Wikinventia — Atlas of discoveries and inventions · Middle Age

Siddhanta Shiromani — Bhaskara II

1150 AD · Transmission: Silenced
MathematicsTreatiseIndian

Bhaskara II completes the Siddhanta Shiromani ('Crown of Treatises') at age 36, a work of 1,450 Sanskrit verses divided into four parts: Lilavati (arithmetic), Bijaganita (algebra), Grahaganita (planetary mathematics), and Goladhyaya (the sphere). The Bijaganita is the first text to recognize that every positive number has two square roots (positive and negative) and systematizes the chakravala method for solving Pell equations (Nx² + 1 = y²) centuries before Fermat. In the Siddhanta Shiromani he introduces results on derivatives of trigonometric functions anticipating differential calculus — the interpretation as a precursor of Newton/Leibniz is valid with caveats. MacTutor states that he 'achieved an understanding of the number system and the solution of equations which was not to be achieved in Europe for several centuries.'

InstitutionAstronomical observatory of Ujjain — the principal mathematical center of medieval India
Historical regionCentral India, Ujjain (present-day Madhya Pradesh)
Primary sourceSiddhānta Śiromaṇi, Bhaskara II, 1150 — edition with English translation: Lancelot Wilkinson, Calcutta, 1861; modern edition: Muralidhara Chaturveda, Varanasi, 1981
Secondary sourceMacTutor — mathshistory.st-andrews.ac.uk/Biographies/Bhaskara_II/; New World Encyclopedia — newworldencyclopedia.org/entry/Bhāskara_II
Original languageClassical Sanskrit (metrical, ārya style)
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