| _version_ | 1866901209359581184 |
|---|---|
| author | Bhat, Girisha B |
| author_facet | Bhat, Girisha B |
| contents | <div> <div>ithin the domain of Indian mathematical astronomy, Siddhānta Jyotisa serves as a foundational pillar, specifically for the construction of the pañcāṅga (almanac) and the determination of grahasphuta (true planetary longitudes). Central to these astronomical computations is the science of Jyotpatti the derivation and calculation of chord- based sine functions. This paper explores the theoretical framework of Jyotpatti as expounded by the pre- eminent mathematician Bhāskarācārya in his seminal work, Siddhāntasīromani \citep{siddhantasiromani2010}. The study focuses on the four fundamental sine quantities : bhujājyā (sine), kotijyā (cosine), utkramajyā (versed sine), and koṭyutkramajyā (versed cosine). By analyzing primary verses from the Golādhyāya and Gaṇitādhyāya, this research presents a detailed study of Bhāskarācārya's geometric and algebraic methods. Key derivations discussed include the sine of half- arcs, the theorem of addition and subtraction of sines, and the computation of sines for specific angles such as \(30^{\circ}\) and 45. This study highlights the historical significance and technical sophistication of Indian trigonometry prior to its modern developments.</div> </div> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_19366414 |
| institution | Zenodo |
| language | |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Bhāskarācārya's Theories on the Construction of the Sine Bhat, Girisha B Jyā, Bhujajyā, Koṭijyā, Bhujotkramajyā, Koṭyutkramajyā <div> <div>ithin the domain of Indian mathematical astronomy, Siddhānta Jyotisa serves as a foundational pillar, specifically for the construction of the pañcāṅga (almanac) and the determination of grahasphuta (true planetary longitudes). Central to these astronomical computations is the science of Jyotpatti the derivation and calculation of chord- based sine functions. This paper explores the theoretical framework of Jyotpatti as expounded by the pre- eminent mathematician Bhāskarācārya in his seminal work, Siddhāntasīromani \citep{siddhantasiromani2010}. The study focuses on the four fundamental sine quantities : bhujājyā (sine), kotijyā (cosine), utkramajyā (versed sine), and koṭyutkramajyā (versed cosine). By analyzing primary verses from the Golādhyāya and Gaṇitādhyāya, this research presents a detailed study of Bhāskarācārya's geometric and algebraic methods. Key derivations discussed include the sine of half- arcs, the theorem of addition and subtraction of sines, and the computation of sines for specific angles such as \(30^{\circ}\) and 45. This study highlights the historical significance and technical sophistication of Indian trigonometry prior to its modern developments.</div> </div> |
| title | Bhāskarācārya's Theories on the Construction of the Sine |
| topic | Jyā, Bhujajyā, Koṭijyā, Bhujotkramajyā, Koṭyutkramajyā |
| url | https://doi.org/10.5281/zenodo.19366414 |