Book Source: Digital Library of India Item : ioned. Bija ganita [of Bhāskara Āchārya]: or The algebra of the Hindus. [Tr.] by E By Bhāskara Āchārya. About this book · Terms of Service · Plain text · PDF. Lilavati (mathematics); Bijaganita (algebra); Siddhantasiromani; Vasanabhasya ( commentary Bhaskaracharya is finding integer solution to x = y +

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Bhaskara II is a famous Indian mathematician. He also goes by the name of Bhaskara or Bhaskaracharya, which means Bhaskara the Teacher. Bhaskara is famous for a number of innovations in mathematics.

His knowledge of solving equations and number systems were at such a high level that it would take European mathematicians hundreds of years to attain this level. Bhaskara is viewed as one of the greatest mathematicians of medieval India and his work has influenced both Indian and Islamic mathematicians as well as European ones.

It is known that he was born in A. His father was a famous astrologer and mathematician biijaganita the name of Mahesvara. In fact, Bhaskara also taught mathematics to his son Loksamudra.

Bhaskara worked at the astronomical observatory at Ujjain and soon became the head of the facility. This observatory was the top mathematical center in India and excellent mathematicians, such as Varahamihira and Brahmagupta, had also worked at the observatory.

Bhaskara, as did other Indian mathematicians, wrote in verse. He looked at various branches of mathematics, such as algebra, trigonometry, and calculus. He also studied and wrote about astronomy.

In fact, half of his most famous work dealt with mathematical astronomy. Bhaskara died in at Ujjain. His work was built on and developed after his death by another Indian mathematician, Madhava of Sangamagrama, as well as by mathematicians at the Kerala School. Bhaskara wrote a number of books but the work that has had the most influence in the mathematics field is the Siddhanta Siromani Crown of Treatises.

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The book was written in A. It has verses and is divided into four parts; although, sometimes the books are viewed as separate books.

Each section deals with a different area of mathematics and astronomy. Sometimes the last two books Grahaganita and Goladhyaya have been treated as the only two parts of the Siddhanta Siromaniwhile the first two books Lilavati and Bijaganita are viewed as two independent books. The Lilavati focuses on arithmetic and according to a story that was written in a Persian translation of the book, the book was written for his daughter, who was named Lilavati.

According to the story, Bhaskara made a horoscope of his daughter and found that her husband would die shortly after the couple were married. The only way to prevent the death was to make sure that the marriage happened exactly at a specific time. To ensure that the marriage happened at the correct time, Bhaskara made a small hole in a cup and placed it in a pail filled with water.

Bhaskara had calculated how long it would take for the cup to fill and sink. He placed the cup in the water so that it would sink at the exact time Lilavati was supposed to get married. Bhaskara then warned Lilavati to stay away from the cup. While she was looking at the device, a pearl from her dress fell into the cup and blocked the hole. As a result, the hour set for the marriage passed without the marriage taking place. As a result, Lilavati was widowed soon after her marriage took place.


To make Lilavati feel better, Bhaskara wrote her a book about mathematics.

Lilavatihas thirteen chapters bijaganira covers a number of topics. The book deals with definitions and terms as well as looking at the properties of zero.

Bhaskara also looked at negative numbers and surds in this book. Surds are simply square roots that are not whole numbers. Bhaskara looked at different methods to perform calculations, such as multiplication and squaring, and he also wrote about the rule of three. Bhaskara covered a number of other topics in Lilavati as well, such as trigonometry and mensuration, and even included a number of problems that readers of the book could work on. The work Bhaskara did in the book on indeterminate equations and integer solutions is the most important material in the book.

The rules that Bhaskara wrote about were the same rules that Oof mathematicians would come up with almost five hundred years later.

The Bijaganita focuses on algebra and has twelve chapters. In this book, Bhaskara wrote about his discovery that each positive number can have both a positive square root and a negative square root. He was the first person to realize this. In addition to his work on positive and negative numbers, Bhaskara also looked methods to determine unknown quantities and did more work on the number zero. Bhaskara also looked at ways to expand bhaskata some of the work done by Brahmagupta.

In addition to indeterminate equations, the book looks at quadratic, and simple equations as well as methods for evaluating surds. Bhaskara realized that when dividing one by a fraction, the smaller the fraction gets, the more pieces are created. Bhaskara came to the conclusion that if you divide one by zero, you will end up with an infinite number of pieces.

At first glance this might seem to be correct, but when looked at from the terms of multiplication, it becomes obvious that it is wrong. This would mean that all numbers are the same, which is obviously not true. The problem was that Indian mathematicians were not able to accept the fact that it is impossible to divide by 0. The Ganitadhyaya deals with mathematical astronomy. Bhaskara based his astronomy on the earlier work by Aryabhata. Bhaskara viewed the solar system as being heliocentric it revolves around the sun and the planets have an elliptical orbit.

Bhaskara also used the law of gravity that was proposed by Brahmagupta. This book consists of bijaganlta chapters and covers a variety of astronomical topics. Bhaskara looked at the mean longitudes and the true longitudes of the planets as well as latitudes. He also looked at both bjjaganita and solar eclipses. Bhaskara discussed the conjunction of the planets with each other and with fixed stars as well as with the orbits of both the Sun and the Moon. This book also examined the problems associated with diurnal rotation as well as syzygies.

Syzygy is the alignment of three celestial bodies into an almost straight line. Bhaskara calculated that it would take In the Goladhyaya, Bhaskara looked at the sphere. It is broken into thirteen chapters and covers areas such as the nature of a sphere and the armillary sphere. An armillary sphere is a model showing the globe. It used rings and hoops to depict the equator and the tropics. Bhaskara also covered cosmography, geography and the seasons.


He looked at planetary mean motion and methods for calculating ellipses and lunar crescents. He also discussed astronomical instruments and the difficulties involved with making astronomical calculations. In addition, the book covers an epicycle model of the planets. An epicycle model means that some planets, for example, the sun and the moon, move in small circles.

These small circles then orbit the Earth bhaskar some other planetary body. Both the Golahhyaya and the Ganitadhyaya show that Bhaskara had strong knowledge of trigonometry.

He knew about the sine table bijagaanita relationships between various trigonometric functions. One of his discoveries in this book was spherical trigonometry.

Bhaskara seems to have an actual interest in trigonometry and used it to ghaskara the sines of and degree angles. The beginnings of infinitesimal calculus and mathematical analysis can be seen in his work. Bhaskara showed that when a planet is at its farthest or at its closest from Earth, the equation of the centre vanishes.

The equation of the centre is the measure of the distance between where a planet is and where it is predicted to be given the assumption that its movement is uniform. From this, Bhaskara concluded that at some point, the differential of the bbijaganita of the centre is equal to zero.

Bhaskara also discovered spherical trigonometry. This is a field in spherical geometry and is very important in the fields of astronomy, geodesy, and navigation. Bhaskara did a lot of important work in calculus and developed ways to use the principles of differential calculus to deal bijwganita problems in astronomy.

Bijaganita – Wikipedia

Even though Isaac Newton and Gottfried Leibniz are viewed as the founders of differential and integral calculus, there is a lot of evidence that shows Bhaskara developed a bhaskafa of the principles of differential calculus and that he may have been the first to biaganita up with both the derivative and the differential coefficient as well as differential calculus.

He also came up with the beginnings of infinitesimal calculus and made a number of contributions in the field of integral calculus. This influence can be if in the writings of various Islamic mathematicians. His Writings Bhaskara wrote a number of books but bijaganitz work that has had the most influence in the mathematics field is the Siddhanta Siromani Crown of Treatises. The Lilavati The Lilavati focuses on arithmetic and according to a story that was written in a Persian translation of the book, the book was written for his daughter, who was named Lilavati.

The Bijaganita The Bijaganita focuses on algebra and has twelve chapters. The Ganitadhyaya The Ganitadhyaya deals with mathematical astronomy. The Goladhyaya In the Goladhyaya, Bhaskara looked at the sphere.