4574 WordsNov 25, 201219 Pages

Running Head: History of Trigonometry
History 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 term Trigonometry 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*…show more content…*

Though there is no trigonometry in the works of Euclid and Archimedes, there are theorems presented in a geometric method that are similar to particular trigonometric laws or rules. Theorems on the lengths of chords are applications of the law of sines. In addition Archimedes' theorem on broken chords is similar to rules for sines of sums and differences of angles. From the primitive landmarks of shadow tables and the Greeks’ gain and expansion of astronomical knowledge from the Babylonians, there was a gap in the improvement of trigonometry until the time of Hipparchus.
Hipparchus
The first trigonometric table was in fact compiled by Hipparchus of, who is known as an as "the father of trigonometry"(Boyer, 1991). Hipparchus was the first to put into a table the corresponding values of arc and chord for a series of angles. He did this by considering every triangle was inscribed in a circle of fixed radius. Each side of the triangle became a chord, a straight line drawn between two points on a circle. To find the parts of the triangle he needed to find the length of the chord as a function of the central angle. [pic] For Example, in the diagram triangle ACB is
inscribed in circle O. So the sides of the triangle become chord
AC, chord CB and chord AB. Hipparchus would have sought to
find the length of the chord, AC, as a function of the central
angle. He deduced a trigonometric formula for the
length of a chord sketched from one

Related

## Architecture : Architecture And Architecture

1211 Words | 5 Pagesspaces in a functional manner that is also aesthetically appealing which requires proportion, balance, and conjunction with its surroundings. This report looks at architecture and how trigonometry and mathematics have been used in developing St. Peter’s Basilica and the Pantheon through sectors and right triangle trigonometry. St. Peter’s Basilica is a late Renaissance church located in Vatican City built at the place of crucifixion of St. Peter the Emperor Constantine at request of pope St. Slyvester

## The Discovery Of The Logarithm

836 Words | 4 Pagesnumber” (University of Minnesota 2004). On the other hand, Napier had defined logarithms as a ratio of two distances in a geometric form. John Wallis in 1685, and Johann Bernoulli in 1694, recognized defining logarithms as exponents (Logarithms: Brief History and Brief Math 2010). This essay discusses the fruitful discovery of logarithms, with a great contribution of Joost Burgi, John Napier and Henry Brigs. Primarily, Joost Burgi, a Swiss mathematician published a table that related geometric and arithmetic

## Annual Islamic Symposium On The Arts And Sciences

1042 Words | 5 Pagesfigures met in the “House of Wisdom” in order to hold panel discussions and present displays on the advancements in the fields of Art and Science through the 15th century. Mathematics took center stage at the symposium with Al-Khwarizmi speaking about history of his field during the Arab empire and discussing major contributors to the field. Arabic Mathematics derived from the simple system of finger reckoning, using one 's fingers in order to do basic forms of arithmetic. After some time “Finger reckoning

## Application And Significance Of Pi

1383 Words | 6 Pagesdue to the extensive influence Pi has in mathematics, this investigation will focus specifically on Pi’s application in the fields of calculus, trigonometry, topics that fall within the standard level mathematics syllabus, but also differential geometry, a topic that is not in the standard level mathematics syllabus to broaden my knowledge of pi. History and Properties of : The concept of pi has been known to humans for centuries. Its relationship with circles meant early civilizations also had

## The History of Mathematics Essay

627 Words | 3 PagesWhat is the meaning of history? According to Merriam-Webster’s online dictionary, history is: past events that relate to a particular subject, place, organization, etc (Merriam-Webster, 2014). Math began in 30000BC and is still changing now in 2014. During each year, something new has happened. From 30000BC to 127BC there were many things happening for the beginning of math. In 30000BC, Palaeolithics in Europe and France recorded numbers on bones. Around 25000BC, there were signs of early

## The Father of Trigonometry

3474 Words | 14 Pagesconsequently 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

## The Renaissance Was A Time Of `` Rebirth `` And Changing Thoughts

1226 Words | 5 Pagesnot provide people with the encouragement to learn something new. The middle age was very focused on pleasing god. The renaissance re-introduced people’s passion for learning others topics then god. People believed that studying the subjects like history, literature and philosophy would help to understand the problems of humanity. The renaissance was very different from the middle ages because there were a lot of important people making important discoveries and producing a lot of very famous artwork

## Leonhard Euler Essay

672 Words | 3 PagesLeonhard Euler Euler made large bounds in modern analytic geometry and trigonometry. He made decisive and formative contributions to geometry, calculus and number theory. Born: 15 April 1707 in Basel, Switzerland Died: 18 Sept 1783 in St Petersburg, Russia Introduction Euler's father wanted his son to follow him into the church and sent him to the University of Basel to prepare for the ministry. However geometry soon became his favourite subject. Euler obtained his father's consent

## Animation is motion a round us, the movement of object, animals and human in sequence. Usually, the

500 Words | 2 Pagesthat are supposed to be considered like timing, anticipation, etc. believe in making a better animation involves a factor various mathematics. Here I will talk about trigonometry and how it is involved in animation. An ancient Greek astronomer and mathematician called Hipparchus. Hipparchus was the first to introduced trigonometry as part of a major branch of geometry in about 140BC. It was mainly used for solving spherical triangle and cords of triangle in ancient astrology, discovering the equinoxes

## Pi And The Real World

995 Words | 4 PagesAbstract Pi has a rich history and numerous applications to go along with it. Pi is used in mathematics, science and engineering. Pi has been traced back to over 1600 BC in Egypt, and today it is celebrated world – wide. Students from elementary school through college know of pi and its multiple applications. It has been used in physics, as well as in geometry. Students will even use it in trigonometry when they are doing sine waves. Students need to see how necessary pi is in mathematics and

### Architecture : Architecture And Architecture

1211 Words | 5 Pages### The Discovery Of The Logarithm

836 Words | 4 Pages### Annual Islamic Symposium On The Arts And Sciences

1042 Words | 5 Pages### Application And Significance Of Pi

1383 Words | 6 Pages### The History of Mathematics Essay

627 Words | 3 Pages### The Father of Trigonometry

3474 Words | 14 Pages### The Renaissance Was A Time Of `` Rebirth `` And Changing Thoughts

1226 Words | 5 Pages### Leonhard Euler Essay

672 Words | 3 Pages### Animation is motion a round us, the movement of object, animals and human in sequence. Usually, the

500 Words | 2 Pages### Pi And The Real World

995 Words | 4 Pages

- Precalculus: Mathematics for Calculus (Standalone Book)
- Calculus (MindTap Course List)
- Finite Mathematics and Applied Calculus (MindTap Course List)
- Applied Calculus
- Nutrition Through The Life Cycle
- Calculus of a Single Variable
- Single Variable Calculus
- General Chemistry - Standalone book (MindTap Course List)
- Applied Calculus
- Physical Chemistry
- Single Variable Calculus: Early Transcendentals, Volume I
- Single Variable Calculus: Early Transcendentals
- Single Variable Calculus: Early Transcendentals, Volume I
- Calculus: An Applied Approach (MindTap Course List)
- International Edition---engineering Mechanics: Statics, 4th Edition