Bhaskaracharya – The Great Indian Astronomer and Mathematician
April 10, 2017
Bhaskaracharya – The Great Indian Astronomer and Mathematician. Since the childhood, we have been told that the period between 500 and 1200 A.D. is the Golden Age of Indian Astronomy. During this golden period, many Indian wizards were born who contributed greatly to the conception of Science and Mathematics. One such greatest mathematician of medieval India is Bhaskaracharya, whose contribution to Astronomy and Mathematics in the 12th century was unparalleled and significant.
Bhaskaracharya Biography
Bhaskaracharya, the renowned Mathematician
Bhaskaracharya Early Life
Bhaskaracharya (1114–1185), otherwise known as Bhaskara II was born in Bijapur in Karnataka into the Brahmin family. His father, Mahesvara, was a well-known scholar. At his feet, Bhaskaracharya acquired the interest in Mathematics. After going through the works of the popular mathematician, Brahmagupta, Bhaskaracharya was very much inspired that he decided to dedicate his remaining life to mathematics. He achieved proficiency in 5 books of Bharat Shastras, 8 books of Grammar, 5 books of Mathematics, 6 texts of Medicine, 2 Mimansas, 4 Vedas and 6 books on Yoga. The innovations and researches made by him were not achieved in Europe, till the later period of time.
Works done by Bhaskaracharya
The textbooks written by Bhaskaracharya followed a simple and easy to understand methodology so as to stimulate student’s interests. These books gained a huge popularity that, even after four or five centuries of its inception, it was translated into Persian.
- The Siddhanta Shiromani scripted in two parts, (the first on mathematical astronomy), (the second part on the sphere);
- Lilavati, (on Mathematics);
- Bijaganita, (on Algebra);
- The Vasanabhasya of Mitaksha (commentary on the Siddhanta Shiromani);
- Karana-kutuhala (Calculations of Astronomical Wonders);
- Vivarana (commentary on the Shishyadhividdhidatantra).
However, among these six works, the first three lay more focus on mathematics. It’s translation in several languages of the world bear testimony to its eminence.
Siddhanta Shiromani Bhaskaracharya
The “Crown of treatises,” (Siddhanta Shiromani) includes work in arithmetic, algebra, mathematics of the planets, and spheres. This work contains about 1450 verses. Bhaskara’s astronomical findings on positions of planets, instance of eclipses and cosmography, were composed in this treatise much before the world could even notice these findings. This book is considered as the pinnacle of all the astronomical works done for 700 years. It can be aptly called the “essence of ancient Indian Astronomy and Mathematics.
Siddhanta Shirmoani was split into four parts:
- Lilavati [Quadratic and Intermediate Equation] (278 Verses)
- Bijaganita [Algebraic Calculation] (213 Verses)
- Grahaganita [Astronomical Calculations] (451 Verses)
- Goladhyaya [Trigonometry] (501 Verses)
Each part is so huge that they can be individually considered as a separate book. This book has literally surpassed all the ancient books present on astronomy and is enough to provide the complete knowledge of Ancient Indian Astronomy.
Bhaskaracharya Lilavati
Lilawati provides a clear example of Bhaskara’s expertise in putting a tough subject like mathematics into poetic language. This work has been translated into several languages throughout the world. Nearly for about 700 years, all the concepts of mathematics were taught from this textbook. It is the first and last book to enjoy such a long lifespan.
Work of Lilavati by Bhaskaracharya
Bhaskaracharya Bijaganita
Bijaganita encompasses 12 chapters and covers topics like numbers, Zero, Surds, the kuttaka, Indeterminate quadratic equation with more than one unknown, Quadratic equation with more than one unknown, functions with products of several unknown.
Bhaskaracharya Karanakutuhala
“Karanakutuhala,” was the second book written by Bhaskara at the age of 69. This book puts key-focus on several astronomical calculations. This scripture remains as a reference book, even today in making the calendars.
Bhaskaracharya Contributions in the field of Mathematics
Bhaskaracharya’s innumerable contribution had earned him an outstanding position among the ancient Hindu mathematicians. His significant contributions towards the mathematical world continue to leave a tremendous impact in the numerical field even today.
Bhaskaracharya Pythagorean theorem
Some of several contributions to mathematics include:
- A proof of the Pythagorean theorem just in two lines.
- Arrived at the answers of quadratic and cubic indeterminate equations.
- Primary concept of mathematical analysis, infinitesimal calculus, along with defined contributions within integral calculus.
- Exhibited major work on differential calculus, after uncovering the derivative and differential coefficient.
- Articulated Rolle’s theorem and the mean value theorem.
- Developed spherical trigonometry and arrived at trigonometrical results.
- Provided simple solutions to find the squares, cube, square roots, and cube roots of large numbers.
- Suggested solutions for several problems on permutations and combinations.
- Calculated an exact value of PI as 22/7 and more approximate value as 3.1416.
Sulbasutras of the Pythagorean Theorem
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