On The Value Implied In The Data Referred To In The Mahābhārata for π

Dipak Jadhav

Abstract


E. Washburn Hopkins interpreted, in 1902, the values for  from the data referred to in some verses contained in the Bhīṣma Parva of the Mahābhārata where  is a non-terminating and non-recurring fixed ratio of the circumference, , of a circle to its diameter, . The values interpreted for it by him from the data referred to for the dimensions, including , , and vipulatva , of the Rāhu, the Moon, and the Sun are 3.5, 3.5+, and 3.58 respectively. R. C. Gupta found, in 1990, these values to be the yielding of the gross misinterpretations. He pointed out that the value implied in the data of each of the three cases is only 3. The present paper is mainly aimed at probing when and why 3 was used in the Mahābhārata as the value for . The date when those above verses were incorporated in the Mahābhārata is the one when 3 as the value for  was used in the same if consistency is preferred to as a sound criterion in determining so. It tends to 500 BCE in its range extending from 500 BCE to 500 CE. It may go even beyond 500 BCE. 3 as the value for  seems to have been borrowed from some older forms of the Purāṇas into the Mahābhārata. If simplicity, prevalence, and traditionalism are preferred to as a sound criterion to calculate for a given , no other option for  is better than 3. The support for this option was available not only in the interior of India right from the Ṛgveda but also in the exterior of India at least right from the old Babylonian text.


Keywords


Mahābhārata, π, Purāṇa.

Full Text:

PDF

References


Anonymous Editor. 1928. Jyotiṣakaraṇḍaka of Vallabhīcārya (with Malayagiri’s commentary). Ratlam: Śrī Ṛṣabhadevaji Keśarīmaletyākhyā Śvetāmbara Saṃsthā. Beckmann, Petr. 1974. A History of . New York: The Golem Press.

Bose, D. M., Sen, S. N. and Subbarayappa, B. V. 1971. A Concise History of Science in India. New Delhi: Indian National Science Academy.

Cappeller, Carl (ed.) 1891. Sanskrit-English Dictionary. Strassburg.

Chatterjee, B. (ed. and tr.) 1981. Śiṣyadhīvṛddhidatantra of Lalla (with Mallikārjunasūri’s commentary). New Delhi: Indian National Science Academy.

Datta, B. B. 1929. The Jaina school of mathematics. Bulletin of the Calcutta Mathematical Society 21: 115-145.

Deakin, Michael A. B. and Lausch, Hans. 1998. The Bible and pi. The Mathematical Gazette 82: 162-166.

Dikshit, Shankar Balkrishna. 1969. History of Indian Astronomy (Translation of Bhāratīya Jyotiṣa Śāstrā into English by R. V. Vaidya), Part I: History of Astronomy During the Vedic and Vedāṅga Periods. New Delhi: The Manager of Publications. Originally published in Marāṭhī with the title Bhāratīya Jyotiṣa Śāstrā cā Itihāsa āṇi Paricaya, 1896, Poona.

Dvivedi, Sudhakara (ed.). 1899. Triśatikā of Śrīdhara. Benares: Chandraprabha Press.

Ganguli, Kisari Mohan (tr.) 2003. The Mahābhārata of Krishna-Dwaipayana Vyasa. Translated into English from Sanskrit by Ganguli during from 1883 to 1896. Scanned at sacred texts.com, 2003.

Gupta, R. C. 1975. Some ancient values of pi and their use in India. The Mathematics Education 9.4: 1-5.

Gupta, R. C. 1988. New Indian values of from the Mānava Śulba Sūtra. Centaurus 31: 114-125.

Gupta, R. C. 1990. The value of in the Mahābhārata. Gaṇita Bhāratī 12.1-2 : 45-47.

Gupta, R. C. 1990/91. The “Molten Sea” and the value of . The Jewish Bible Quarterly 19.2: 127-135.

Gupta, R. C. 1997. On the approximation: . Gaṇita Bhāratī 19.1-4: 91-96.

Gupta, R. C. 2003. Ptolemy’s value of in India. HPM Newsletter 53 (July): 3-4.

Hayashi, T., Kusuba, T. and Yano, M. 1989. Indian values for derived from Āryabhaṭa’s value. Historia Scientiarum 37: 1-16.

Hayashi, T. 1997. Calculations of the surface of a sphere in India. The Science and Engineering Review of Doshisha University 37.4: 194-238.

Hazra, Rajendra Chandra. 1963a. The Purāṇas. In S. K. De et al. (eds.) The Cultural Heritage of India, Vol. II, 240-270. Calcutta: The Ramakrishna Mission Institute of Culture, 1937/1963a.

Hazra, Rajendra Chandra. 1963b. The Upapurāṇas. In S. K. De et al. (eds.) The Cultural Heritage of India, Vol. II, 271-286. Calcutta: The Ramakrishna Mission Institute of Culture, 1937/1963a.

Hopkins, E. Washburn. 1901. The Great Epic of India: Its Character and

Origin. New York: Charles Scribner’s Sons.

Hopkins, E. Washburn. 1902. Remarks on the form of numbers, the method of using them, and the numerical categories found in the Mahābhārata. Journal of the American Oriental Society 23: 109-155.

Jadhav, Dipak. 2013. Mensuration in India from Jaina Sources. Ph. D. Thesis (Unpublished). Indore: Devi Ahilya University.

Jain, H. L. Jain et al. (eds.). 1996. Ṣaṭkhaṇḍāgama of Puṣpadanta and Bhūtabalī (with Dhavalā commentary of Vīrasena), Khaṇḍa I, Vol. 4. Sholapur: Jaina Sanskṛti Saṃrakṣaka Saṅgha, 1940-50/1996.

Kak, Subhash C. 1997. Three old Indian values of . Indian Journal of History of Science 32.4: 307-314.

Kak, Subhash. 2001. On the chronological framework for Indian culture. Journal of the Indian Council of Philosophical Research (Special Issue: Chronology and Philosophy): 1-24.

Kalicharan and Vastiram (eds.). 1892. Matsyapurāṇa Saṭīka. Lucknow: Muṃśi Navalakiśora.

Kramrisch, Stella and Burnier, Raymond. 1976. The Hindu Temple, Volume 2. Delhi: Motilal Banarsidass.

Madhukara, Miśrīmalajī Mahārāja and his team (eds.). 1987. Anuyogadvāra Sūtra of Āryarakṣita. Beawar: Śrī Āgama Prakāśana Samiti.

Madhukara, Miśrīmalajī Mahārāja and his team (eds.) 1989. Jīvājīvābhigama Sūtra, Part I. Beawar: Śrī Āgama Prakāśana Samiti.

Madhukara, Miśrīmalajī Mahārāja and his team (eds.). 1991. Uttarādhyayana Sūtra. Beawar: Śrī Āgama Prakāśana Samiti.

Madhukara, Miśrīmalajī Mahārāja and his team (eds.). 1995. Sūryaprajñapti Candraprajñapti. Beawar (Rajsthan): Śrī Āgama Prakāśana Samiti.

Mahāprajña, Ācārya and his team (eds.) 2005. Bhagavaī, Vol. III (Sayas 8-11). Ladnun: Jain Vishva Bharati

Mikami, Yoshio. 1913. The Development of Mathematics in China and Japan. Leipzig: B. G. Tenubner.

Mishra, R. D. 1949. Vṛttakṣetra kā gaṇita: Jaina tathā Jainetara ācāryo ke siddhānta. The Jaina Siddhānta Bhāskara 15.2: 105-111.

Mitra, Rājendralāla (ed.) 1879. The Vāyu Purāṇa, Vol. I. Calcutta: The Asiatic Society of Bengal.

Mukhopādhyāya, Nīmaṇi (ed.). 1890. The Kūrma Purāṇa. Calcutta: The Asiatic Society of Bengal.

Murthy, S. S. N. 2003. The questionable historicity of the Mahabharata. Electronic Journal of Vedic Studies 10.5: 1-15.

Needham, Joseph. 1959. Science and Civilization in China, Vol. III. Cambridge: Cambridge University Press.

Padmavathamma (ed. and tr. for Kannada) 2000. Gaṇitasārasaṅgraha of Mahāvīra (along with the translation offered by M. Rangacharya in 1912 into English). Hombuja: Śrī Siddhārtakirti Granthamālā.

Pāṇḍeya, Paṇḍita Ramanārāyaṇadatta Śāstrī (tr.). Mahābhārata, Vol. I (Books 1-2), Vol. II (Books 3-4), Vol. III (Books 5-6), and Vol. VI (Books 13-18). Translated into Hindi from Sanskrit by Pāṇḍeya. Gorakhpur: Gītā Press. Year of publication not given.

Patni, C. P. (ed.) 1997. Tiloyapaṇṇatti of Yativṛṣabha (with Āryikā Viśuddhamati’s Hindi commentary), Vol. II. Dehra-Tijara: Śrī 1008 Candraprabha Digambara Jaina Atiśayakṣetra.

Pottage, Jhon. 1968. The Vitruvian value of . Isis 59: 190-197.

Pruden, Leo M. (tr.). 1988-1990. Abhidharmakoṣabhāṣyam, Vol. II. Berkeley: Asian Humanities Press.

Ray, Jogesh Chandra. 1913. The date of the Mahabharat war.” The Journal of the Astronomical Society of India 3.8: 202-208.

Rao, U. (2017). Understanding Buddhism through Pali in India and Thailand. Vidyottama Sanatana: International Journal of Hindu Science and Religious Studies, 1(2), 115-121.

Sachau, Edward C. 1910. Alberuni’s India, Vol. I. London: Kegan Paul, Trench, Trubner & Co. Ltd.

Sastri, Dwarkadas (ed.). 1981. Abhidharmakośa of Vasubandhu (with the auto commentary of Vasubandhu and the explanation of Yaśomitra). Two Parts. Varanasi: Baudha Bharati.

Sastri, Chhaganlal. (ed. and tr.) 1994. Jambūdvīpaprajñapti Sūtra. Beawar: Śrī Āgama Prakāśana Samiti.

Satyaprakash and Sharma, Ram Swarup. (eds.) 1980. Baudhāyana Śulba Sūtram (with Sanskrit commentary by Dwarka Nath Yajvan and English and critical notes by G. Thibout). New Delhi: Mahalakshmi Publishing House.

Sen, S. N. and Bag, A. K. (eds.) 1983. The Śulbasūtras (of Baudhāyan, Āpastamba, Kātyāyana and Mānava). New Delhi: Indian National Science Academy.

Sharma, Virendra N. 2004. On astronomical references in the Mahābharāta – An exercise in archaeoastronomy. Purāṇa 46.2 (July): 83-112.

Sharma, Ram Swarup and his team. 1966. Brāhmasphuṭasiddhānta of Brahmagupta, Vol. II. New Delhi: Indian Institute of Astronomical and Sanskrit Research.

Shukla, Kripa Shankar (ed.). 1957. Sūryasiddhānta. Lucknow: Department of Mathematics and Astronomy, Lucknow University.

Shukla, Kripa Shankar. 1976. Āryabhaṭīya of Āryabhaṭa (with the commentary of Bhāskara I and Someśvara). New Delhi: Indian National Science Academy.

Sinha, Kripanath. 2000. Mathematics from Vedic Saṃhitās. Gaṇita Bhāratī 22.1-4: 1-10.

Smeur, A. J. E. M. 1970. On the value equivalent to in ancient mathematical texts. A new interpretation. Archive for History of Exact Sciences 6.4: 249-270.

Suastika, I. M., Jirnaya, I. K., Sukersa, I. W., & Puspawati, L. P. (2017). The Process Of Transforming The Mahabharata Literary Work Written In The Old Javanese Into Geguritan Sarpayajnya And Geguritan Kicaka Written In The Balinese Language. Vidyottama Sanatana: International Journal of Hindu Science and Religious Studies, 1(2), 103-114.

Sukthankar, V. S. 1957. The Meaning of the Mahābhārata. Bombay: The Asiatic Society of Bombay.

Sullivan, Bruce M. 1994. The religious authority of the Mahābharāta: Vyāsa and Brahmā in the Hindu scriptural tradition. Journal of the American Academy of Religion 62.2: 377-401.

Sūrīśvara, Śrīmadvijayarāmacandra (ed.). 1994. Tattvārthādhigamasūtram of Umāsvāti (with his own Bhāṣya). Navasari.

Tagare, G. V. (tr.). 1983. The Brahmāṇḍa Purāṇa, Part I. Delhi: Motilal Banarsidass.

Thibaut, G. and Dvivedi, Sudhakara (eds and trs.). 1889. Pañcasiddhāntikā of Varāhamihira. Benares.

Vaidya, C. V. 1905. Mahābharāta: A Criticism. Bombay: A. J. Combridge and Co.

Vijayaji, Vajrasena (ed.). 1988. Bṛhatkṣetrasamāsa of Jinabhadra Gaṇī. Ahemdabad: Bhadrankar Prakashan.

Winternitz, M. 1981. History of Indian Literature, Vol. I (Translated into English from German by V. S. Sarma). New Delhi: Motilal Banarsidass, 1922/1981.




DOI: http://dx.doi.org/10.25078/ijhsrs.v2i1.511

Refbacks

  • There are currently no refbacks.


Vidyottama Sanatana: International Journal of Hindu Science and Religious Studies Indexed By :

 

 

Vidyottama Sanatana: International Journal of Hindu Science and Religious Studies site and its metadata are licensed under CC BY-SA

 

web
analytics View My Stats