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 QuestionTrigonometry 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 DebateHistorians 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 AppliedBoth / Interdisciplinary 1 Connections
Associated With
Source Trigonometry (Wikipedia)
Includes
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 Wang Zhenyi (astronomer) (Wikipedia)
Source Willebrord Snellius (Wikipedia)
Source MacTutor History of Mathematics, University of St Andrews: William Hopkins (biography)
Source William Oughtred (Wikipedia)
Showing 51 to 60 of 60 in Includes, page 2 of 2.
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1. Trigonometry (Wikipedia)
Wikimedia FoundationLead 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 CollegeQuote, 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 workQuote, 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, SummaryQuote, Includes: Ulugh Beg, Summary
He did important early work on trigonometry.
View the Source Regiomontanus (Wikipedia)
Includes: Regiomontanus, WorkQuote, 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 workQuote, 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 workQuote, 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 circkelQuote, 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 workQuote, 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, sinesQuote, 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, trigonometryQuote, 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 workQuote, 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 workQuote, 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 workQuote, 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, prosthaphaeresisQuote, 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 workQuote, 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 workQuote, 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 workQuote, 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 workQuote, 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 workQuote, 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 workQuote, 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 workQuote, 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 workQuote, 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 workQuote, 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 trianglesQuote, 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 notationQuote, 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 workQuote, 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 workQuote, 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, LeadQuote, Includes: Anders Johan Lexell, Lead
contributed to spherical trigonometry
View the Source Antoine Deparcieux (Wikipedia)
Includes: Antoine Deparcieux, Article textQuote, Includes: Antoine Deparcieux, Article text
Traité de trigonométrie rectiligne et sphérique
View the Source James Hume (mathematician) (Wikipedia)
Includes: James Hume, Works, 1636 trigonometryQuote, 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 textQuote, Includes: Georg Simon Klügel, Article text
exceptional contribution to trigonometry
View the Source James Gregory (mathematician) (Wikipedia)
Includes: James Gregory, Lead, field of workQuote, 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 workQuote, 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 workQuote, 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 workQuote, Includes: John Keill, Lead, field of work
Trigonometriae Planae & Sphaericae Elementa.
View the Source Nicolaus Rohlfs (Wikipedia)
Includes: Nicolaus Rohlfs, Lead, field of workQuote, 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 José Anastácio da Cunha (Wikipedia)
Includes: José Anastácio da Cunha, Lead, field of workQuote, Includes: José Anastácio da Cunha, Lead, field of work
He is best known for his work on the theory of equations, algebraic analysis, plain and spherical trigonometry, analytical geometry, and differential calculus.
View the Source Jean-François Callet (Wikipedia)
Includes: Jean-François Callet, Lead, field of workQuote, Includes: Jean-François Callet, Lead, field of work
Jean-François Callet (25 October 1744-14 November 1798) was a French professor of mathematics who wrote an influential compilation of logarithmic tables and taught spherical trigonometry and navigation.
View the Source Nicolas Fuss (Wikipedia)
Includes: Nicolas Fuss, Lead, field of workQuote, Includes: Nicolas Fuss, Lead, field of work
He contributed to spherical trigonometry, differential equations, the optics of microscopes and telescopes, differential geometry, and actuarial science.
View the Source George Darley (Wikipedia)
Includes: George Darley, Works, mathematical textsQuote, Includes: George Darley, Works, mathematical texts
A System of Popular Trigonometry (John Taylor, London, 1827).
View the Source Olinthus Gregory (Wikipedia)
Includes: Olinthus Gregory, Works, mathematical textsQuote, Includes: Olinthus Gregory, Works, mathematical texts
Elements of plane and spherical trigonometry etc.
View the Source Wang Zhenyi (astronomer) (Wikipedia)
Includes: Wang Zhenyi (astronomer), Works, mathematical textsQuote, Includes: Wang Zhenyi (astronomer), Works, mathematical texts
Her paper The Explanation of the Pythagorean Theorem and Trigonometry focuses on foundational geometric principles
View the Source Karl Mollweide (Wikipedia)
Includes: Karl Mollweide, Article, field of workQuote, Includes: Karl Mollweide, Article, field of work
In trigonometry, he rediscovered the formula now known as Mollweide
View the Source David Friesenhausen (Wikipedia)
Includes: David Friesenhausen, Source text, trigonometryQuote, Includes: David Friesenhausen, Source text, trigonometry
Kelil Heshbon a Hebrew language manual on algebra and trigonometry
View the Source MacTutor History of Mathematics, University of St Andrews: William Hopkins (biography)
MacTutor History of Mathematics, University of St AndrewsIncludes: William Hopkins, Biography, his textbookQuote, Includes: William Hopkins, Biography, his textbook
a two volume text Elements of Trigonometry written in 1833 and 1847
View the Source MacTutor History of Mathematics, University of St Andrews: Louis Puissant (biography)
MacTutor History of Mathematics, University of St AndrewsIncludes: Louis Puissant, Biography, writingsQuote, Includes: Louis Puissant, Biography, writings
Puissant wrote on geodesy, the shape of the earth and spherical trigonometry.
View the Source Al-Battani (Wikipedia)
Includes: Al-Battani, Lead, trigonometryQuote, Includes: Al-Battani, Lead, trigonometry
Using trigonometry, he created an equation for finding the qibla
View the Source Johann Georg von Soldner (Wikipedia)
Includes: Johann Georg von Soldner, Article text, MunichQuote, Includes: Johann Georg von Soldner, Article text, Munich
to work on trigonometry for the newly formed Tax Survey Commission
View the Source Petrus Apianus (Wikipedia)
Includes: Petrus Apianus, WorksQuote, Includes: Petrus Apianus, Works
On trigonometry, contains sine tables.
View the Source Jean-Louis Calandrini (Wikipedia)
Includes: Jean-Louis Calandrini, Body, workQuote, Includes: Jean-Louis Calandrini, Body, work
an important but unpublished work on flat and spherical trigonometry
View the Source Antonio Cagnoli (Wikipedia)
Includes: Antonio Cagnoli, WorksQuote, Includes: Antonio Cagnoli, Works
Trigonometria Piana e Sferica (Plane and Spherical Trigonometry)
View the Source Barnaba Oriani (Wikipedia)
Includes: Barnaba Oriani, AstronomyQuote, Includes: Barnaba Oriani, Astronomy
he published a series of memoirs on spherical trigonometry
View the Source Georg Peurbach (MacTutor)
Includes: Georg von Peuerbach, SummaryQuote, Includes: Georg von Peuerbach, Summary
published observations as well as a textbook on trigonometric calculation
View the Source Anaximander of Miletus (MacTutor)
Includes: Anaximander, Biography, closing paragraphQuote, Includes: Anaximander, Biography, closing paragraph
These are shown in [ 17 ] to be among the early Greek works that led to the modern study of trigonometry.
View the Source Haversine Formula (Wikipedia)
Includes: Haversine formula, Lead paragraphQuote, 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 paragraphQuote, 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 classificationsQuote, Includes: Angle Trisection, Subject classifications
Geometry Trigonometry
View the Source Pythagorean trigonometric identity (Wikipedia)
Includes: Pythagorean Trigonometric Identity, Lead sectionQuote, 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 sectionQuote, 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, SummaryQuote, Includes: Hipparchus, Summary
Hipparchus was a Greek mathematician who compiled an early example of trigonometric tables and gave methods for solving spherical triangles.
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