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History Of Geometry - College Essay

History Of Geometry

The history of trigonometry goes back to the earliest recorded mathematics in Egypt and Babylon. The Babylonians established the measurement of angles in degrees, minutes, and seconds. Not until the time of the Greeks, however, did any considerable amount of trigonometry exist. In the 2nd century BC the astronomer Hipparchus compiled a trigonometric table for solving triangles. Starting with 71° and going up to 180° by steps of 71°, the table gave for each angle the length of the chord subtending that angle in a circle of a fixed radius r. Such a table is equivalent to a sine table. The value that Hipparchus used for r is not certain, but 300 years later the astronomer Ptolemy used r = 60 ...

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theorem for solving spherical triangles, as well, and for several centuries his trigonometry was the primary introduction to the subject for any astronomer. At perhaps the same time as Ptolemy, however, Indian astronomers had developed a trigonometric system based on the sine function rather than the chord function of the Greeks. This sine function, unlike the modern one, was not a ratio but simply the length of the side opposite the angle in a right triangle of fixed hypotenuse. The Indians used various values for the hypotenuse.
Late in the 8th century, Muslim astronomers inherited both the Greek and the Indian traditions, but they seem to have preferred the sine function. By the end of the 10th century they had completed the sine and the five other functions and had discovered and proved several basic theorems of trigonometry for both plane and spherical triangles. Several mathematicians suggested using r = 1 instead of r = 60; this exactly produces the modern values of the ...

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Added: 6/22/2011 10:41:31 AM
Submitted By: setan
Category: Education
Type: Premium Paper
Words: 752
Pages: 3

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