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Yuktibhāṣā, also known as Gaṇita-yukti-bhāṣā and Gaṇitanyāyasaṅgraha, is a major treatise on mathematics and astronomy, written by the Indian astronomer Jyesthadeva of the Kerala school of mathematics around 1530. The treatise, written in Malayalam, is a consolidation of the discoveries by Madhava of Sangamagrama, Nilakantha Somayaji, Parameshvara, Jyeshtadeva, Achyuta Pisharati, and other astronomer-mathematicians of the Kerala school. It also exists in a Sanskrit version, with unclear author and date, composed as a rough translation of the Malayalam original.
Tantrasamgraha, or Tantrasangraha, is an important astronomical treatise written by Nilakantha Somayaji, an astronomer/mathematician belonging to the Kerala school of astronomy and mathematics. The treatise was completed in 1501 CE. It consists of 432 verses in Sanskrit divided into eight chapters. Tantrasamgraha had spawned a few commentaries: Tantrasamgraha-vyakhya of anonymous authorship and Yuktibhāṣā authored by Jyeshtadeva in about 1550 CE. Tantrasangraha, together with its commentaries, bring forth the depths of the mathematical accomplishments the Kerala school of astronomy and mathematics, in particular the achievements of the remarkable mathematician of the school Sangamagrama Madhava. In his Tantrasangraha, Nilakantha revised Aryabhata's model for the planets Mercury and Venus. According to George G Joseph his equation of the centre for these planets remained the most accurate until the time of Johannes Kepler in the 17th century.
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Madhava's sine table is the table of trigonometric sines constructed by the 14th century Kerala mathematician-astronomer Madhava of Sangamagrama. The table lists the jya-s or Rsines of the twenty-four angles from 3.75° to 90° in steps of 3.75°. Rsine is just the sine multiplied by a selected radius and given as an integer. In this table, as in Aryabhata's earlier table, R is taken as 21600 ÷ 2π ≈ 3437.75.
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In astronomy, Jyotirmimamsa is a treatise on the methodology of astronomical studies authored by Nilakantha Somayaji (1444–1544) in around 1504 CE. Nilakantha somayaji was an important astronomer-mathematician of the Kerala school of astronomy and mathematics and was the author of the much celebrated astronomical work titled Tantrasamgraha. This book stresses the necessity and importance of astronomical observations to obtain correct parameters for computations and to develop more and more accurate theories. It even discounts the role of revealed wisdom and divine intuitions in studying astronomical phenomena. Jyotirmimamsa is sometimes cited as proof to establish that modern methodologies of scientific investigations were known to ancient and medieval Indians. Neelkantha Somayaji insisted that computational results should tally with that of observations and astronomical parameters and constants should be revised periodically. To come to more precise conclusions, Neelkantha Somayaji have discussions with the astronomer and mathematicians of other schools.
In mathematics, a Madhava series is one of the three Taylor series expansions for the sine, cosine, and arctangent functions discovered in 14th or 15th century Kerala by the mathematician and astronomer Madhava of Sangamagrama or his followers in the Kerala school of astronomy and mathematics. Using modern notation, these series are:
In mathematics, Bhāskara I's sine approximation formula is a rational expression in one variable for the computation of the approximate values of the trigonometric sines discovered by Bhāskara I, a seventh-century Indian mathematician. This formula is given in his treatise titled Mahabhaskariya. It is not known how Bhāskara I arrived at his approximation formula. However, several historians of mathematics have put forward different hypotheses as to the method Bhāskara might have used to arrive at his formula. The formula is elegant and simple, and it enables the computation of reasonably accurate values of trigonometric sines without the use of geometry.
Kriyakramakari (Kriyā-kramakarī) is an elaborate commentary in Sanskrit written by Sankara Variar and Narayana, two astronomer-mathematicians belonging to the Kerala school of astronomy and mathematics, on Bhaskara II's well-known textbook on mathematics Lilavati. Kriyakramakari, along with Yuktibhasa of Jyeshthadeva, is one of the main sources of information about the work and contributions of Sangamagrama Madhava, the founder of Kerala school of astronomy and mathematics. Also the quotations given in this treatise throw much light on the contributions of several mathematicians and astronomers who had flourished in an earlier era. There are several quotations ascribed to Govindasvami a 9th-century astronomer from Kerala.
A Yuga Cycle is a cyclic age (epoch) in Hindu cosmology. Each cycle lasts for 4,320,000 years and repeats four yugas : Krita (Satya) Yuga, Treta Yuga, Dvapara Yuga, and Kali Yuga.
Garga-samhita, is an Indian Sanskrit-language text on jyotisha, written as a dialogue between the sages Bharadvaja and Garga. Although attributed to Garga, it was definitely not composed by the ancient astrologer of that name, and can be dated to 6th-7th century CE.
References
- 1 2 Charles Whish (1834), "On the Hindu Quadrature of the circle and the infinite series of the proportion of the circumference to the diameter exhibited in the four Sastras, the Tantra Sahgraham, Yucti Bhasha, Carana Padhati and Sadratnamala", Transactions of the Royal Asiatic Society of Great Britain and Ireland, Royal Asiatic Society of Great Britain and Ireland, 3 (3): 509–523, doi:10.1017/S0950473700001221, JSTOR 25581775
- ↑ Datta, Bibhutibhushan; A.N. Singh (1993). "Uses of series in India". Indian Journal of History of Science. 28 (3): 103–129.
- 1 2 3 Bag, Amulya Kumar (1966). "Trigonometrical series in the Karanapaddhati and the probable date of the text" (PDF). Indian Journal of History of Science. Indian National Science Academy. 1 (2): 98–106.[ permanent dead link ]
- ↑ Rajaraja Varma Vadakkumkuur. History of Sanskrit Literature in Kerala (1–6 Volumes). Vol. 1. p. 529.
- ↑ N. Gopalakrishnan (2004). Baharatheeya Vijnana / Saastra Dhaara ( Handbbok of Ancient Indian Scientific Books) (PDF). Heritage Publication Series. Vol. 78. Thiruvanannthapuram, India: Indian Institute of Scientific Heritage. pp. 18–20. Retrieved 12 January 2010.[ permanent dead link ]
Venketeswara Pai R, K Ramasubramanian, M S Sriram and M D Srinivas, Karanapaddhati of Putumana Somayaji, Translation with detailed Mathematical notes, Jointly Published by HBA (2017) and Springer (2018).
