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Yuktibhāṣā contains a derivation and proof for the power series of inverse tangent, discovered by Madhava. [5] In the text, Jyesthadeva describes Madhava's series in the following manner: The first term is the product of the given sine and radius of the desired arc divided by the cosine of the arc.
Jyeṣṭhadeva (c. 1500 – c. 1575) [1] [2] was an astronomer-mathematician of the Kerala school of astronomy and mathematics founded by Madhava of Sangamagrama (c. 1350 – c. 1425). He is best known as the author of Yuktibhāṣā, a commentary in Malayalam of Tantrasamgraha by Nilakantha Somayaji (1444–1544).
Madhava developed the power series expansion for some trigonometry functions which were further developed by his successors at the Kerala school of astronomy and mathematics. [24] (Certain ideas of calculus were known to earlier mathematicians.) Madhava also extended some results found in earlier works, including those of Bhāskara II. [24]
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 in Kerala, India by the mathematician and astronomer Madhava of Sangamagrama (c. 1350 – c. 1425) or his followers in the Kerala school of astronomy and mathematics. [1]
Madhava's correction term is a mathematical expression attributed to Madhava of Sangamagrama (c. 1340 – c. 1425), the founder of the Kerala school of astronomy and mathematics, that can be used to give a better approximation to the value of the mathematical constant π (pi) than the partial sum approximation obtained by truncating the Madhava–Leibniz infinite series for π.
The Kerala school of astronomy and mathematics or the Kerala school was a school of mathematics and astronomy founded by Madhava of Sangamagrama in Tirur, Malappuram, Kerala, India, which included among its members: Parameshvara, Neelakanta Somayaji, Jyeshtadeva, Achyuta Pisharati, Melpathur Narayana Bhattathiri and Achyuta Panikkar.
The extant works of the Dvaita founder-philosopher, Madhvacharya, called the Sarvamūla Granthas, are many in number.The works span a wide spectrum of topics concerning Dvaita philosophy in specific and Vedic thought in general.
In comparison, Yuktibhasha, composed in pure Malayalam and published in the middle of the sixteenth century, is an advanced text on mathematics and astronomy addressed to the advanced students and scholars of mathematics. The book is composed in verses and it also contains a commentary both in Manipravalam language.