Trigonometry began during the Third Century B.C. At this time, geometry concepts were used for astronomical studies only. The word trigonometry was derived from two Greek words. Trigonometry is from the word trigonon, meaning triangle, and the word metron, meaning measure. Trigonometry studies involve the lengths of sides and angles of triangles. The early astronomers of this time period first discovered that the lengths of the sides of a right-angle triangle and the angles between those sides are correlated. Because of those relationships, if the length of at least one side and the value of one angle are known, then all other angles and lengths can be determined using a system of proportions. This branch of mathematics has had many contributions
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During his lifetime he wrote a six-book treatise on chords, however, his only surviving work is a three-book work called Sphaerica. This book contains information about the development of trigonometry and spherical trigonometry. In the first book of Sphaerica, Menelaus describes a spherical triangle by its area and the use of semicircles. He also gives the main ideas about spherical triangles corresponding to those of Euclid 's about plane triangles. The second book contains astronomical information, which was nothing new to the trigonometry branch at that moment; however, the third book dealt with trig ratios. The very first proposition of the third book is Menelaus 's theorem. This theorem referenced a spherical triangle and any transversal that cuts the sides of the triangle; it used two intersecting great circles rather than a spherical …show more content…
It did not gain great popularity until the Chinese mathematicians expressed the need of spherical trigonometry for astronomical and calendar purposes. Just like other mathematicians before him, Shen Kuo used trigonometric functions to solve problems of chords and arcs using the technique of intersecting circles in which he created a formula to approximate the answer. This then led to the expansion of his work by Guo Shoujing which used spherical trigonometry to improve the Chinese calendar system and astronomy. He was able to find the degrees of equator corresponding to degrees of ecliptic, values of chords for given ecliptic arcs, difference between chords of arcs differing by 1 degree. Even though Shen and Guo 's work in trigonometry was substantial, another large work in Chinese trigonometry would not be published until 1607 after the work of the
During his lifetime he wrote a six-book treatise on chords, however, his only surviving work is a three-book work called Sphaerica. This book contains information about the development of trigonometry and spherical trigonometry. In the first book of Sphaerica, Menelaus describes a spherical triangle by its area and the use of semicircles. He also gives the main ideas about spherical triangles corresponding to those of Euclid 's about plane triangles. The second book contains astronomical information, which was nothing new to the trigonometry branch at that moment; however, the third book dealt with trig ratios. The very first proposition of the third book is Menelaus 's theorem. This theorem referenced a spherical triangle and any transversal that cuts the sides of the triangle; it used two intersecting great circles rather than a spherical …show more content…
It did not gain great popularity until the Chinese mathematicians expressed the need of spherical trigonometry for astronomical and calendar purposes. Just like other mathematicians before him, Shen Kuo used trigonometric functions to solve problems of chords and arcs using the technique of intersecting circles in which he created a formula to approximate the answer. This then led to the expansion of his work by Guo Shoujing which used spherical trigonometry to improve the Chinese calendar system and astronomy. He was able to find the degrees of equator corresponding to degrees of ecliptic, values of chords for given ecliptic arcs, difference between chords of arcs differing by 1 degree. Even though Shen and Guo 's work in trigonometry was substantial, another large work in Chinese trigonometry would not be published until 1607 after the work of the