Mahavir (mathematician)
Mahavira (or Mahavaracharya) was a famous astrologer and mathematician of India in the ninth century. He was a resident of Gulburg. He was a follower of Jainism. He did a lot of remarkable work on permutations and introduced the generalized formula for the first time in the world to remove the number of permutations and reserves (combinations). They lived in the shelter of a great nation named Amoghava I.
He composed mathematical literature called mathematics literature in which many topics of topics and topics of geometry are discussed. His book, Pavuluri Malvan, was translated into Telugu by the name 'Saranshantra Ganitam'.
Mahaveer has said so great about the importance of mathematics - MultiballPa'l: Kim, Trilokey Sachrachare It is not without mathematical form. (What is the benefit of having a lot of babble? In this past world, whatever is in the world is not without mathematics / it can not be understood without mathematics)
main work Nomenclature of large numbers Separation of fractions
Mahavira gave a different way to express the different forms of the sum of unit fractions (Unit Fractions). In it there are many rules given in the department called 'Bhagjati' (verses 55 to 9 8). Some of them are: - Variations of gold ornaments green: respectively Bidyabhishanbhayastava Adimacharamou Phal variants (Manthan Shastra Kala Shastra 75) Meaning: When the result is 1 then the fraction of 1 degree, starting with every 1, will be multiplied by 3, respectively. The first and the last will be multiplied by 2 and 2/3 respectively. 1 = 1 1 & # x22C5; 2 + 1 3 + 1 3 2 + & # X22EF; + 1 3 n & # x2212; 2 + 1 2 3 & # x22C5; 3 n & # x2212; 1 {\displaystyle 1={\frac {1}{1\cdot 2}}+{\frac {1}{3}}+{\frac {1}{3^{2}}}+\dots +{\frac {1}{3^{n-2}}}+{\frac {1}{{\frac {2}{3}}\cdot 3^{n-1}}}} Equation of order
Mahavira presented a solution for the n type and the high degree equations of the following types. The second chapter of mathematics collection is called the operation of the reduction of fractions. & # xA0; a x n = q {\displaystyle \ ax^{n}=q} And a x n & # x2212; 1 x & # x2212; 1 = p {\displaystyle a{\frac {x^{n}-1}{x-1}}=p}
Formula of cyclic quadrilateralAditya and his former Brahmagupta had highlighted the properties of cyclic quadrilateral. After this, Mahavira gave equations to find the lengths of sides and diagonals of cyclic quadrilaterals.
If a, b, c, d are the sides of a cyclic quadrilateral and the length of its diagonals is x and y,
& # xA0; x = a d + b c a b + c d ( a c + b d ) {\displaystyle \ x={\sqrt {{\frac {ad+bc}{ab+cd}}(ac+bd)}}}
और
Y = a b + c d a d + b c ( a c + b d ) {\displaystyle y={\sqrt {{\frac {ab+cd}{ad+bc}}(ac+bd)}}}
अत:, & # xA0; x Y = a c + b d {\displaystyle \ xy=ac+bd}
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