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[[File:Bakhshali numerals 1.png|thumb|350px|The numerals used in the Bakhshali manuscript]] |
[[File:Bakhshali numerals 1.png|thumb|350px|The numerals used in the Bakhshali manuscript]] |
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The '''Bakhshali manuscript''' is a [[Mathematics|mathematical]] text written on [[Birch bark document|birch bark]] that was found in 1881 near the [[British Raj|British-ruled]] village of [[Bakhshali]] (near [[Mardan]] in present-day [[Pakistan]]). It is notable for being "the oldest extant manuscript in [[Indian mathematics]]",<ref name=HayashiEncy/> with portions dated to AD 224–383. It contains the earliest known use of a [[zero]] symbol |
The '''Bakhshali manuscript''' is a [[Mathematics|mathematical]] text written on [[Birch bark document|birch bark]] that was found in 1881 near the [[British Raj|British-ruled]] village of [[Bakhshali]] (near [[Mardan]] in present-day [[Pakistan]]). It is notable for being "the oldest extant manuscript in [[Indian mathematics]]",<ref name=HayashiEncy/> with portions dated to AD 224–383. It contains the earliest known [[Indian people|Indian]] use of a [[zero]] symbol.<ref>{{Cite news|url=http://www.theguardian.com/science/2017/sep/14/much-ado-about-nothing-ancient-indian-text-contains-earliest-zero-symbol|title=Much ado about nothing: ancient Indian text contains earliest zero symbol|last=Devlin|first=Hannah |date=2017-09-13|work=The Guardian|access-date=2017-09-14|issn=0261-3077}}</ref><ref>{{cite news|url=http://www.bodleian.ox.ac.uk/bodley/news/2017/sep-14|title=Carbon dating finds Bakhshali manuscript contains oldest recorded origins of the symbol 'zero'|date=2017-09-14|work=Bodleian Library|access-date=2017-09-14}}</ref> |
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==Discovery== |
==Discovery== |
Revision as of 19:34, 23 September 2017
![](https://upload.wikimedia.org/wikipedia/commons/thumb/3/36/Bakhshali_numerals_1.png/350px-Bakhshali_numerals_1.png)
The Bakhshali manuscript is a mathematical text written on birch bark that was found in 1881 near the British-ruled village of Bakhshali (near Mardan in present-day Pakistan). It is notable for being "the oldest extant manuscript in Indian mathematics",[1] with portions dated to AD 224–383. It contains the earliest known Indian use of a zero symbol.[2][3]
Discovery
The manuscript was discovered in 1881,[4] by a peasant in the village of Bakhshali, which is near Mardan, now in Khyber Pakhtunkhwa, Pakistan.[1] The first research on the manuscript was done by A. F. R. Hoernlé.[1][5] After the death of Hoernlé, it was examined by G. R. Kaye, who edited the work and published it as a book in 1927.[6]
The extant manuscript is incomplete, consisting of seventy leaves of birch bark,[1][4] whose intended order is not known.[1] It is in the Bodleian Library at the University of Oxford[1][4] (MS. Sansk. d. 14), and is said to be too fragile to be examined by scholars.
Contents
The manuscript is a compendium of rules and illustrative examples. Each example is stated as a problem, the solution is described, and it is verified that the problem has been solved. The sample problems are in verse and the commentary is in prose associated with calculations. The problems involve arithmetic, algebra and geometry, including mensuration. The topics covered include fractions, square roots, arithmetic and geometric progressions, solutions of simple equations, simultaneous linear equations, quadratic equations and indeterminate equations of the second degree.[6][7]
Composition
The manuscript is written in an earlier form of Śāradā script, which was mainly in use from the 8th to the 12th century, in the northwestern part of India, such as Kashmir and neighbouring regions.[1] The language is the Gatha dialect (which is a combination of the ancient Indian languages of Sanskrit and Prakrit).
A colophon to one of the sections states that it was written by a brahmin identified as "the son of Chajaka", a "king of calculators," for the use of Vasiṣṭha's son Hasika. The brahmin might have been the author of the commentary as well as the scribe of the manuscript.[7] Near the colophon appears a broken word rtikāvati, which has been interpreted as the place Mārtikāvata mentioned by Varāhamihira as being in northwestern India (along with Takṣaśilā, Gandhāra etc.), the supposed place where the manuscript might have been written.[1]
Mathematics
The manuscript is a compilation of mathematical rules and examples (in verse), and prose commentaries on these verses.[1] Typically, a rule is given, with one or more examples, where each example is followed by a "statement" (nyāsa / sthāpanā) of the example's numerical information in tabular form, then a computation that works out the example by following the rule step-by-step while quoting it, and finally a verification to confirm that the solution satisfies the problem.[1] This is a style similar to that of Bhāskara I's commentary on the gaṇita (mathematics) chapter of the Āryabhaṭīya, including the emphasis on verification that became obsolete in later works.[1]
The rules are algorithms and techniques for a variety of problems, such as systems of linear equations, quadratic equations, arithmetic progressions and arithmetico-geometric series, computing square roots approximately, dealing with negative numbers (profit and loss), measurement such as of the fineness of gold, etc.[4]
Numerals and zero
The Bakshali manuscript uses numerals with a place-value system, using a dot as a place holder for zero.[8] The dot symbol came to be called the shunya-bindu (literally, the dot of the empty place). References to the concept are found in Subandhu's Vasavadatta, which has been dated between 385 and 465 by the scholar Maan Singh.[9]
Prior to the 2017 carbon dating, a 9th-century inscription of zero on the wall of a temple on the grounds of Gwalior Fort[10] in Gwalior, Madhya Pradesh, was thought to be the oldest Indian use of a zero symbol.[11]
Date
In 2017, three samples from the manuscript were shown by radiocarbon dating to come from three different centuries: from AD 224–383, 680–779, and 885–993. It is not known how fragments from different centuries came to be packaged together.[12][13][14]
Prior to this finding, most scholars agreed that the physical manuscript was a copy of a more ancient text, whose date had to be estimated based on content. Hoernlé thought that the manuscript was from the 9th century, but the original was from the 3rd or 4th century.[a] Indian scholars assigned it an earlier date. Datta assigned it to the "early centuries of the Christian era".[6] Channabasappa dated it to AD 200–400, on the grounds that it uses mathematical terminology different from that of Aryabhata.[16] Hayashi stated that it was from no later than the 7th century.[17]
See also
Notes
References
- ^ a b c d e f g h i j k l Takao Hayashi (2008), "Bakhshālī Manuscript", in Helaine Selin (ed.), Encyclopaedia of the History of Science, Technology, and Medicine in Non-Western Cultures, vol. 1, Springer, pp. B1–B3, ISBN 9781402045592
- ^ Devlin, Hannah (2017-09-13). "Much ado about nothing: ancient Indian text contains earliest zero symbol". The Guardian. ISSN 0261-3077. Retrieved 2017-09-14.
- ^ "Carbon dating finds Bakhshali manuscript contains oldest recorded origins of the symbol 'zero'". Bodleian Library. 2017-09-14. Retrieved 2017-09-14.
- ^ a b c d John Newsome Crossley; Anthony Wah-Cheung Lun; Kangshen Shen; Shen Kangsheng (1999). The Nine Chapters on the Mathematical Art: Companion and Commentary. Oxford University Press. ISBN 0-19-853936-3.
- ^ Hoernle, Augustus (1887), On the Bakshali manuscript, Vienna: Alfred Hölder (Editor of the Court and of the University)
- ^ a b c d
Bibhutibhusan Datta (1929). "Book Review: G. R. Kaye, The Bakhshâlî Manuscript—A Study in Mediaeval Mathematics, 1927". 35 (4). Bull. Amer. Math. Soc.: 579–580.
{{cite journal}}
: Cite journal requires|journal=
(help) - ^ a b Plofker, Kim (2009), Mathematics in India, Princeton University Pres, p. 158, ISBN 978-0-691-12067-6
- ^ Pearce, Ian (May 2002). "The Bakhshali manuscript". The MacTutor History of Mathematics archive. Retrieved 2007-07-24.
- ^ Singh, Maan (1993). Subandhu, New Delhi: Sahitya Akademi, ISBN 81-7201-509-7, pp. 9–11.
- ^ Joseph, George Gheverghese (26 Jul 2016). Indian Mathematics: Engaging with the World from Ancient to Modern Times. World Scientific. ISBN 1786340631.
In a temple on the path up to Gwalior Fort [...] where we find a circular zero in the terminal position.
{{cite book}}
:|access-date=
requires|url=
(help) - ^ "Carbon dating finds Bakhshali manuscript contains oldest recorded origins of the symbol 'zero'". Bodleian Library. 2017-09-14. Retrieved 2017-09-14.
- ^ Devlin, Hannah (2017-09-13). "Much ado about nothing: ancient Indian text contains earliest zero symbol". The Guardian. ISSN 0261-3077. Retrieved 2017-09-14.
- ^ Mason, Robyn (2017-09-14). "Oxford Radiocarbon Accelerator Unit dates the world's oldest recorded origin of the zero symbol". School of Archaeology, University of Oxford. Retrieved 2017-09-14.
- ^ "Carbon dating finds Bakhshali manuscript contains oldest recorded origins of the symbol 'zero'". Bodleian Library. 2017-09-14. Retrieved 2017-09-14.
- ^ Joseph, G. G. (2000), The Crest of the Peacock, non-European roots of Mathematics, Princeton University Press, pp. 215–216
- ^
E. F. Robinson (May 2002). "The Bakhshali manuscript". The MacTutor History of Mathematics archive. Archived from the original on 9 August 2007. Retrieved 2007-07-24.
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suggested) (help) - ^ T Hayashi, The Bakhshali manuscript: An ancient Indian mathematical treatise (Groningen, 1995).
Further reading
- Sarasvati, Svami Satya Prakash; Jyotishmati, Usha (1979), The Bakhshali Manuscript: An Ancient Treatise of Indian Arithmetic (PDF), Allahabad: Dr. Ratna Kumari Svadhyaya Sansthan with complete text in Devanagari, 110 pages
- M N Channabasappa (1976). "On the square root formula in the Bakhshali manuscript" (PDF). Indian J. History Sci. 11 (2): 112–124Template:Inconsistent citations
{{cite journal}}
: CS1 maint: postscript (link) - David H. Bailey, Jonathan Borwein (2011). "A Quartically Convergent Square Root Algorithm: An Exercise in Forensic Paleo-Mathematics" (PDF)Template:Inconsistent citations
{{cite web}}
: CS1 maint: postscript (link)
External links
- The Bakhshali manuscript
- 6 – The Bakhshali manuscript
- Hoernle: On the Bakhshali Manuscript, 1887, archive.org
- "A Big Zero: Research uncovers the date of the Bakhshali Manuscript", YouTube video, University of Oxford