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Bhaskara II

Bhaskara II (c. 1114 – c. 1185 CE)

Bhaskara II, also called Bhaskaracharya, was one of India’s greatest medieval mathematicians and astronomers. Born in Bijapur, Karnataka, he inherited a rich tradition of Indian astronomy and became the head of the astronomical observatory at Ujjain, a major center of scientific learning.

Siddhanta Shiromani

Bhaskara II’s most famous work, Siddhanta Shiromani ("Crown of Treatises"), composed in 1150 CE, consists of four parts:

Lilavati (Arithmetic)
Bijaganita (Algebra)
Grahaganita (Mathematics of Planets)
Goladhyaya (Spherical Astronomy)

Each section demonstrates sophisticated mathematical methods and practical astronomical calculations.

Mathematical Contributions

Lilavati

Introduced rules for basic arithmetic, including fractions and square roots
Discussed permutations, combinations, and progressions
Offered problem-solving techniques with poetic flair, enhancing accessibility

Bijaganita

Detailed the solutions to quadratic, cubic, and indeterminate equations
Described the Chakravala method for solving Pell’s equation — centuries before it appeared in European mathematics
Applied surds, zero, and negative numbers logically and consistently

Early Concepts of Calculus

Bhaskara II hinted at differential calculus by describing instantaneous velocity and rates of change. He stated that:
"The change in the sine is proportional to the cosine," — an insight that predated Newton by over 500 years.

Astronomy and Instruments

Improved calculations of planetary orbits and conjunctions
Discussed lunar phases, eclipses, and calendar reform
Described instruments like the gnomon and armillary sphere

Legacy

Bhaskara II’s works were used for centuries in Indian schools and later studied by Islamic and European scholars. His Lilavati remained a standard mathematics textbook well into the colonial period.