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Matematika India

Perkembangan Matematika di Asia Selatan
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Matematika India muncul di anak benua India[1] dari 1200 SM[2] sampai akhir abad ke-18. Pada zaman klasik dari matematika India (400 M sampai 1200 M), kontribusi menonjol dibuat oleh para cendekiawan seperti Aryabhata, Brahmagupta, Bhaskara II, dan Varāhamihira. Sistem bilangan desimal yang sekarang dipakai[3] pertama kali tercatat dalam matematika India.[4] Para matematikawan India membuat kontribusi awal untuk kajian konsep nol sebagai sebuah bilangan,[5] bilangan negatif,[6] aritmatika, dan algebra.[7] Selain itu, trigonometri[8] berkembang di India, dan definisi modern sinus dan kosinus juga dikembangkan disana.[9] Konsep matematika tersebut dibawa ke Timur Tengah, Tiongkok dan Eropa[7] dan berujung pada pengembangan lanjutan yang sekarang membentuk fondasi-fondasi dari banyak bidang matematika.

Catatan

  1. ^ Kesalahan pengutipan: Tag <ref> tidak sah; tidak ditemukan teks untuk ref bernama plofker
  2. ^ (Hayashi 2005, hlm. 360–361)
  3. ^ Ifrah 2000, hlm. 346: "The measure of the genius of Indian civilisation, to which we owe our modern (number) system, is all the greater in that it was the only one in all history to have achieved this triumph. Some cultures succeeded, earlier than the Indian, in discovering one or at best two of the characteristics of this intellectual feat. But none of them managed to bring together into a complete and coherent system the necessary and sufficient conditions for a number-system with the same potential as our own."
  4. ^ Plofker 2009, hlm. 44–47
  5. ^ Bourbaki 1998, hlm. 46: "...our decimal system, which (by the agency of the Arabs) is derived from Hindu mathematics, where its use is attested already from the first centuries of our era. It must be noted moreover that the conception of zero as a number and not as a simple symbol of separation) and its introduction into calculations, also count amongst the original contribution of the Hindus."
  6. ^ Bourbaki 1998, hlm. 49: Modern arithmetic was known during medieval times as "Modus Indorum" or method of the Indians. Leonardo of Pisa wrote that compared to method of the Indians all other methods is a mistake. This method of the Indians is none other than our very simple arithmetic of addition, subtraction, multiplication and division. Rules for these four simple procedures was first written down by Brahmagupta during 7th century AD. "On this point, the Hindus are already conscious of the interpretation that negative numbers must have in certain cases (a debt in a commercial problem, for instance). In the following centuries, as there is a diffusion into the West (by intermediary of the Arabs) of the methods and results of Greek and Hindu mathematics, one becomes more used to the handling of these numbers, and one begins to have other "representation" for them which are geometric or dynamic."
  7. ^ a b "algebra" 2007. Britannica Concise Encyclopedia. Encyclopædia Britannica Online. 16 May 2007. Quote: "A full-fledged decimal, positional system certainly existed in India by the 9th century (AD), yet many of its central ideas had been transmitted well before that time to China and the Islamic world. Indian arithmetic, moreover, developed consistent and correct rules for operating with positive and negative numbers and for treating zero like any other number, even in problematic contexts such as division. Several hundred years passed before European mathematicians fully integrated such ideas into the developing discipline of algebra."
  8. ^ (Pingree 2003, hlm. 45) Quote: "Geometry, and its branch trigonometry, was the mathematics Indian astronomers used most frequently. Greek mathematicians used the full chord and never imagined the half chord that we use today. Half chord was first used by Aryabhata which made trigonometry much more simple. In fact, the Indian astronomers in the third or fourth century, using a pre-Ptolemaic Greek table of chords, produced tables of sines and versines, from which it was trivial to derive cosines. This new system of trigonometry, produced in India, was transmitted to the Arabs in the late eighth century and by them, in an expanded form, to the Latin West and the Byzantine East in the twelfth century."
  9. ^ (Bourbaki 1998, hlm. 126): "As for trigonometry, it is disdained by geometers and abandoned to surveyors and astronomers; it is these latter (Aristarchus, Hipparchus, Ptolemy) who establish the fundamental relations between the sides and angles of a right angled triangle (plane or spherical) and draw up the first tables (they consist of tables giving the chord of the arc cut out by an angle   on a circle of radius r, in other words the number  ; the introduction of the sine, more easily handled, is due to Hindu mathematicians of the Middle Ages)."

Referensi

Bacaan tambahan

Buku sumber dalam bahasa Sanskerta

  • Keller, Agathe (2006), Expounding the Mathematical Seed. Vol. 1: The Translation: A Translation of Bhaskara I on the Mathematical Chapter of the Aryabhatiya, Basel, Boston, and Berlin: Birkhäuser Verlag, 172 pages, ISBN 978-3-7643-7291-0 .
  • Keller, Agathe (2006), Expounding the Mathematical Seed. Vol. 2: The Supplements: A Translation of Bhaskara I on the Mathematical Chapter of the Aryabhatiya, Basel, Boston, and Berlin: Birkhäuser Verlag, 206 pages, ISBN 978-3-7643-7292-7 .
  • Neugebauer, Otto; Pingree (eds.), David (1970), The Pañcasiddhāntikā of Varāhamihira, New edition with translation and commentary, (2 Vols.), Copenhagen .
  • Pingree, David (ed) (1978), The Yavanajātaka of Sphujidhvaja, edited, translated and commented by D. Pingree, Cambridge, MA: Harvard Oriental Series 48 (2 vols.) .
  • Sarma, K. V. (ed) (1976), Āryabhaṭīya of Āryabhaṭa with the commentary of Sūryadeva Yajvan, critically edited with Introduction and Appendices, New Delhi: Indian National Science Academy .
  • Sen, S. N.; Bag (eds.), A. K. (1983), The Śulbasūtras of Baudhāyana, Āpastamba, Kātyāyana and Mānava, with Text, English Translation and Commentary, New Delhi: Indian National Science Academy .
  • Shukla, K. S. (ed) (1976), Āryabhaṭīya of Āryabhaṭa with the commentary of Bhāskara I and Someśvara, critically edited with Introduction, English Translation, Notes, Comments and Indexes, New Delhi: Indian National Science Academy .
  • Shukla, K. S. (ed) (1988), Āryabhaṭīya of Āryabhaṭa, critically edited with Introduction, English Translation, Notes, Comments and Indexes, in collaboration with K.V. Sarma, New Delhi: Indian National Science Academy .

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