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Counting Systems - Essay Example

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The first operation to be considered is numeration, which is defined in a rather modern vein as the representation of numbers by symbols. To fully appreciate the task the Treviso's author is undertaking in this section, one should understand the level of acceptance for the "Hindu-Arabic" numeral system that existed in Europe at this time (Al-Daffa, 1977)…
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Counting Systems
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Download file to see previous pages There was a certain social status and prestige associated with the use of a counting table.
Hindu mathematics presents interesting features of notation. Valuable information on this development is revealed by the Bakhsh'l' Manuscript. First, Hindu Arabic numeral system was mentioned in the 9th century. It is classified as a positional decimal numeral system consisted of symbols (Smith and Karpinski 1911). It has been generally believed that the so-called Arabic numerals, from which arise those in use by us today, were derived by the Muslim peoples from India, and that the Hindus invented (1) the principle of position or place value of the decimal point and (2) the nine digits and zero (or dot). In the astrological treatise written by Ch''-t'an Hsi-ta, who flourished under the T'ang Dynasty in the early eighth century A.D., the so-called Hindu decimal notation and rules are implied, so that they were introduced, or re-introduced into China, at that time or possibly earlier (Datta and Singh 1998).
Whereas Hindu astronomy made improvement through Greek influence, mathematics in India, as Professor Sarton has stated, had no need to wait for Hellenism: we are, therefore, at present disinclined to refuse legitimate claims for Hindu originality in respect of the nine numerals and decimal system (Al-Daffa, 1977). "The basic idea of the system is the primacy of grouping (and of the rhythm of the symbols in their regular sequence) in "packets" of tens, hundreds (tens of tens), thousands (tens of tens of tens), and so on" (Ifrah et al. 2000, p. 25).
In the Bakhshali Manuscript researchers find a small sign used to represent negative quantity: it is a cross, like the present 'plus' sign, but placed to the right of the quantity to which it refers. Zero is represented by a dot. The dot is also used to indicate an unknown quantity. There is an absence from the Bakshali Manuscript of symbols of operation, even the negative sign already noted not being used as such. In Bhaskara's Bija-Ganita, however, the dot is used as the negative sign of operation (Datta and Singh 1998). Operation is indicated in the Bakhsh'l' Manuscript by an ad hoc term, or by relative position, In general, Hindu mathematicians used the terms "ya" (as many as") for the first unknown quantity, now usually denoted by x; for the second unknown, say y for the constant quantity in an expression; "v or va" for a square and the initial letters of the words representing various colours for other unknown quantities (Al-Daffa, 1977).
During his khalifate and later, there flourished Al-Kindi. Al-Kindi, like many eminent scholars of the Middle Ages, was an encyclopedialist, and wrote numerous works on many subjects. He translated extesively from the Greek, and his treatise on geometrical and physiological optics (known in the Latin form as De Aspectibus) was based on the optical works of Euclid, Heron, and Ptolemy. He was interested in large-scale natural phenomena, studying particularly the tides, and also the rainbow ion accordance with the principles of optical reflection. Further, his scientific studies embraced the Hindu numerals and a musical notation relating to pitch (Smith and Karpinski 1911). He was sufficiently far-sighted to regard much alchemy as spurious and non-scientific Eminent among writers on mechanical and mathematical subjects were the three sons of M's' ibn Sh'kir, the Ban' M's', who engaged also the ...Download file to see next pagesRead More
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