I'm doing some research about the beginning of trigonometry. I want to know why and who draw the first time the sine function. Do you have one site or something that can help me ?
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3$\begingroup$ When you say "draw" you mean drawing the graph? I would think graphs were much later than trig functions in tables. $\endgroup$ – Gerald Edgar Feb 12 '16 at 14:07
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$\begingroup$ At the beginnings of trigonometry there were no such things as functions or graphs en.wikipedia.org/wiki/History_of_trigonometry those did not appear for over a thousand years after en.wikipedia.org/wiki/History_of_the_function_concept $\endgroup$ – Conifold Feb 15 '16 at 1:26
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$\begingroup$ For a recent book, see The Mathematics of the Heavens and the Earth. The Early History of Trigonometry by Glen Van Brummelen (2009) First Chapter. See also Vorlesungen über Geschichte der Trigonometrie by Anton von Braunmühl (1903) for what I believe was for a long time (and still may be) the most complete historical treatment of trigonometry, and it's freely available on the internet (but it's in German, which I can't read BTW). $\endgroup$ – Dave L Renfro Feb 26 '16 at 20:33
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Ancient Greeks did not have the sine function; their only trigonometric function was the chord which is related to sine by the formula $\mathrm{chd(x)}=2\sin(x/2)$. The first known tables of chords are due to Ptolemy. Greek trigonometry penetrated to India during the Hellenistic period. Sine was introduced Aryabhata in India (476-550).
https://en.wikipedia.org/wiki/%C4%80ryabha%E1%B9%ADa%27s_sine_table
From India it penetrated to the Muslim world, where several astronomers developed trigonometry further, one notable figure was Abu al Wafa (940-998), who composed sine tables. He also introduced tangent.
In Europe people were not interested in mathematics at that time. Later the knowledge penetrated Europe, and the first European sine tables (other than copies of the Arab tables) were made by Johannes Muller (Regiomontanus, 1436-1476).
See Wikipedia articles on Abu al Wafa and Johann Muller.
answered Feb 12 '16 at 14:07
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$\begingroup$ en.wikipedia.org/wiki/Ptolemy%27s_table_of_chords $\qquad$ $\endgroup$ – Michael Hardy Feb 26 '16 at 18:26
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$\begingroup$ This is perhaps also of interest: hsm.stackexchange.com/questions/5258/… $\endgroup$ – fdb Nov 12 '16 at 12:00
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See at least :
- Albrecht Dürer, Underweysung der Messung mit dem Zirckel und Richtscheyt (or Instructions for Measuring with Compass and Ruler), Nürnberg 1525, page 17.
An overview of the early history of trigonometry is into:
- Enrique González Velasco, Journey through Mathematics (2011), Ch.1 Trigonometry, page 1-on.
The first modern textbook: Bartholomaeus Pitiscus, Trigonometriae sive de dimensione triangulorum libri quinque (1600, first edition 1595) does not seem to have graphs, but only tables.
We may suppose that to draw the graph of the trigonometric functions, we must have a "modern" idea of function.
The first (quite) clear understanding of it is:
- Leonhard Euler, Introductio in analysin infinitorum (1748), CAPUT PRIMUM De functionibus in genere, page 4:
Functio quantitatis variabilis, est expressio analytica quomodocunque composita ex illa quantitate variabili, et numeris seu quantitatibus constantibus.
See also CAPUT VIII De quantitatibus trascendentibus ex Circulo оrtis, page 90-on, for trigonometry.
Maybe in the Plates... see Planche 12, Fig.104.
answered Feb 12 '16 at 12:47
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$\begingroup$ Is link-only answer tolerable? $\endgroup$ – user1709 Feb 13 '16 at 6:34
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1$\begingroup$ @user36790, this isn't "link only" in my eyes. $\endgroup$ – vonbrand Feb 13 '16 at 21:12
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$\begingroup$ @vonbrand: Have you seen his answer before the edit? $\endgroup$ – user1709 Feb 14 '16 at 2:46
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In the second century CE, Ptolemy created a table of chords that is in some sense equivalent to the sine function.
