4574 Words19 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

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

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

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