Brahmagupta, one of the greatest Indian mathematicians

Brahmagupta:

Brahmagupta (c. 598- c. 670) was one of the most significant mathematicians of ancient India. He introduced extremely influential concepts to basic mathematics, including the use of zero in mathematical calculations and the use of mathematics and algebra in describing and predicting astronomical events.

He was born in 598 at Bhillmala, a city in the state of Rajasthan of present-day Northwest India. As a result, he is often referred to as Bhillmalacharya (the teacher from Bhillmala). He was the head of the astronomical observatory at Ujjain. His father’s name was Jisnugupta.

Works of Brahmagupta:

Brahmagupta wrote two surviving treatises, both on mathematics and astronomy:

1. The Brahmasphutasiddhanta and
2. The Khandakhadyaka
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The Brahmasphutasiddhanta:

The Brahmasphutasiddhanta was written in 628. It is arguably Brahmagupta’s most famous work. It is a theoretical treatise which contains 25 chapters. In the first 10 astronomical chapters, the topics covered are

     

        i        Mean longitudes of the planets

      ii.            True longitudes of the planets
    iii.            The three problems of diurnal rotation
     iv.            Lunar eclipses
       v.            Solar eclipses
     vi.            Risings and settings
   vii.            The moon’s crescent
 viii.            The moon’s shadow
     ix.            Conjunctions of the planets with each other
       x.            Conjunctions of the planets with the fixed stars 

The remaining 15 chapters cover the mathematical topics-
        i.            Solution of the linear equation
      ii.            Solution of quardratic equation
    iii.            Solution of simultaneous indeterminate equations
     iv.            Appearance of four fundamental operations (addition, substraction, multiplication and division)
       v.            Rules for dealing with five types of combinations of fractions
     vi.            The sum of the squares and cubes
   vii.            Mentioning zero as a number
 viii.            A formula useful for generating Pythagorean triples
     ix.            A theorem on rational triangles
       x.            Value of pi
     xi.            Brahmgupta’s interpolaton formula
   xii.            Brahmagupta’s formula for quadrilaterals
 xiii.            Brahmagupta’s famous theorum

The Khandakhadyaka:

The Khandakhadyaka was written in 665. It is a more practical text which contains 8 chapters. Brahmagupta believed in a static earth and he gave the length of the year as 365 days 6 hours 12 minutes 36 seconds in this book.

This great mathematician died in 670. He was one of the greatest mathematicians in Indian history and his contribution to mathematics have made major differences to various mathematical problems by establishing the basic rules which now allow us to find their solutions. He was honored by a fellow scientist ‘Ganita Chakra Chudamani’ which is translated as “The gem of the circle of mathematicians”.