Sanskrit astronomical table texts: the mathematical models underlying their construction and the chief approaches to their taxonomy. We begin by explaining in more detail the algorithms and models that were briefly outlined in Section 1.2.2. The subsequent section broadly surv...

The early development of Sanskrit astronomical tables described in Section 1.5 blossomed by the mid-second millennium into the profuse variety of table-text types categorized in Section 2.3, whose typical components were analyzed in more detail in Chapter 4. As numerical tables became more central to the work of astronomers/astrologers, the mathema...

The previous overview reinforces our original impression that the proliferation of table texts was one of the most important developments in Sanskrit astronomy in the second millennium. The flexible and innovative construction of sāraṇı̄s increased computational convenience and efficiency for their users as well as affording new outlets for the cre...

The canonical structure and sequence of astronomical topics as represented in most major siddhānta and karaṇa works (see Section 1.4) are modified in the table-text genre in a number of different ways.

Popular attention has recently been captured by the results of the Bodleian Library's 2017 project of radiocarbon datingportions of the birch-bark fragments constituting what is known as the Bakhshālī Manuscript. In this paper, we disagree with the interpretation of the findings announced by the Bodleian team. In particular, we argue that the earli...

We present here a critical edition of the numerical tables of the Karaṇakesarī, an eclipse-computation table-text authored by Bhāskara in the laer half of the 17th century, and known to us from three manuscripts.

A short survey on Islamic mathematical astronomy practiced during the period running from the eight century until the fifteenth is presented. Various pertinent themes, such as the translation of foreign scientific works and their impact on the tradition; the introduction, assimilation, and critique of the Ptolemaic model; and the role of observatio...

In a famous passage from his al-Bāhir, al-Samaw’al proves the identity which we would now write as \((ab)^n=a^n b^n\) for the cases \(n=3,4\). He also calculates the equivalent of the expansion of the binomial \((a+b)^n\) for the same values of n and describes the construction of what we now call the Pascal Triangle, showing the table up to its 12t...

The ability to address and solve problems in minimally familiar contexts is the core business of research mathematicians. Recent studies have identified key traits and techniques that individuals exhibit while problem solving, and revealed strategies and behaviours that are frequently invoked in the process. We studied advanced calculus students wo...

Sanskrit sources offer a wide variety of numerical tables, most of which remain little studied. Tabular information can be found encoded in verse, woven into prose, sometimes arranged in aligned grids of rows and columns but also in other, less standard patterns. We will consider a large range of topics from mathematical (gaṇita) and astral science...

Critical edition, translation and commentary for the verse instructions accompanying a late seventeenth-century set of eclipse tables in Sanskrit by Bhāskara of Saudāmikā (fl. 1681).

## Citations

... Many of these Persian renderings, especially those of the Mahabhārata and Rāmāyaṇa were lavishly illustrated by the painters at Akbar's atelier. 3 Quite different from these in content and style is Bhāskara's Līlāvatī on arithmetic and geometry which too was rendered into Per-sian. It may be noted that no manuscripts of this work were illustrated at Akbar's court. ...

... Having heard of his exceptional talents, Akbar summoned him to his court in 1567 and made him the Poet Laureate (malik 6 Līlāvatī 1: prītiṃ bhaktajanasya yo janayate vighnaṃ vinighnan smṛtaḥ taṃ vṛndārakavṛndavanditapadaṃ natvā mataṅgānanam | pāṭīṃ sadgaṇitasya vacmi caturaprītipradāṃ prasphuṭāṃ saṃkṣiptākṣara-komalāmalapadair lālitya-līlāvatīm || al-shu arā) in 1588. 9 Faiẓī was an outstanding scholar and an acclaimed poet. He wrote an exegesis on the Qur'ān in Persian, employing only the undotted letters of the alphabet. ...

... Many scholars have worked on both the parts of Siddhāntaśiromaṇi in the past. The verses of Grahagaṇitādhyāya have been translated into English by Arka-DOI: 10.16943/ijhs/2020/v55i2/154678 * Email: sriram.physics@gmail.com ...

... It has been shown that this story of Bhāskara's daughter does not occur in any Sanskrit source, that it occurs 13 16 It is interesting to note that while the Persian translation was commissioned by the Mughal Emperor Akbar, its editio princeps was printed 240 years later under the authority of the Governor General of the East-India Company, which succeeded the Mughal Empire. ...

... Naisān is the first month in the Syrian calendar and corresponds to April.15 All translations from the Persian and Sanskrit are by the authors, unless otherwise specified. ...

... The most comprehensive work on the history of mathematics in India is by Plofker (2009), to which readers are referred to for further information, with references, on most of the points discussed here. Classic and more recent contributions include: Bag (1979), Colebrooke ([1817Colebrooke ([ ] 1973, Singh 1962 [1935]), Delire (2016), Filliozat (2004, Hayashi (1994Hayashi ( , 1995aHayashi ( , 2003Hayashi ( , 2013, Joseph (2011), Kaye (1908Kaye ( , 1915Kaye ( , 1927Kaye ( -1933, Keller (2006 and, Kusuba (1993), Kusuba and Plofker (2013), Patte (2004), , Plofker (2007), Plofker et al. (2017), SaKHYa (2009), Sarasvati Amma (1979), Sarma (2003 and), Sen and Bag (1983), Shukla (1959), Srinivasiengar (1967), Staal (1999Staal ( , 2006, and Thibaut (1875). The reader interested in the history of Indian mathematical astronomy in the Indian subcontinent can refer to the numerous publications by Montelle and Plofker. 2 The term jyotiṣa refers to a mix of astronomy, astrology, and calendrics; a thorough history of jyotiḥśāstra literature is found in . ...

... While studying problem-solving behaviors in small groups of students, Clark et al. (2014) extended Carlson and Bloom's (2005) framework by introducing two new categories/codes. They termed them questioning and group synergy. ...