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 EdgarCommented Feb 12, 2016 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 $\endgroup$– ConifoldCommented Feb 15, 2016 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 RenfroCommented Feb 26, 2016 at 20:33
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3 Answers
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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, 2016 at 14:07
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$\begingroup$ en.wikipedia.org/wiki/Ptolemy%27s_table_of_chords $\qquad$ $\endgroup$ Commented Feb 26, 2016 at 18:26
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$\begingroup$ This is perhaps also of interest: hsm.stackexchange.com/questions/5258/… $\endgroup$– fdbCommented Nov 12, 2016 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, 2016 at 12:47
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$\begingroup$ Is link-only answer tolerable? $\endgroup$– user1709Commented Feb 13, 2016 at 6:34
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1$\begingroup$ @user36790, this isn't "link only" in my eyes. $\endgroup$– vonbrandCommented Feb 13, 2016 at 21:12
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$\begingroup$ @vonbrand: Have you seen his answer before the edit? $\endgroup$– user1709Commented Feb 14, 2016 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.
