Anju Malhotra Reward Points : 61200 Member Since : Tuesday, March 31, 2009
In India a decimal system was already in place during the Harappan period as indicated by an analysis of Harappan weights and measures. I want to know more about this...............
Posted On : 04/08/09 10:33:32 PM
Maniam PS Reward Points : 273700 Member Since : Wednesday, March 18, 2009
D An early decimal system was clearly in use by the inhabitants of the Indus valley civilization by 3000 BC. Excavations at both Harappa and Mohenjo Daro reveal decimal weights belonging to two series both being decimal in nature with each decimal number multiplied and divided by two, giving for the main series ratios of 0.05, 0.1, 0.2, 0.5, 1, 2, 5, 10, 20, 50, 100, 200, and 500. Also, marked rulers at Lodhar ?Lothal reveal gradations of 1.32 inches 3.35 centimetres , ten of which are 13.2 inches, possibly something akin to a foot similar measures exist in other parts of Asia and beyond . Markings on these and other texts reveal a number system with symbols for the numbers one through nine, and separate symbols for 10, 20, 100 thus the decimal system is highly developed though place-value is not used. Linguistic comparison among Indo-European languages ca. 3000 BC , shows a decimal enumeration system . In early Vedic texts, composed between 2500 BC and 1800 BC, we find Sanskrit number words not only for counting numbers in very large ranges, ranging up to 1019, with some puranas referring to numbers as large as 1062. Historians trace modern numerals in most languages to the Brahmi numerals, which were in use around the middle of the third century BC. The place value system, however, evolved later. The Brahmi numerals have been found in inscriptions in caves and on coins in regions near Pune, Mumbai, and Uttar Pradesh. These numerals with slight variations were in use over quite a long time span up to the 4th century AD. During the Gupta period early 4th century AD to the late 6th century AD , the Gupta numerals developed from the Brahmi numerals and were spread over large areas by the Gupta empire as they conquered territory . Beginning around 7th century, the Gupta numerals evolved into the Nagari numerals. There is indirect evidence that the Babylonians had a place value system as early as the 19th century BC, to the base 60, with a separator mark in empty places. This separator mark never was used at the end of a number, and it was not possible to tell the difference between 2 and 20. This innovation was brought about by Brahmagupta of India. Further, the Babylonian place value marker did not stand alone, as per the Indian 0 citation needed . There is indirect evidence that the Indians developed a positional number system as early as the first century CE 6 . The Bakhshali manuscript c. 3d c. BCE uses a place value system with a dot to denote the zero, which is called shunya-sthAna, empty-place , and the same symbol is also used in algebraic expressions for the unknown as in the canonical x in modern algebra . However, the date of the Bakhshali manuscript is hard to establish, and has been the subject of considerable debate. The oldest dated Indian document showing use of the modern place value form is a legal document dated 346 in the Chhedi calendar, which translates to 594 CE. While some historians have claimed that the date on this document was a later forgery, it is not clear what might have motivated it, and it is generally accepted that enumeration using the place-value system was in common use in India by the end of the 6th century. . Indian books dated to this period are able to denote numbers in the hundred thousands using a place value system. Many other inscriptions have been found which are dated and make use of the place-value system for either the date or some other numbers within the text , although some historians claim these to also be forgeries. In his seminal text of 499, Aryabhata devised a positional number system without a zero digit. He used the word kha for the zero position. Evidence suggests that a dot had been used in earlier Indian manuscripts to denote an empty place in positional notation. The same documents sometimes also used a dot to denote an unknown where we might use x. Later Indian mathematicians had names for zero in positional numbers yet had no symbol for it. The use of zero in these positional systems are the final step to the system of numerals we are familiar with today. The first inscription showing the use of zero which is dated and is not disputed by any historian is the inscription at Gwalior dated 933 in the Vikrama calendar 876 CE. The oldest known text to use zero is the Jain text from India entitled the Lokavibhaga , dated 458 AD. The first indubitable appearance of a symbol for zero appears in 876 in India on a stone tablet in Gwalior. Documents on copper plates, with the same small o in them, dated back as far as the sixth century AD, abound
The zero was known to the ancient Indians and most probably the knowledge of it spread from India to other cultures. Brahmagupta 598-668 ,who had worked on mathematics and astronomy, was the head of the astronomy observatory in Ujjain, which was at that point of time, the foremost mathematical centre in India he and Bhaskar the second 1114-1185 , who reached understanding on the number systems and solving equations, have together provided many rules for arithmetical operations with the zero. he decimal system is based on a ten-number system from zero to nine. The word decimal derives from the union of Indian Sanskrit dasha ten and English numeral which means symbol representing a number . English numeral derives from Arabic nummee coin which becomes Latin nummus coin and German die Nummer number .