भास्कर II
Bhaskara also known as Bhaskara II and Bhaskaracharya ("Bhaskara the teacher"), (1114 - 1185), was an Indian mathematician and astronomer. He was born near Vijjadavida (Bijapur in modern Karnataka). Bhaskara is said to have been the head of an astronomical observatory at Ujjain, the leading mathematical center of ancient India. He lived in the Sahyadri region (Patnadevi, Jalgaon, Maharashtra). Bhaskara and his works represent a significant contribution to mathematical and astronomical knowledge in the 12th century. He has been called the greatest mathematician of medieval India. His main work Siddhanta Shiromani, (Sanskrit for "Crown of treatises") is divided into four parts called Lilavati, Bijaganita, Grahaganita and Goladhyaya. These four sections deal with arithmetic, algebra, mathematics of the planets, and spheres respectively. He also wrote another treatise named Karan Kautoohal. Bhaskara's work on calculus predates Newton and Leibniz by over half a millennium. He is particularly known in the discovery of the principles of differential calculus and its application to astronomical problems and computations. While Newton and Leibniz have been credited with differential and integral calculus, there is strong evidence to suggest that Bhaskara was a pioneer in some of the principles of differential calculus. He was perhaps the first to conceive the differential coefficient and differential calculus.
Contributions of Bhaskara to Mathematics:
Contribution of Bhaskara in Astronomy:
Contribution of Bhaskara in Engineering:
Contributions of Bhaskara to Mathematics:
- Preliminary concept of mathematical analysis.
- Calculated the derivatives of trigonometric functions and formulae.
- A proof of the Pythagorean theorem by calculating the same area in two different ways .
- Conceived differential calculus, after discovering the derivative and differential coefficient.
- In Lilavati, solutions of quadratic, cubic and quadrtic indeterminate equations are explained.
- Solved quadratic equations with more than one unknown, and found negative and irrational solutions.
- Preliminary concept of infinitesimal calculus, along with notable contributions towards integral calculus.
- Stated Rolle's theorem, a special case of one of the most important theorems in analysis, the mean value theorem.
- In Siddhanta Shiromani, Bhaskara developed spherical trigonometry along with a number of other trigonometric results.
Contribution of Bhaskara in Astronomy:
- The time that is required for the Earth to orbit the Sun, as 365.2588 days which is same as in Suryasiddhanta. The modern accepted measurement is 365.2563 days, a difference of just 3.5 minutes.
- His mathematical astronomy text Siddhanta Shiromani is written in two parts: the first part on mathematical astronomy and the second part on the sphere.
- The twelve chapters of the first part cover topics such as: Mean longitudes of the planets, True longitudes of the planets, Lunar eclipses, Latitudes of the planets, Sunrise equation, Conjunctions of the planets with each other and with stars etc.
Contribution of Bhaskara in Engineering:
- The earliest reference to a perpetual motion machine date back to 1150, when Bhaskara II described a wheel that he claimed would run forever.
- Bhaskara II used a measuring device known as Yasti-yantra. This device could vary from a simple stick to V-shaped staffs designed specifically for determining angles with the help of a calibrated scale.