Indian mathematics: Difference between revisions

{{Short description|Development of mathematics in South Asia}}

'''Indian mathematics''' emerged in the [[Indian subcontinent]]<ref name=plofker/> from 1200 BCE<ref name=hayashi2005-p360-361>{{Harv|Hayashi|2005|pp=360–361}}</ref> until the end of the 18th century. In the classical period of Indian mathematics (400 CE to 1200 CE), important contributions were made by scholars like [[Aryabhata]], [[Brahmagupta]], [[Bhaskara II]], and [[Varāhamihira]]. The [[Decimal|decimal number system]] in use today<ref name=irfah346>{{Harv|Ifrah|2000|p=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. "</ref> was first recorded in Indian mathematics.<ref>{{Harv|Plofker|2009|pp=44–47}}</ref> Indian mathematicians made significant early contributions to the study of the concept of [[0 (number)|zero]] as a number,<ref name=bourbaki46>{{Harv|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."</ref> [[negative numbers]],<ref name=bourbaki49>{{Harv|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 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."</ref> [[arithmetic]], and [[algebra]].<ref name=concise-britannica/> In addition, [[trigonometry]]<ref>{{Harv|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."</ref>