رياضيات هندية

ظهرت الرياضيات الهندية Indian mathematics في شبه القارة الهندية^[1] من عام 1200 BCE^[2] حتى نهاية القرن 18. في الفترة الكلاسيكية من الرياضيات الهندية (400 حتى 1600م)، كانت هناك إسهامات هامة من قبل الباحثين أمثال أرياباتا، براماگوپتا، ماهاڤيرا، باسكارا الثاني، ماداڤا من سانگامگاما، ونيلاكانتا سوماياجي. نظام العد العشري المستخدم في عالمياً اليوم كان مسجلاً في الرياضيات الهندية.^[3] قام الرياضياتيون الهنود بإسهامات مبكرة في دراسة مفهوم الصفر كعدد،^[4] الأعداد السالبة،^[5] الحسابيات، والجبر.^[6] بالإضافة إلى ذلك، فقد شهدت حساب المثلثات^[7] تطوراً كبيراً في الهند، وبصفة خاصة، تم تطوير التعريفات الحديثة للجيب والدوال المثلثية.^[8] تم نقل هذه المفاهيم الرياضية إلى الشرق الأوسط، الصين، وأوروپا^[6] والتي أدت بورها إلى المزيد من التطورات والتي تمثل الآن أساسات للكثير من الحقول الرياضية.

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ما قبل التاريخ

الفترة الڤيدية

الساميتية والبارمانية

سولبا سوترا

پينگالا

الرياضيات الجيانية (400 ق.م. - 200 م)

التقليد الشفهي

أنماط الحفظ

نوع سوترا

The design of the domestic fire altar in the Śulba Sūtra

التقليد المكتوب: تعليق النثر

الترقيم ونظام العد العشري

مخطوطة بخشالي

مقالة مفصلة: مخطوطة بخشالي

مخطوطة بخشالي هي مخطوطة رياضية مكتوبة على لحاء البتيولا عـُثر عليها بالقرب من قرية بخشالي (بالقرب من مردان في پاكستان الحالية) في 1881. وترجع أهميتها لكونها أقدم مخطوطة موجودة في الرياضيات الهندية."^[9] أجزاء منها تم تسنينها إلى 224–383 م.

وهي أقدم دليل على استخدام الهنود لرمز صفر.^[10]^[11]

الفترة الكلاسيكية (400–1600)

القرن الخامس والسادس

القرن السابع والثامن

Brahmagupta's theorem states that AF = FD.

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القرن العاشر والحادي عشر

رياضيات كرالا (1300–1600)

انظر أيضاً

الهوامش

^ خطأ استشهاد: وسم <ref> غير صحيح؛ لا نص تم توفيره للمراجع المسماة plofker
^ (Hayashi 205, pp. 360–361)
^ Plofker 2009, pp. 44–47
^ Bourbaki 1998, p. 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."
^ Bourbaki 1998, p. 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 CE. "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."
^ ^أ ^ب "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 (CE), 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."
^ (Pingree 2003, p. 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."
^ (Bourbaki 1998, p. 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 $\theta <\pi$ on a circle of radius r, in other words the number $2r\sin \left(\theta /2\right)$ ; the introduction of the sine, more easily handled, is due to Hindu mathematicians of the Middle Ages)."
^ خطأ استشهاد: وسم <ref> غير صحيح؛ لا نص تم توفيره للمراجع المسماة HayashiEncy
^ 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.

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قراءات إضافية

كتب مرجعية بالسنسكريتية

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 3-7643-7291-5 .
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 3-7643-7292-3 .
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 .

وصلات خارجية

Science and Mathematics in India
An overview of Indian mathematics, MacTutor History of Mathematics Archive, St Andrews University, 2000.
Index of Ancient Indian mathematics, MacTutor History of Mathematics Archive, St Andrews University, 2004.
Indian Mathematics: Redressing the balance, Student Projects in the History of Mathematics. Ian Pearce. MacTutor History of Mathematics Archive, St Andrews University, 2002.
Indian Mathematics on In Our Time at the BBC.
InSIGHT 2009, a workshop on traditional Indian sciences for school children conducted by the Computer Science department of Anna University, Chennai, India.
Mathematics in ancient India by R. Sridharan
Combinatorial methods in ancient India
Mathematics before S. Ramanujan

خلفية
تاريخ العلوم

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صفحات للتصفح
الخطوط الزمنية
البوابة
تصنيفات

الكلمات الدالة:

[plofker-1] خطأ استشهاد: وسم <ref> غير صحيح؛ لا نص تم توفيره للمراجع المسماة plofker

[hayashi2005-p360-361-2] (Hayashi 205, pp. 360–361)

[3] Plofker 2009, pp. 44–47

[bourbaki46-4] Bourbaki 1998, p. 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."

[bourbaki49-5] Bourbaki 1998, p. 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 CE. "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."

[concise-britannica-6] أ ^ب "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 (CE), 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."

[7] (Pingree 2003, p. 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."

[8] (Bourbaki 1998, p. 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 $\theta <\pi$ on a circle of radius r, in other words the number $2r\sin \left(\theta /2\right)$ ; the introduction of the sine, more easily handled, is due to Hindu mathematicians of the Middle Ages)."

[HayashiEncy-9] خطأ استشهاد: وسم <ref> غير صحيح؛ لا نص تم توفيره للمراجع المسماة HayashiEncy

[10] 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.

[11] "Carbon dating finds Bakhshali manuscript contains oldest recorded origins of the symbol 'zero'". Bodleian Library. 2017-09-14. Retrieved 2017-09-14.

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