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A Brief History of Trigonometry

A painting of the famous greek geometrist, and "father of measurement", Euclid. In the times of the greeks, trigonometry and geometry were important mathematical principles used in building, agriculture and education.

The Babylonians could measure angles, and are believed to have invented the division of the cirle into 360º.[1] However, it was the Greeks who are seen as the original pioneers of trigonometry. A Greek mathematician, Euclid, who lived around 300 BC was an important figure in geometry and trigonometry. He is most renowned for Euclid's Elements, a very careful study in proving more complex geometric properties from simpler principles. Although there is some doubt about the originality of the concepts contained within Elements, there is no doubt that his works have been hugely influential in how we think about proofs and geometry today; indeed, it has been said that the Elements have "exercised an influence upon the human mind greater than that of any other work except the Bible.<Complete Dictionary of Scientific Biography, 2008>

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[edit]First Tables of Sines or Cosines

Hiparchus
In the second century BC a Greek mathematician, Hipparchus, is thought to have been the first person to produce a table for solving a triangle's lengths and angles.[2] -------------------------------------------------

[edit]The Pythagorean Theorem

Pythagoras, depicted on a 3rd-century coin
In a right triangle: The square of the hypotenuse is equal to the sum of the squares of the other two sides. The Pythagorean theorem is named after the Greek mathematician Pythagoras, who by tradition is credited with its discovery and proof,[1][2] although it is often argued that knowledge of the theorem predates him. There is much evidence that Babylonian mathematicians understood the formula.[3]...

...Running Head: History of TrigonometryHistory of Trigonometry
Rome Fiedler
History of Mathematics 501
University of Akron
April 29, 2012
History of Trigonometry: An Introduction
Trigonometry is useful in our world. By exploring where these concepts come from provides an understanding in putting this mathematics to use. The termTrigonometry comes from the Greek word trigon, meaning triangle and the Greek word meatria meaning measurement. However it is not native to Greek in origin. The mathematics comes from multiple people over a span of thousands of years and has touched over every major civilization. It is a combination of geometry, and astronomy and has many practical applications over history.
Trigonometry is a branch of math first created by 2nd century BC by the Greek mathematician Hipparchus. The history of trigonometry and of trigonometric functions sticks to the general lines of the history of math.
Early research of triangles could be found in the 2nd millennium BC, in Egyptian and Babylonian math. Methodical research of trigonometric functions started in Greek math, and it reached India as part of Greek astronomy. In Indian astronomy, the research of trigonometric functions flourished in the Gupta dynasty,...

...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 chords and inscribed angles in circles, and proved theorems that are equivalent to modern trigonometric formulae, although they presented them geometrically rather than algebraically. Claudius Ptolemy expanded 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 century Indian 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 mathematician Regiomontanus. Trigonometry was still so little...

...The History of Trigonometry is one type of mathematics that deals with the sides and the angles. In the First paragraph I would like to explain the main history of trigonometry and also go into detail about the certain aspects of the mathematic branch. In the Second paragraph I will explain details on 4 of the great trigonometry mathematicians who discovered information about trigonometry, as well as improved existing theories as well. In the Third paragraph I would like to explain how these theories and techniques are applied today by various corporate companies. The improvement of trigonometry is still improving today, and all of the details talked about have either been elaborated or been used for extraordinary purposes.
Paragraph 1, In the beginning trigonometry started of in these job branches Navigation, surveying, and astronomy. In all of these job aspects, proper distance between things needed to be determined. Such as the distance between the earth and the moon, or for distances that can be measured directly, or the distance from one continent to another. In all of this trigonometry was applied. Today most trigonometry is still applied in the same places , only with chemistry, physics, and at least all branches of engineering.
Paragraph 2, some of the greatest mathematicians are quoted for there superior workings in...

...Shawnje Granville
Benjamin Banneker Academy
January 17,2013
Trigonometry
TRIGANOMETRY
The history of algebra goes way back in time (more than 4000 years . Algebra is a sub within mathematics, but for historical reasons, the word "algebra" has three meanings that can all suffice in defining the word or term . Algebra can mean use of letters and symbols to represent values and their relations, especially for solving equations,major branch of mathematics which studies relations and operations or mathematical structure as a "linear" ring, is also called "algebra," or sometimes .algebra is one of main branches of pure mathematics, together with geometry, analysis, topology,statistics and number theory.
Algebra s often taught from anywhere between secondary school to the 12th grade . But does anyone ever stop to wonder were it originated ? Historians trace the roots of algebra back to ancient Babylon society , they developed the first arithmetic mathematical system .It is believed that priests used mathematics and algebra along side their religious rituals. in the 1st millennium BC, mathematicians usually solved such equations by geometric methods, such as those described in the Rhind Mathematical Papyrus, Euclid's Elements, and The Nine Chapters on the Mathematical Art. Much of our knowledge of ancient Egyptian mathematics, including algebra, is based on the Rhind papyrus. This was written about 1650 B.C. The Greek...

...Paper - I
1. Sources: Archaeological sources:Exploration, excavation, epigraphy, numismatics, monuments Literary sources: Indigenous: Primary and secondary; poetry, scientific literature, literature, literature in regional languages, religious literature. Foreign accounts: Greek, Chinese and Arab writers.
2. Pre-history and Proto-history: Geographical factors; hunting and gathering (paleolithic and mesolithic); Beginning of agriculture (neolithic and chalcolithic).
3. Indus Valley Civilization: Origin, date, extent, characteristics, decline, survival and significance, art and architecture.
4. Megalithic Cultures: Distribution of pastoral and farming cultures outside the Indus, Development of community life, Settlements, Development of agriculture, Crafts, Pottery, and Iron industry.
5. Aryans and Vedic Period: Expansions of Aryans in India. Vedic Period: Religious and philosophic literature; Transformation from Rig Vedic period to the later Vedic period; Political, social and economical life; Significance of the Vedic Age; Evolution of Monarchy and Varna system.
6. Period of Mahajanapadas: Formation of States (Mahajanapada): Republics and monarchies; Rise of urban centres; Trade routes; Economic growth; Introduction of coinage; Spread of Jainism and Buddhism; Rise of Magadha and Nandas. Iranian and Macedonian invasions and their impact.
7. Mauryan Empire: Foundation of the Mauryan Empire, Chandragupta, Kautilya and Arthashastra; Ashoka;...

...Teaching trigonometry using Empirical Modelling
0303417
Abstract
The trigonometric functions sin(x), cos(x) and tan(x) are relationships that exist between the angles
and length of sides in a right-angled triangle. In Empirical Modelling terms, the angles in a triangle
and the length of the sides are observables, and the functions that connect them are the definitions.
These well-defined geometric relationships can be useful when teaching GCSE-level students about
the functions, as they provide a way to visualise what can be thought of as fairly abstract functions.
This paper looks at how different learning styles apply to Empirical Modelling, and presents a practical example of their use in a model to teach trigonometry.
1 Introduction
The trigonometric functions sin(x), cos(x) and tan(x)
are relationships that exist between the angles and
length of sides in a right-angled triangle. In Empirical Modelling terms, the angles in a triangle and the
length of the sides are observables, and the functions
that connect them are the definitions. These welldefined geometric relationships can be useful when
teaching GCSE-level students about the functions,
as they provide a way to visualise what can be
thought of as fairly abstract functions. Rather than
teaching students by showing them diagrams in an
instructive way (already a good way of doing it), a
constructive approach may allow students to gain a
better understanding...

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...
Today one of the most cherished ideologies of America is the fact that everyone is and should be created equal. With this cherished ideology bringing a sense of pride and diversity to America we must keep in mind that this cherished ideology did not always exist. Since 1865 various individuals and groups have not been able to receive and express their rights to full equal status in the United States. These different individuals and groups have seemingly fought for their rights in equality and have become pioneers in the fight for evolution for equality.
In 1865 African Americans in the United States under the 13th amendment were freed from the terrible burden of slavery. Through the 14th amendment they were given the right to citizenship and the right to equal protection. The 15th amendment gave them the right to vote regardless of their skin color race or any other type of servitude. These amendments were meant to be enforced and make a serious change in the everyday life of the average American.
With these amendments passing in 1865 they were meant to make a serious change towards the evolution of equality. These changes did not seem to happen right away and African Americans were still not being treated with equality. The average African American at this time were being denied there newly given rights every day making life extremely hard to stay...

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