Tidslinje för matematisk innovation i Syd- och Västasien

Syd- och Västasien består av en stor region som sträcker sig från det nuvarande landet Turkiet i väster till Bangladesh och Indien i öster.

Tidslinje

• 3:e årtusendet f.Kr. Sumerernas sexagesimala system :
• 2:a årtusendet f.Kr. Babyloniska Pythagoras trippel . Enligt matematikern SG Dani , den babyloniska kilskriftstavlan Plimpton 322 skriven ca. 1850 f.Kr. "innehåller femton Pythagoras trippel med ganska stora poster, inklusive (13500, 12709, 18541) vilket är en primitiv trippel, vilket i synnerhet indikerar att det fanns en sofistikerad förståelse om ämnet" i Mesopotamien.
• 1:a årtusendet f.v.t. Baudhayana Śulba Sūtras Det tidigaste uttalandet av Pythagoras sats : Enligt ( Hayashi 2005 , s. 363), innehåller Śulba Sūtras "det tidigaste bevarade verbala uttrycket av Pythagoras sats, även om det redan hade varit känt för det i världen . Babylonier ."

  Det diagonala repet ( akṣṇayā-rajju ) i en avlång (rektangel) producerar både som flanken ( pārśvamāni ) och den horisontella ( tiryaṇmānī ) <rep> producerar separat."

  Eftersom påståendet är en sūtra , är det nödvändigtvis det som komprimerar producera utvecklas inte, men sammanhanget antyder tydligt de kvadratiska ytorna konstruerade på deras längder, och skulle ha förklarats så av läraren för eleven.

Se även

• Tidslinje för odling och domesticering i Syd- och Västasien
• Tidslinje för matematik

Anteckningar

•   Bourbaki, Nicolas (1998), Elements of the History of Mathematics , Berlin, Heidelberg och New York: Springer-Verlag , 301 sidor, ISBN 3-540-64767-8 .
•   Boyer, CB; Merzback (fwd. av Isaac Asimov), UC (1991), History of Mathematics , New York: John Wiley and Sons, 736 sidor, ISBN 0-471-54397-7 .
•    Bressoud, David (2002), "Was Calculus Invented in India?", The College Mathematics Journal , 33 (1): 2–13, doi : 10.2307/1558972 , ISSN 0746-8342 , JSTOR 1558972 .
•   Bronkhorst, Johannes (2001), "Panini and Euclid: Reflections on Indian Geometry", Journal of Indian Philosophy , Springer Netherlands, 29 (1–2): 43–80, doi : 10.1023/A:1017506118885 , S2CID 5835 .
•   Burnett, Charles (2006), "The Semantics of Indian Numerals in Arabic, Greek and Latin", Journal of Indian Philosophy , Springer-Nederländerna, 34 (1–2): 15–30, doi : 10.1007/s10781-005-8153 -z , S2CID 170783929 .
• Burton, David M. (1997), The History of Mathematics: An Introduction , The McGraw-Hill Companies, Inc., s. 193–220 .
•   Cooke, Roger (2005), The History of Mathematics: A Brief Course , New York: Wiley-Interscience, 632 sidor, ISBN 0-471-44459-6 .
• Dani, SG (25 juli 2003), "On the Pythagorean triples in the Śulvasūtras" (PDF) , Current Science , 85 (2): 219–224 .
•    " Early Literary Evidence of the Use of the Zero in India", The American Mathematical Monthly , 38 (10): 566–572, doi : 10.2307/2301384 , ISSN 0002-98 0002-98 .
• Datta, Bibhutibhusan; Singh, Avadesh Narayan (1962), History of Hindu Mathematics: A Source Book , Bombay: Asia Publishing House .
• De Young, Gregg (1995), "Euclidean Geometry in the Mathematical Tradition of Islamic India", Historia Mathematica , 22 (2): 138–153, doi : 10.1006/hmat.1995.1014 .
• Encyclopædia Britannica ( Kim Plofker ) (2007), "mathematics, South Asian" , Encyclopædia Britannica Online : 1–12 , hämtad 18 maj 2007 .
•   Filliozat, Pierre-Sylvain (2004), "Ancient Sanskrit Mathematics: An Oral Tradition and a Written Literature", i Chemla, Karine ; Cohen, Robert S.; Renn, Jürgen; Gavroglu, Kostas (red.), History of Science, History of Text (Boston Series in the Philosophy of Science) , Dordrecht: Springer Netherlands, 254 sidor, s. 137-157, s. 360–375, doi : 10.1007/1 -4020-2321-9_7 , ISBN 978-1-4020-2320-0 .
•    Fowler, David (1996), "Binomial Coefficient Function", The American Mathematical Monthly , 103 (1): 1–17, doi : 10.2307/2975209 , ISSN 0002-9890 , JSTOR 2975209 .
•   Hayashi, Takao (1995), The Bakhshali Manuscript, Ancient Indian mathematical treatise , Groningen: Egbert Forsten, 596 sidor, ISBN 90-6980-087-X .
• Hayashi, Takao (1997), "Aryabhata's Rule and Table of Sine-Differences", Historia Mathematica , 24 (4): 396–406, doi : 10.1006/hmat.1997.2160 .
•   Hayashi, Takao (2003), "Indian Mathematics", i Grattan-Guinness, Ivor (red.), Companion Encyclopedia of the History and Philosophy of the Mathematical Sciences, vol. 1, s. 118-130, Baltimore, MD: The Johns Hopkins University Press, 976 sidor, ISBN 0-8018-7396-7 .
•   Hayashi, Takao (2005), "Indian Mathematics", i Flood, Gavin (red.), The Blackwell Companion to Hinduism , Oxford: Basil Blackwell, 616 sidor, s. 360-375, s. 360–375, ISBN 978- 1-4051-3251-0 .
•   Henderson, David W. (2000), "Square roots in the Sulba Sutras" , i Gorini, Catherine A. (red.), Geometry at Work: Papers in Applied Geometry , vol. 53, s. 39-45, Washington DC: Mathematical Association of America Notes, 236 sidor, s. 39-45, ISBN 0-88385-164-4 .
•   Ifrah, Georges (2000), A Universal History of Numbers: From Prehistory to Computers , New York: Wiley, 658 sidor, ISBN 0-471-39340-1 .
•   Joseph, GG (2000), The Crest of the Peacock: The Non-European Roots of Mathematics , Princeton, NJ: Princeton University Press, 416 sidor, ISBN 0-691-00659-8 .
•   Katz, Victor J. (1995), "Ideas of Calculus in Islam and India", Mathematics Magazine , 68 (3): 163–174, doi : 10.2307/2691411 , JSTOR 2691411 .
•   Katz, Victor J., red. (2007), The Mathematics of Egypt, Mesopotamia, China, India, and Islam: A Sourcebook , Princeton, NJ: Princeton University Press, 685 sidor, s 385-514, ISBN 978-0-691-11485-9 .
• Keller, Agathe (2005), "Making diagrams speak, in Bhāskara I's commentary on the Aryabhaṭīya " (PDF) , Historia Mathematica , 32 (3): 275–302, doi : 10.1016/j.hm.2004.09 .
• Kichenassamy, Satynad (2006), "Baudhāyanas regel för cirkelns kvadratur", Historia Mathematica , 33 (2): 149–183, doi : 10.1016/j.hm.2005.05.001 .
•   Pingree, David (1971), "On the Greek Origin of the Indian Planetary Model Employing a Double Epicycle", Journal of Historical Astronomy , 2 (1): 80–85, Bibcode : 1971JHA.....2...80P , doi : 10.1177/002182867100200202 , S2CID 118053453 .
•   Pingree, David (1973), "The Mesopotamian Origin of Early Indian Mathematical Astronomy", Journal of Historical Astronomy , 4 (1): 1–12, Bibcode : 1973JHA.....4....1P , doi : 10.1177 /002182867300400102 , S2CID 125228353 .
•   Pingree, David ; Staal, Frits (1988), "Reviewed Work(s): The Fidelity of Oral Tradition and the Origins of Science av Frits Staal", Journal of the American Oriental Society , 108 (4): 637–638, doi : 10.2307/603154 , JSTOR 603154 .
•    Pingree, David (1992), "Hellenophilia versus the History of Science", Isis , 83 (4): 554–563, Bibcode : 1992Isis...83..554P , doi : 10.1086 /356288 , JSTOR 25425ID 46 , S
•   Pingree, David (2003), "The logic of non-western science: matematiska upptäckter i det medeltida Indien" , Daedalus , 132 ( 4): 45–54, doi : 10.1162/001152603771338779 , S2CID 157 .
• Plofker, Kim (1996), "An Example of the Secant Method of Iterative Approximation in a Fifteenth-Century Sanskrit Text", Historia Mathematica , 23 (3): 246–256, doi : 10.1006/hmat.1996.0026 .
• Plofker, Kim (2001), "The "Error" in the Indian "Taylor Series Approximation" to the Sine", Historia Mathematica , 28 (4): 283–295, doi : 10.1006/hmat.2001.2331 .
•   Plofker, K. (2007), "Mathematics of India", i Katz, Victor J. (red.), The Mathematics of Egypt, Mesopotamia, China, India, and Islam: A Sourcebook , Princeton, NJ: Princeton University Press, 685 sidor, s. 385-514, s. 385-514, ISBN 978-0-691-11485-9 .
•   Plofker, Kim (2009), Mathematics in India: 500 BCE–1800 CE , Princeton, NJ: Princeton University Press. pp. 384., ISBN 978-0-691-12067-6 .
•   Price, John F. (2000), "Applied geometry of the Sulba Sutras" (PDF) , i Gorini, Catherine A. (red.), Geometry at Work: Papers in Applied Geometry , vol. 53, s. 46-58, Washington DC: Mathematical Association of America Notes, 236 sidor, s. 46-58, ISBN 0-88385-164-4 .
•   Roy, Ranjan (1990), "Discovery of the Series Formula for $\pi$ av Leibniz, Gregory och Nilakantha", Mathematics Magazine , 63 (5): 291–306, doi : 10.2307/2690896 , JSTOR089 626 , JSTOR089 626 .
•     Singh, AN (1936), "On the Use of Series in Hindu Mathematics", Osiris , 1 (1): 606–628, doi : 10.1086/368443 , ISSN 0369-7827 , JSTOR 301627 , S47601 , S476011
• Staal, Frits (1986), The Fidelity of Oral Tradition and the Origins of Science , Mededelingen der Koninklijke Nederlandse Akademie von Wetenschappen, Afd. Letterkunde, NS 49, 8. Amsterdam: North Holland Publishing Company, 40 sidor .
•   Staal, Frits (1995), "The Sanskrit of Science", Journal of Indian Philosophy , Springer Netherlands, 23 (1): 73–127, doi : 10.1007/BF01062067 , S2CID 170755274 .
•   Staal, Frits (1999), "Greek and Vedic Geometry", Journal of Indian Philosophy , 27 (1–2): 105–127, doi : 10.1023/A:1004364417713 , S2CID 170894641 .
•   Staal, Frits (2001), "Squares and oblongs in the Veda", Journal of Indian Philosophy , Springer Netherlands, 29 (1–2): 256–272, doi : 10.1023/A:1017527129520 , S2CID 170403800 .
•   Staal, Frits (2006), "Artificial Languages ​​Across Sciences and Civilizations", Journal of Indian Philosophy , Springer Netherlands, 34 (1): 89–141, doi : 10.1007/s10781-005-8189-0 , S2CID 171096888 .
•   Stillwell, John (2004), Berlin och New York: Mathematics and its History (2 uppl.), Springer, 568 sidor, ISBN 0-387-95336-1 .
• Thibaut, George (1984) [1875], Mathematics in the Making in Ancient India: nytryck av 'On the Sulvasutras' och 'Baudhyayana Sulva-sutra', Calcutta och Delhi: KP Bagchi and Company (orig. Journal of the Asiatic Society of Bengalen), 133 sidor .
•   van der Waerden, BL (1983), Geometry and Algebra in Ancient Civilizations , Berlin och New York: Springer, 223 sidor, ISBN 0-387-12159-5
•   van der Waerden, BL (1988), "On the Romaka-Siddhānta", Archive for History of Exact Sciences , 38 (1): 1–11, doi : 10.1007/BF00329976 , S2CID 189788738
•   van der Waerden, BL (1988), "Reconstruction of a Greek table of chords", Archive for History of Exact Sciences , 38 (1): 23–38, doi : 10.1007/BF00329978 , S2CID 189793547
•   Van Nooten, B. (1993), "Binary numbers in Indian antiquity", Journal of Indian Philosophy , Springer Netherlands, 21 (1): 31–50, doi : 10.1007/BF01092744 , S2CID 171039636
•   Whish, Charles (1835), "Om cirkelns hinduiska kvadratur och den oändliga serien av proportionen mellan omkretsen och diametern som visas i de fyra S'ástras, Tantra Sangraham, Yucti Bháshá, Carana Padhati och Sadratnamála" , Transactions of the Royal Asiatic Society of Great Britain and Ireland , 3 (3): 509–523, doi : 10.1017/S0950473700001221 , JSTOR 25581775
•   Yano, Michio (2006), "Oral and Written Transmission of the Exact Sciences in Sanskrit", Journal of Indian Philosophy , Springer Nederländerna, 34 (1–2): 143–160, doi : 10.1007/s10781-005-8175-6 , S2CID 170679879