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 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, particularly as a result of Aryabhata. Throughout the Middle Ages, the research of trigonometry continued in Islamic math, while it was implemented as a discrete subject in the Latin West beginning in the Renaissance with Regiomontanus. The growth of contemporary trigonometry shifted in the western Age of Enlightenment, starting with 17th-century math and reaching its contemporary type with Leonhard Euler (1748)

Etymology

The word "trigonometry" originates from the Greek "trigonometria", implying "triangle measuring", from triangle + to measure. The name developed from the study of right triangles by applying the relation ships between the measures of its sides and angles to the study of similar triangles (Gullberg, 1996). The word was introduced by Barthoolomus ptiticus in the title of his work Trigonometria sice de solutione triangularumtractus brevis et perspicius… in 1595. The contemporary word "sine", is originated from the Latin word sinus, which implied "bay", "bosom" or "fold", translation from Arabic word jayb. The Arabic word is in origin of version of Sanskrit jīvā "chord". Sanskrit jīvā in learned used was a synonym of jyā "chord", primarily the word for "bow-string". Sanskrit jīvā was taken into Arabic as jiba (Boyer, 1991). This word was then changed into the real Arabic word jayb, implying "bosom, fold, bay", either by the Arabs or erroneously of the European translators such as Robert of Chester, who translated jayb into Latin as sinus. In particular Fibonacci's sinus rectus arcus was significant in creating the word sinus. Early Beginnings

The origin of the subject has rich diversity. Trigonometry is not the work of one particular person or place but rather a development over time. The primitive Egyptians and Babylonians had known of theorems on the ratios of the sides of analogous triangles for many centuries. However pre-Greek societies were deficient of the concept of an angle measure and as a result, the sides of triangles were analyzed rather, a field that would be better known as "trilaterometry"(Boyer, 1991). The Babylonian astronomers kept comprehensive records on the rising and setting of stars, the movement of the planets, and the solar and lunar eclipses, all of which needed knowledge with angular distances measured on the celestial sphere. Founded on one explanation of the Plimpton 322 cuneiform tablet, some have even claimed that the primitive Babylonians had a table of secants. There was, on the other hand, much discussion as to whether it is a table of Pythagorean triples, a solution of quadratic equations, or a trigonometric table. The Egyptians, in contrast, applied an ancient kind...