Brahmagupta was a famous Indian mathematician. He was the head of the space laboratory of the famous city of Ujjain (currently in Madhya Pradesh) under the then Gurjar Pradesh (Bhinmal). During this time he wrote two texts – Brahmasphuta Siddhanta and KhandaKhadyak. The 'Brahmasphut Siddhanta' is considered to be the first text in which zero is mentioned as a different number. The main credit for the invention of zero goes to the Indian scholar 'Brahmagupta', because he introduced zero with principles in 628 AD. Before Brahmagupta, India's great mathematician and astrologer Aryabhata had used zero, so many people considered Aryabhata as the father of zero.
Brief Introduction 

Brahmagupta 

Birth Date 
598 AD 
Birth Place 
Bhinmal,
Rajasthan (India) 
Father Name 
Jishnu 
Nationality 
Indian 
Occupation 
Mathematician, Astronomer 
Achievement 
The first mathematician to provide the formula for the
area of a cyclic quadrilateral, the value of 'Pi' as square root ten to be
accurate and 3 as the practical value 
Known for 
The first mathematician to provide the formula for the area of a cyclic
quadrilateral, the value of 'Pi' as square root ten to be accurate and 3 as the
practical value 
Death 
668
AD 
Brahmagupta Birth and Family
Brahmagupta was born in the year 598 in a village called Bhinmal in the state of Rajasthan. His father's name was Jishnu. Brahmagupta is also known as Bhillamalacharya. He was a famous mathematician of India. After Aryabhata, India's first mathematician Bhaskaracharya was the first, followed by Brahmagupta. Brahmagupta was a great master of mathematical astrology.
Brahmagupta Life Introduction
He also wrote Karana texts on the basis of the ancient Brahmapitamahasiddhanta and Khandakhadyak, which were translated into Arabic, under the names of Sindhind and alAkrand, during the time of the presumptive Caliph Mansur. On one hand, the name of his book is also 'Dhyanagrahopadesha'. Some of the results of these texts have an unparalleled place in world mathematics.
He was followed by many mathematicians who wrote on the subject of arithmetic and algebra. He was also an astronomer and discovered the rules for the use of 'zero'. The famous astrologer Bhaskaracharya called Brahmagupta 'Ganakachakrachudamani' and considered his moolakas as the basis of his 'siddhant shiromani'.
His famous works are 'Brahmasphutasiddhanta' and 'KhandKhadyak'. The medieval traveler Alberuni also mentioned Brahmagupta. During the reign of the Caliphs, their translations were also done in the Arabic language, which was also called 'Al Sind Hind' and 'Al Arkand' in the Arab country. His first book is a translation of 'Brahmasphut Siddhanta', and the second is also a translation of 'KhandKhadyak'.
Brahmagupta Mathematical Operation
The earliest text of Brahmagupta is considered to be 'Brahmasphutasiddhanta' in which zero is mentioned as a separate number. Not only this but in this book all the rules for doing mathematics on negative numbers and zero have also been described.
These rules are very close to today's understanding. Yes, there is definitely a difference that Brahmagupta could not give the correct rule of division by zero 0/0 = 0.
Brahmagupta Research as Astronomer
Brahmagupta Space Lab
It is believed Brahmagupta that he was the capital of the then Gujarat region and contemporary of King Vyaghramukh who came under the Harshavardhana Empire. Brahmagupta was also made the head of the first space vestry of ancient India, which was established in Ujjain.
Brahmagupta Two Great Books
While serving as the head of the observatory, Brahmagupta composed two texts called Brahmasphuta Siddhanta in 628 AD and KhandaKhadyaka in 665 AD.
Brahmasphuta Siddhanta
The Brahmasphuta principle is the first such principle in which zero is used as an independent number. Not only this but all the rules of mathematics based on negative numbers and zero have also been mentioned in this book.
He wrote two special texts 
1. Brahmasphutasiddhanta (628 AD)
2. Khandfood (A.D. 665 AD)
Four and a half chapters of "Brahmasphutasiddhanta" are devoted to basic mathematics. Chapter 12 is about Mathematics, Arithmetic Series and Geometry. The method of solving Aryabhata's linear indeterminate equation, equations of the form ax − by = c, is discussed in Chapter 18, Kuttak (Algebra). (The case of algebra in which nondeterministic equations are studied, its old name is 'Kuttak'.
Brahmagupta named this science after the name of the above case, 'Kuttak math' in AD 628.) Brahmagupta also discovered the method of solving quadratic undetermined equations (Nx2 1 = y2).
The name of his method is Chakraval method. Brahmagupta was the first person to use the principles of mathematics in astrology. It was through his Brahmasphutasiddhanta that the Arabs came to know about Indian astrology. The Abbasid Caliph AlMansur (712–775) founded Baghdad and developed it into a center of learning. He invited Kanka of Ujjain who explained Indian astrology with the help of Brahmasphutasiddhanta. AlFazri translated it into Arabic on the orders of Abbasid.
Brahmagupta also tried to transfer the area of a circle by a square of equal area.
Brahmagupta had also known the circumference of the earth, which is close to the value of the modern age.
Let the value of Brahmagupta Pi (3.14159265) be equal to the square root of 10 (3.16227766).
Brahmagupta was familiar with the theory of fractions. He gave a comprehensive solution of an exponential undetermined equation in integers, which is found in this form in modern books, and also attempted to solve the undetermined square equation, K y2 1 = x2.
Planetary Position
In the Brahmasphuta Siddhanta, he has written that the location of the planets is not clearly mentioned by the calculations of Aryabhatta, Srisena, Vishnuchandra etc.
Calculation Accuracy
From this statement of Brahmagupta, it is proved that he composed the 'Brahmasphutik Siddhanta' only after directly observing the planets. He understood very well that whenever there was a difference between calculation and perforation, then the calculation should be purified through the perforation.
Different Chapters
Brahmagupta was the first teacher who gave a special order to the creation of mathematical astrology and mentioned different topics of astrology and mathematics by dividing them into different chapters.
Poetic Form
Many of Brahmagupta's works were composed in ellipsoidal verses that were given a poetic form. But till now no such evidence has been available related to where the theory of mathematics composed by Brahmagupta originated.
Sindh Hindu
The historian of Baghdad, AlBiruni, in his book TariqalHind, has mentioned that the Absid Caliph alMa'mun has an embassy located in India. A book was brought from India itself to Baghdad which was translated into Arabic as Sindhhind. It is believed that Sindhhind is a form of Brahmagupta theory of Brahmagupta.
Relations with Islamic Countries
This fact attests to the fact that India's science, astronomy, technology and mathematics have been closely related with the rise and development of science and mathematics in Islamic countries.
Brahmagupta's Sutras
Brahmagupta's most important contribution is on the cyclic quadrilateral. He said that the diagonals of a cyclic quadrilateral are perpendicular to each other. Brahmagupta has also given the approximate formula and the exact formula for finding the area of a cyclic quadrilateral.
Approximate formula for the area of a cyclic quadrilateral:
(\tfrac{p r}{2}) (\tfrac{q s}{2})
Exact formula for the area of a cyclic quadrilateral:
\sqrt{(t  p)(t  q)(t  r)(t  s)}.
where t = semiperimeter of a cyclic quadrilateral and p, q, r, s are the measures of its sides.
Brahmagupta Death
Brahmagupta died in the year 668. Brahmagupta was a great master of mathematical astrology. He will always be remembered as a great mathematician.
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