Gaṇeśa Daivajña's Grahalāghava stands out among the Indian astronomical texts for its approach to the calculation and usage of ahargaṇa, unlike texts such as Āryabhaṭīya and Tantrasaṅgraha that rely on well-established epochs or the other texts like Pañcasiddhāntikā that incorporate personalized epochs. Its uniqueness comes through the introduction of 'cakras', the cycles of 11 years, where the ahargaṇa gets recalibrated at the start of every cycle. Gaṇeśa uses both cakra and ahargaṇa in the computation of the position of the Sun and planets. This study explores the methodology employed by Gaṇeśa and gives a rationale for his method. We show systematically through the continued fractions approach that his method arises naturally. Our study also highlights how the accuracy of determining astronomical events remains uncompromised despite its simplified approach. Furthermore, given that the motivation for Grahalāghava is to simplify the calculations in astronomy without using trigonometric functions, we discuss how a deeper understanding of it contributes to broadening our appreciation of the mathematical ingenuity present in the Indian astronomical work.

The prāṇakalāntara, which is the difference between the longitude of a point on the ecliptic and its corresponding right ascension, is an important parameter in the computation of the lagna (ascendant). Mādhava, in his Lagnaprakaraṇa, proposes six different methods for determining the prāṇakalāntara. Kolachana et al. (Indian J Hist Sci 53(1):1–15, 2018) have discussed these techniques and their underlying rationale in an earlier paper. In this paper, we bring out the geometric significance of these computations, which was not fully elaborated upon in the earlier study. We also show how some of the sophisticated relations can be simply derived using similar triangles.

The kuṭṭaka algorithm for solving linear indeterminate equations is one of the most important contributions of India in the field of mathematics. Right from Āryabhatīya we find a description of the kuṭṭaka process employed in the context of planetary computations. The kuṭṭaka finds extensive treatment in Brahmagupta's Brāhmasphuṭasiddhānta in the eponymous chapter (called the kuṭṭakādhyāya) along with other allied algebraic tools such as bhāvitaka, varga-prakṛti etc. While the Brāhmasphuṭasiddhānta is recorded to have several commentaries written on it by Balabhadra, Varuṇa etc, it is the commentary by Pṛthūdakasvāmin called the Vāsanābhāṣya that seems to most extant in terms of completeness and number of manuscripts. In this regard, we would like to show our work on a rare manuscript of Vāsanābhāṣya that, as our survey goes, uniquely has the full commentary of the chapter of kuṭṭaka. While the kuṭṭaka has already been worked upon by many scholars previously: Colebrooke (1817), Dvivedi (1902), Sharma (1966), Iyengar (1988) and Heroor (2021) to name a few, there is a compelling need for a complete analysis of kuṭṭaka , especially with a view to bring out the mathematical rationale along with the valuable insights offered by Pṛthūdakasvāmin. In our paper, we provide the translation of all the verses of kuṭṭakādhyāya along with select portions of Vāsanābhāṣya and bring out the underlying mathematical rationale of the kuṭṭaka algorithm with valuble insights from Pṛthūdakasvamin's Vāsanābhāṣya. We also situate the text and the commentary in a more broader context of the mathematics methodology in its multiform social-cultural settings.

The “paṭaha” is a two-faced, horizontally played percussion instrument from India, widely referenced in texts from various historical periods. It has been out of use for at least a few centuries. There are two primary variations: mārgapaṭaha and deśīpaṭaha, signifying the mainstream and colloquial forms, respectively. Despite its former prominence, only a few musicological treatises—primarily the Mānasollāsa of Someśvara (12th century CE) and Saṅgītaratnākara of Śārṅgadeva (13th century CE) —offer detailed accounts of its characteristics and construction. Although the Saṅgītaratnākara provides relatively clear descriptions, some essential technical terms remain ambiguous. In contrast, the descriptions of the paṭaha in the Mānasollāsa appear in a highly obscure form in published editions due to erroneous readings in the source manuscripts. To overcome this challenge, we have gathered and analyzed previously unexamined manuscripts of the Mānasollāsa. Along with the cross-referencing with the Saṅgītaratnākara’s descriptions, we have critically edited the descriptive literature, and given an informed translation. We intend to present the characteristics of paṭaha along with the process of its construction, the materials used, its dimensions and make historically-informed observations on ways of playing it, as delineated in these sources.