Branches of Mathematic

Trigonometry

Geometry

Trigonometry is a branch of mathematics concerned with the relationships between the angles and side lengths of triangles, with its trigonometric functions relating the angles of a right triangle to the ratios of its sides. The discipline developed in the Hellenistic period around the third century BC out of geometric methods applied to astronomy, and Indian mathematicians later produced the first known tables of trigonometric ratios such as the sine.

Facts
Central Question
Trigonometry asks how the angles and side lengths of triangles relate to one another, and how those relationships can be captured as functions usable for computation in astronomy, navigation and surveying. 1
Key Debate
Historians dispute where trigonometry as its own independent mathematical discipline actually began, whether with the chord tables the Hellenistic Greeks Hipparchus and Ptolemy built for astronomy, or only later with the Persian polymath Nasir al-Din al-Tusi, who has been credited as the first to treat it as a discipline separate from astronomy. 1
Classification
Pure or Applied
Both / Interdisciplinary 1
Trigonometry
Filter Results2 entries
Connections

Associated With

Source Trigonometry (Wikipedia)

Includes

Source Adriaan van Roomen (Wikipedia)
Source Albert Girard (MacTutor)
Source Anders Johan Lexell (Wikipedia)
Source Wolfram MathWorld: Angle Trisection
Source Antoine Deparcieux (Wikipedia)
Source Bartholomaeus Pitiscus (Wikipedia)
Source Benjamin Bramer (Wikipedia)
Source Christoph Grienberger (Wikipedia)
Source Christopher Clavius (Wikipedia)
Source De Moivre's formula (Wikipedia)
Source Differentiation of Trigonometric Functions (Wikipedia)
Source Edmund Gunter (Wikipedia)
Source Edward Wright (mathematician) (Wikipedia)
Source Georg Joachim Rheticus (Wikipedia)
Source Georg Simon Klügel (Wikipedia)
Source Giovanni Antonio Magini (Wikipedia)
Source Haversine Formula (Wikipedia)
Source Henry Gellibrand (Wikipedia)
Source MacTutor biography of Hipparchus, St Andrews
Source James Gregory (mathematician) (Wikipedia)
Source James Hume (mathematician) (Wikipedia)
Source James Inman (Wikipedia)
Source Jan Jansz de Jonge Stampioen (Wikipedia)
Source Jean-Baptiste Morin (mathematician) (Wikipedia)
Source Johann Gabriel Doppelmayr (Wikipedia)
Source John Caswell (Wikipedia)
Source John Keill (Wikipedia)
Source Jonas Moore (Wikipedia)
Source Jost Burgi (Wikipedia)
Source Jyeṣṭhadeva (Wikipedia)
Source Leonty Magnitsky (Wikipedia)
Source Ludolph Van Ceulen (MacTutor)
Source Nicolaus Rohlfs (Wikipedia)
Source Paul Wittich (MacTutor)
Source Pythagorean trigonometric identity (Wikipedia)
Source Regiomontanus (Wikipedia)
Source Samuel Foster (Wikipedia)
Source Thomas Fincke (Wikipedia)
Source Ulugh Beg (MacTutor)
Source Valentinus Otho (Wikipedia)
Source Willebrord Snellius (Wikipedia)
Source William Oughtred (Wikipedia)
Sources
1. Trigonometry (Wikipedia)
Wikimedia Foundation
  • Lead section
    Trigonometry (from Ancient Greek τρίγωνον (trígōnon) 'triangle' and μέτρον (métron) 'measure') is a branch of mathematics concerned with relationships between angles and side lengths of triangles.
  • History section, Nasir al-Din al-Tusi passage
    The Persian polymath Nasir al-Din al-Tusi has been described as the creator of trigonometry as a mathematical discipline in its own right. He was the first to treat trigonometry as a mathematical discipline independent from astronomy, and he developed spherical trigonometry into its present form.
  • Associated With: Geometry, Wikipedia lead paragraph, Trigonometry
    The field emerged in the Hellenistic world during the 3rd century BC from applications of geometry to astronomical studies.
  • In Group: Classical and Elementary Geometry, lead paragraph
    is a branch of mathematics concerned with relationships between angles and side lengths of triangles.
View the Source
James Inman (Wikipedia)
Includes: James Inman, Professor, Royal Naval College
Quote, Includes: James Inman, Professor, Royal Naval College
to simplify the calculation of distances between two points on the surface of the earth using spherical trigonometry
View the Source
Jost Burgi (Wikipedia)
Wikimedia FoundationIncludes: Jost Bürgi, Biography, field of work
Quote, Includes: Jost Bürgi, Biography, field of work
Bürgi was able to calculate sines at arbitrary precision
View the Source
Ulugh Beg (MacTutor)
Includes: Ulugh Beg, Summary
Quote, Includes: Ulugh Beg, Summary
He did important early work on trigonometry.
View the Source
Regiomontanus (Wikipedia)
Includes: Regiomontanus, Work
Quote, Includes: Regiomontanus, Work
De triangulis omnimodis was one of the first textbooks presenting the current state of trigonometry
View the Source
Adriaan van Roomen (Wikipedia)
Includes: Adriaan van Roomen, Lead, field of work
Quote, Includes: Adriaan van Roomen, Lead, field of work
van Roomen (29 September 1561-4 May 1615), also known as Adrianus Romanus, was a mathematician, professor of medicine and medical astrologer from the Duchy of Brabant in the Habsburg Netherlands who was active throughout Central Europe in the late
View the Source
Christopher Clavius (Wikipedia)
Includes: Christopher Clavius, Lead, field of work
Quote, Includes: Christopher Clavius, Lead, field of work
Clavius, (25 March 1538-6 February 1612) was a Jesuit German mathematician and physicist, head of mathematicians at the Collegio Romano, and astronomer who was a member of the Vatican commission that accepted the proposed calendar invented by
View the Source
Ludolph Van Ceulen (MacTutor)
Includes: Ludolph van Ceulen, Biography, Struik on Vanden circkel
Quote, Includes: Ludolph van Ceulen, Biography, Struik on Vanden circkel
also shows Van Ceulen to be as expert in trigonometry as his contemporary Viète
View the Source
Christoph Grienberger (Wikipedia)
Includes: Christoph Grienberger, Lead, field of work
Quote, Includes: Christoph Grienberger, Lead, field of work
He studied in Prague and Vienna, and subsequently succeeded his tutor, Christopher Clavius, as professor of mathematics at the Collegio Romano in 1612.
View the Source
Benjamin Bramer (Wikipedia)
Includes: Benjamin Bramer, Career, sines
Quote, Includes: Benjamin Bramer, Career, sines
he described various measures to calculate sines
View the Source
Giovanni Antonio Magini (Wikipedia)
Includes: Giovanni Antonio Magini, His work, trigonometry
Quote, Includes: Giovanni Antonio Magini, His work, trigonometry
He also worked on the geometry of the sphere and applications of trigonometry
View the Source
Georg Joachim Rheticus (Wikipedia)
Includes: Georg Joachim Rheticus, Lead, field of work
Quote, Includes: Georg Joachim Rheticus, Lead, field of work
Georg Joachim de Porris, also known as Rheticus (; 16 February 1514-4 December 1574), was a mathematician, astronomer, cartographer, navigational-instrument maker, medical practitioner, and teacher.
View the Source
Albert Girard (MacTutor)
Includes: Albert Girard, Biography, fields of work
Quote, Includes: Albert Girard, Biography, fields of work
Girard worked on algebra, trigonometry and arithmetic.
View the Source
Edward Wright (mathematician) (Wikipedia)
Includes: Edward Wright (mathematician), Lead, field of work
Quote, Includes: Edward Wright (mathematician), Lead, field of work
Wright (baptised 8 October 1561; died November 1615) was an English mathematician and cartographer noted for his book Certaine Errors in Navigation (1599; 2nd ed., 1610), which for the first time explained the mathematical basis of the Mercator
View the Source
Paul Wittich (MacTutor)
Includes: Paul Wittich, Biography, prosthaphaeresis
Quote, Includes: Paul Wittich, Biography, prosthaphaeresis
Wittich found how to replace multiplication and division with addition and subtraction using the rules for sines and cosines of the sums and differences of angles
View the Source
Jyeṣṭhadeva (Wikipedia)
Includes: Jyeṣṭhadeva, Lead, field of work
Quote, Includes: Jyeṣṭhadeva, Lead, field of work
Jyeṣṭhadeva (Malayalam: ജ്യേഷ്ഠദേവൻ; c. 1500, c. 1575) was an astronomer-mathematician of the Kerala school of astronomy and mathematics founded by Madhava of Sangamagrama (c. 1350, c. 1425).
View the Source
Thomas Fincke (Wikipedia)
Includes: Thomas Fincke, Lead, field of work
Quote, Includes: Thomas Fincke, Lead, field of work
Thomas Fincke (6 January 1561-24 April 1656) was a Danish mathematician and physicist, and a professor at the University of Copenhagen for more than 60 years. == Biography == Thomas Jacobsen Fincke was born in Flensburg in Schleswig.
View the Source
Valentinus Otho (Wikipedia)
Includes: Valentinus Otho, Lead, field of work
Quote, Includes: Valentinus Otho, Lead, field of work
(also Valentin Otto; born around 1545-46 possibly in Magdeburg, 8 April 1603 in Heidelberg) was a German mathematician and astronomer. == Life == In 1573 he came to Wittenberg, proposing to Johannes Praetorius an approximation of pi as π≈355113 (now
View the Source
William Oughtred (Wikipedia)
Includes: William Oughtred, Lead, field of work
Quote, Includes: William Oughtred, Lead, field of work
William Oughtred ( AWT-urd;5 March 1574-30 June 1660), also Owtred or Uhtred, was an English mathematician and Anglican clergyman.
View the Source
Willebrord Snellius (Wikipedia)
Includes: Willebrord Snellius, Lead, field of work
Quote, Includes: Willebrord Snellius, Lead, field of work
Willebrord Snellius (born Willebrord Snel van Royen, also Willebrord van Roijen Snel (13 June 1580-30 October 1626), commonly known simply as Snellius and Snel, was a Dutch astronomer and mathematician.
View the Source
Edmund Gunter (Wikipedia)
Includes: Edmund Gunter, Lead, field of work
Quote, Includes: Edmund Gunter, Lead, field of work
Edmund Gunter (1581-10 December 1626), was an English clergyman, mathematician, geometer and astronomer of Welsh descent.
View the Source
Jean-Baptiste Morin (mathematician) (Wikipedia)
Includes: Jean-Baptiste Morin, Lead, field of work
Quote, Includes: Jean-Baptiste Morin, Lead, field of work
Morin (February 23, 1583, November 6, 1656), also known by the Latinized name as Morinus, was a French mathematician, astrologer, and astronomer. == Life and work == Born in Villefranche-sur-Saône, in the Lyonnais, he began studying philosophy at
View the Source
Henry Gellibrand (Wikipedia)
Includes: Henry Gellibrand, Lead, field of work
Quote, Includes: Henry Gellibrand, Lead, field of work
Henry Gellibrand (1597-1637) was an English mathematician.
View the Source
Bartholomaeus Pitiscus (Wikipedia)
Includes: Bartholomaeus Pitiscus, Lead, field of work
Quote, Includes: Bartholomaeus Pitiscus, Lead, field of work
classical scholar Samuel Pitiscus (1637-1727) was his nephew. == Mathematics == Pitiscus achieved fame with his influential work, Trigonometria: sive de solutione triangulorum tractatus brevis et perspicuus (Trigonometry: A short and clear treatise on the
View the Source
Samuel Foster (Wikipedia)
Includes: Samuel Foster, Life, spherical triangles
Quote, Includes: Samuel Foster, Life, spherical triangles
John Wallis received from Foster a theorem on spherical triangles
View the Source
Jonas Moore (Wikipedia)
Includes: Jonas Moore, Mathematician and surveyor, cosine notation
Quote, Includes: Jonas Moore, Mathematician and surveyor, cosine notation
Sir Jonas Moore first used the abbreviated notation 'cos' for the trigonometric term cosine
View the Source
John Caswell (Wikipedia)
Includes: John Caswell, Lead, field of work
Quote, Includes: John Caswell, Lead, field of work
Caswell's publications included a book on trigonometry in 1685.
View the Source
Johann Gabriel Doppelmayr (Wikipedia)
Includes: Johann Gabriel Doppelmayr, Lead, field of work
Quote, Includes: Johann Gabriel Doppelmayr, Lead, field of work
His publications covered topics on mathematics and astronomy, including sundials, spherical trigonometry, and celestial maps and globes.
View the Source
Anders Johan Lexell (Wikipedia)
Includes: Anders Johan Lexell, Lead
Quote, Includes: Anders Johan Lexell, Lead
contributed to spherical trigonometry
View the Source
Antoine Deparcieux (Wikipedia)
Includes: Antoine Deparcieux, Article text
Quote, Includes: Antoine Deparcieux, Article text
Traité de trigonométrie rectiligne et sphérique
View the Source
James Hume (mathematician) (Wikipedia)
Includes: James Hume, Works, 1636 trigonometry
Quote, Includes: James Hume, Works, 1636 trigonometry
Traité de la Trigonométric pour resoudre tous Triangles rectilignes et sphériques
View the Source
Georg Simon Klügel (Wikipedia)
Includes: Georg Simon Klügel, Article text
Quote, Includes: Georg Simon Klügel, Article text
exceptional contribution to trigonometry
View the Source
James Gregory (mathematician) (Wikipedia)
Includes: James Gregory, Lead, field of work
Quote, Includes: James Gregory, Lead, field of work
He described an early practical design for the reflecting telescope, the Gregorian telescope, and made advances in trigonometry, discovering infinite series representations for several trigonometric functions.
View the Source
Jan Jansz de Jonge Stampioen (Wikipedia)
Includes: Jan Jansz de Jonge Stampioen, Lead, field of work
Quote, Includes: Jan Jansz de Jonge Stampioen, Lead, field of work
Jan Jansz de Jonge Stampioen (1610, Rotterdam - 1653, The Hague) was a Dutch mathematician famous for his published work on spherical trigonometry.
View the Source
Leonty Magnitsky (Wikipedia)
Includes: Leonty Magnitsky, Lead, field of work
Quote, Includes: Leonty Magnitsky, Lead, field of work
From 1701 and until his death, he taught arithmetic, geometry and trigonometry at the Moscow School of Mathematics and Navigation, becoming its director in 1716.
View the Source
John Keill (Wikipedia)
Includes: John Keill, Lead, field of work
Quote, Includes: John Keill, Lead, field of work
Trigonometriae Planae & Sphaericae Elementa.
View the Source
Nicolaus Rohlfs (Wikipedia)
Includes: Nicolaus Rohlfs, Lead, field of work
Quote, Includes: Nicolaus Rohlfs, Lead, field of work
Trigonometrische Calculation, der Anno Christi 1724. den 22 Maji ... vorfallenden grossen Sonnen-Finsterniss : wie dieselbe über den Hamburgischen Horizont sich praesentiren wird ... auffgesetzet von Nicolaus Rohlfs.
View the Source
Haversine Formula (Wikipedia)
Includes: Haversine formula, Lead paragraph
Quote, Includes: Haversine formula, Lead paragraph
Important in navigation, it is a special case of a more general formula in spherical trigonometry, the law of haversines, that relates the sides and angles of spherical triangles.
View the Source
De Moivre's formula (Wikipedia)
Includes: De Moivre's Formula, Lead paragraph
Quote, Includes: De Moivre's Formula, Lead paragraph
The formula is important because it connects complex numbers and trigonometry.
View the Source
Wolfram MathWorld: Angle Trisection
Wolfram MathWorldIncludes: Angle Trisection, Subject classifications
Quote, Includes: Angle Trisection, Subject classifications
Geometry Trigonometry
View the Source
Pythagorean trigonometric identity (Wikipedia)
Includes: Pythagorean Trigonometric Identity, Lead section
Quote, Includes: Pythagorean Trigonometric Identity, Lead section
The Pythagorean trigonometric identity, also called simply the Pythagorean
View the Source
Differentiation of Trigonometric Functions (Wikipedia)
Includes: Differentiation of Trigonometric Functions, Lead section
Quote, Includes: Differentiation of Trigonometric Functions, Lead section
The differentiation of trigonometric functions is the mathematical process of finding
View the Source
MacTutor biography of Hipparchus, St Andrews
Includes: Hipparchus, Summary
Quote, Includes: Hipparchus, Summary
Hipparchus was a Greek mathematician who compiled an early example of trigonometric tables and gave methods for solving spherical triangles.
View the Source
Comments (0)
No comments yet. Be the first to share a thought.
Reader Challenges (0)
No disputes yet. Spotted an error or a better source? Open the first one.

Mathematics Atlas

How Proof Is Made
Sign In
Text size
100%
Theme