The Father of Trigonometry
The first trigonometric table was apparently compiled by Hipparchus, who is now consequently known as "the father of trigonometry."[3]
Sumerian astronomers introduced angle measure, using a division of circles into 360 degrees.[4]They and their successors the Babylonians studied the ratios of the sides of similar triangles and discovered some properties of these ratios, but did not turn that into a systematic method for finding sides and angles of triangles. The ancient Nubians used a similar methodology.[5] The ancient Greeks transformed trigonometry into an ordered science.[6]
Classical Greek mathematicians (such as Euclid and Archimedes) studied the properties of chordsand inscribed angles in circles, and proved theorems that are equivalent to modern trigonometric formulae, although they presented them geometrically rather than algebraically. Claudius Ptolemyexpanded upon Hipparchus' Chords in a Circle in his Almagest.[7] The modern sine function was first defined in the Surya Siddhanta, and its properties were further documented by the 5th centuryIndian mathematician and astronomer Aryabhata.[8] These Greek and Indian works were translated and expanded by medieval Islamic mathematicians. By the 10th century, Islamic mathematicians were using all six trigonometric functions, had tabulated their values, and were applying them to problems in spherical geometry.[citation needed] At about the same time, Chinese mathematicians developed trigonometry independently, although it was not a major field of study for them. Knowledge of trigonometric functions and methods reached Europe via Latin translations of the works of Persian and Arabic astronomers such as Al Battani and Nasir al-Din al-Tusi.[9] One of the earliest works on trigonometry by a European mathematician is De Triangulis by the 15th century German mathematicianRegiomontanus. Trigonometry was still so little known in 16th century Europe that Nicolaus Copernicus devoted two chapters of De revolutionibus orbium
Sumerian astronomers introduced angle measure, using a division of circles into 360 degrees.[4]They and their successors the Babylonians studied the ratios of the sides of similar triangles and discovered some properties of these ratios, but did not turn that into a systematic method for finding sides and angles of triangles. The ancient Nubians used a similar methodology.[5] The ancient Greeks transformed trigonometry into an ordered science.[6]
Classical Greek mathematicians (such as Euclid and Archimedes) studied the properties of chordsand inscribed angles in circles, and proved theorems that are equivalent to modern trigonometric formulae, although they presented them geometrically rather than algebraically. Claudius Ptolemyexpanded upon Hipparchus' Chords in a Circle in his Almagest.[7] The modern sine function was first defined in the Surya Siddhanta, and its properties were further documented by the 5th centuryIndian mathematician and astronomer Aryabhata.[8] These Greek and Indian works were translated and expanded by medieval Islamic mathematicians. By the 10th century, Islamic mathematicians were using all six trigonometric functions, had tabulated their values, and were applying them to problems in spherical geometry.[citation needed] At about the same time, Chinese mathematicians developed trigonometry independently, although it was not a major field of study for them. Knowledge of trigonometric functions and methods reached Europe via Latin translations of the works of Persian and Arabic astronomers such as Al Battani and Nasir al-Din al-Tusi.[9] One of the earliest works on trigonometry by a European mathematician is De Triangulis by the 15th century German mathematicianRegiomontanus. Trigonometry was still so little known in 16th century Europe that Nicolaus Copernicus devoted two chapters of De revolutionibus orbium