Sankara Varman

Sankara Varman (1774–1839) was an astronomer-mathematician belonging to the Kerala school of astronomy and mathematics. He is best known as the author of Sadratnamala, a treatise on astronomy and mathematics, composed in 1819. Sankara Varman is considered as the last notable figure in the long line of illustrious astronomers and mathematicians in the Kerala school of astronomy and mathematics beginning with Madhava of Sangamagrama. Sadratnamala was composed in the traditional style followed by members of the Kerala school at a time when India had been introduced to the western style of mathematics and of writing books in mathematics. One of Varman's contributions to mathematics was his computation of the value of the mathematical constant π correct to 17 decimal places. Quotes The radius into the sine divided by the cosine is the first quote: this multiplied by the square of the sine, and divided by the square of the cosine, is the second quote; this second, and those obtained continually in the same way, multiply and divide by the square of the sine and the square of the cosine respectively: divide the quotes in order by 1, 3, 5, 7,11, etc. respectively, and the difference of the sum of the first, third, fifth, etc. and of the second, fourth, sixth, etc., will be the arc whose sine was taken. Shankara Varman (1800–1838) in Sadratnamala. verse from the Sadratnamala कोटीहतत्रिगणु बाहुवधे च तस््ममात्तत्तत््फलाच््च भजु वर््गहतात्तु कोट्याः।कृ त््यया हतेषु च धराग््ननिशरादिभक्ते-ष््ववोजैक््यतस््त््यजतु युग््मयुतिं धनुस््तत्॥ Whish, Charles M. ‘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 Sangraham, Yukti Bhasha, Karana Padhati, and Sadratnamala’. Transactions of the Royal Asiatic Society of Great Britain and Ireland, Vol. 3, No. 3, (1834): pp. 509-523. quoted in : Bhaskar Kamble, The Imperishable Seed: How Hindu Mathematics Changed the World and why this History was Erased, Garuda Prakashan Private Limited, 2022 ISBN 9798885750189 Square the diameter and multiply the product by 12, and extract the root of this product; the root obtained will be the modulus of odd quotes, which if you divide by 3, the quotient will be the modulus of even quotes. Divide each modulus continually by 9, and the quotient thus obtained from the former, divide by double the numbers 1, 3, 5, 7, 9, etc. minus 1 respectively, and the quotient obtained by the latter, by double the number 2, 4, 6, 8, 10, etc. minus 1 respectively, add up the new obtained quotes, and subtract the sum of those gotten from the even from the sum of those gotten from the odd modulus, the remainder is the circumference of the circle. Square the diameter and multiply the product by 12, and extract the root of this product; this root divide continually by 3, and the quotients thus obtained by 1, 3, 5, 7, 9, 11, etc., and subtract the sum of the second, fourth, sixth, eighth of the last obtained quotes from the sum of the first, third, fifth, seventh, ninth, etc. If you do thus, and measure the diameter of a great circle by 100000000000000000 equal parts, the circumference will be equal to 314159265358979324 of such parts. A verse from Sadratnamala वर््गगाद् व््ययासस््ययार््कनिघ््ननात् पदं यत् तत्त्र्यंशो यस््तते च तत्तन््नवांशाः।द्विघ््नव््ययेकैकद्विपूर्वौजयुग््मच््छछिन््ननान््ययैक््यद््वव््यन््तरः वृत्तनाहः॥व््ययासार््क घ््नकृ तेः पदेऽग््ननिभिरतो नीते च तत्तत््फला-च््चचाथैक््ययाद्ययुगाहृतेषु परिधिर्भेदो युगौजैक््ययोः।एवं चात्र परार््धविस््ततृतिमहावृत्तस््य नाहोऽक्षरै ःस््ययाद् भद्राम््बबुधिसिद्धजन््मगणितश्रद्धा स््म यद् भपू गीः॥ Whish, Charles M. ‘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 Sangraham, Yukti Bhasha, Karana Padhati, and Sadratnamala’. Transactions of the Royal Asiatic Society of Great Britain and Ireland, Vol. 3, No. 3, (1834): pp. 509-523. quoted in : Bhaskar Kamble, The Imperishable Seed: How Hindu Mathematics Changed the World and why this History was Erased, Garuda Prakashan Private Limited, 2022 ISBN 9798885750189 External links Category:Kerala school of astronomy and mathematics Category:Astronomers from India Category:1774 births Category:1839 deaths Category:Mathematicians from India