SEVEN FASCINATING TOPICS FROM SANSKRIT LITERATURE - 4. ĀRYABHAṬĪYA

 

ĀRYABHAṬĪYA: ADVANCED MATHEMATICS AND ASTRONOMY IN ANCIENT INDIA

The Āryabhaṭīya, composed by the celebrated Indian mathematician and astronomer Āryabhaṭa in 499 CE, is one of the foundational works of classical Indian mathematical astronomy. Written in highly compressed Sanskrit verse, the treatise consists of 121 verses arranged in four sections: Gītikāpāda (13), Gaṇitapāda (33), Kālakriyāpāda (25), and Golapāda (50).

Its mathematical sophistication is particularly evident in the famous approximation of π:

चतुरधिकं शतमष्टगुणं द्वाषष्टिस्तथा सहस्राणाम् । अयुतद्वयविष्कम्भस्यासन्नो वृत्तपरिणाहः ॥                                                                        (Āryabhaṭīya, Gaṇitapāda 10)

Āryabhaṭa states that the circumference of a circle of diameter 20,000 is approximately 62,832, giving π ≈ 3.1416, correct to four decimal places. The Sanskrit word āsanna (“approximately” or “near”) is significant in understanding the mathematical formulation.

The Kālakriyāpāda presents an elaborate system of time-reckoning and planetary computation. Āryabhaṭa's sidereal year is approximately 365 days, 6 hours, 12 minutes and 30 seconds, demonstrating the precision of his astronomical calculations.

His discussion of the Earth's rotation is especially remarkable:

अनुलोमगतिनौस्थः पश्यत्यचलं विलोमगं यद्वत् । अचलानि भानि तद्वत्समपश्चिमगानि लङ्कायाम् ॥                                                                                     Āryabhaṭīya, Golapāda 9

Through the analogy of a person moving in a boat who perceives stationary objects as moving backward, Āryabhaṭa explains the apparent westward motion of the stars as a consequence of the Earth's rotation.

The Golapāda further discusses the celestial sphere, eclipses, and the illumination of celestial bodies. Thus, the Āryabhaṭīya represents a remarkable synthesis of mathematics, geometry, trigonometry, time-reckoning, and astronomy, and remains a major landmark in the history of scientific thought in India.

References:

1. Āryabhaṭa, Āryabhaṭīya, Gaṇitapāda 10; Golapāda 9.
2. Walter Eugene Clark, The Āryabhaṭīya of Āryabhaṭa: An Ancient Indian Work on Mathematics and Astronomy, University of Chicago Press, 1930.
3. Kim Plofker, Mathematics in India, Princeton University Press, 2009.
4. K. V. Sarma, studies and editions of Āryabhaṭa's astronomical works.
5. Narayanan Nampoothiri, “The Value of π,” Manuscript Heritage on Astronomy, Ministry of Culture, Government of India.

(This blogpost is written by me - a team member of Piyush Plotters' which is a part of Blogchatter's Half marathon)