Talk:Trigonometric functions: Difference between revisions

Revision as of 20:56, 25 March 2004

Revision as of 21:55, 25 March 2004

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That seems farfetched and thus potentially interesting—please tell us more! What does ''jiva'' mean in Hindu? What's your source on this? The standard etymology of English ''sine'' is derivation from Latin ''sinus'' [curve, bend], which is pretty suggestive of the 'curvaceous' shape of the sinusoid. [http://www.m-w.com Merriam-Webster] supports me in this. So what's wrong with the well-known, logical and sensible explanation?

<br>&mdash;[[User:Herbee|Herbee]] 20:56, 2004 Mar 25 (UTC)

:My source is Carl B. Boyer, ''A History of Mathematics'', 2nd ed. (see references). He writes (p. 209):

::...Thus was born, apparently in India, the predecessor of the modern trigonometric function known as the sine of an angle; and the introduction of the sine function represents the chief contribution of the ''Siddhantas'' to the history of mathematics. Although it is generally assumed that the change from the whole chord to the half chord took place in India, it has been suggested by Paul Tannery, the leading historian of science at the turn of the century, that this transformation of trigonometry may have occurred at Alexandria during the post-Ptolemaic period. Whether or not this suggestion has merit, there is no doubt that it was through the Hindus, and not the Greeks, that our use of the half chord has been derived; and our word "sine," through misadventure in translation (see below), has descended from the Hindu name, ''jiva''.

:The "(see below)" I think refers to a much later section (p. 252) on translations of Arabic mathematics in Europe in the 12th century. There, Boyer writes:

::It was Robert of Chester's translation from the Arabic that resulted in our word "sine." The Hindus had given the name ''jiva'' to the half-chord in trigonometry, and the Arabs had taken this over as ''jiba''. In the Arabic language there is also the word ''jaib'' meaning "bay" or "inlet." When Robert of Chester came to translate the technical word ''jiba'', he seems to have confused this with the word ''jaib'' (perhaps because vowels were omitted); hence, he used the word ''sinus'', the Latin word for "bay" or "inlet." Sometimes the more specific phrase ''sinus rectus'', or "vertical sine," was used; hence, the phrase ''sinus versus'', or our "versed sine," was applied to the "sagitta," or the "sine turned on its side."

:(Note that the "versed sine" is 1&ndash;cos(&theta).) [[User:Stevenj|Steven G. Johnson]] 21:55, 25 Mar 2004 (UTC)