History of Mathematics; Counting; Computation; Buddhist Literature
摘要
Development of number systems and the computation algorithms in cultures varied from each other, as to the mathematical questions they answer and how deeply those questions were addressed. While some of these systems and the related knowledge are widely researched and well known, some are still to emerge and to mark their importance. Sri Lanka, despite its recorded history spanning over two millennia falls to this second category and the counting and computing abilities available here in the past is an inadequately addressed study area. One possible factor contributing to this inadequacy is the unavailability of early literature exclusively dedicated to the field of the mathematics. Therefore any study aimed at resurrecting the early knowledge on counting and computing calls for some alternative sources. The large volume of Buddhist literature that had been developed at least from the time of the introduction of Buddhism in 3rd century BCE could fulfill this requirement to a certain extent, provided that the contents could be treated as relevant to the Sri Lankan context. Specially the commentaries (Aṭṭhakathā) (circa 5th century CE) and sub-commentaries (12th century CE), the expository treatise on the different texts of the Pāli canon, would be important in this respect.
This paper is aimed at exploring the early counting and computing abilities that prevailed in Sri Lanka based on that Buddhist literature. First part of the study is dedicated to situate the literary contents in Sri Lankan context and then proceed to discuss the mathematical information contained therein. Discussion will cover the operations like counting, addition, subtraction, multiplication, division, evaluation of π and numeral systems. Vuttodaya(12th century CE), a treatise on Pāli prosody contains several operations like patthāra. naṭṭha, uddhiṭṭha, gurukriyā and saṅkhyāna which are relevant to the mathematical knowledge presently discussed under the theme of combination and binomial expansion. Girāsandēśaya, (15th century CE) indicates the possible use of mechanical aids in computations, when it elaborates the subjects learned at the VijayabaPirivena, Totagamuwa, which was one of the foremost institutions of education at the time. Further exploration of commentaries as well as subsequent Buddhist literature should add to the findings of this paper, and also the other mathematical fields like geometry and algebra which have not been covered in this study.
目次
Sources 36 Mathematics as a separate subject field 38 Counting 41 Fundamental Arithmetical Operations 45 Evaluation of π 50 Combination and Binomial Expansion 51 (1) Patthāra 52 (2) Naṭṭha 53 (3) Uddhiṭṭha 54 (4) Gurukriyā 54 (5) Saṅkhyāna 55 Numeral systems 57 Word-numerals 57 Numeral-symbols 58 Mechanical aids 59 Conclusion 62 Endnotes 63
