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The World of τριγωνομετρία

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τριγωνομετρία (Greek) τριγωνομετρία = trigonometria = trigonometry τριγώνου = Trigó ̱ nou = trigonon = triangle μέτρηση = métri ̱ si ̱ = metria = measurement Hence, trigonometry = triangle measurement

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Where did it come from ? Trigonometry was developed from the study of RIGHT TRIANGLES! by applying the relationships between measures of its sides and angles to the study of similar triangles. However, it was not the creation of just one man or nation….

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Egypt Early Egyptians built their famous pyramids using a primitive form of trigonometry!

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Greece Hipparchus, a Greek astronomer, was considered the father of trigonometry. (2nd Century B.C.E.)

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Claudius Ptolemy, another Greek scientist and philosopher, was the most influential in the development of trigonometry. His theorem written in the Almagest was similar to the present day Law of Sines. Greece Proof of Law of Cosines using Ptolemy’s Theorem

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India Influential works from the 4th–5th century, known as the Siddhantas (5 compilations) first defined the sine as the modern relationship between half an angle and half a chord, while also defining the cosine, and inverse sine. ARYABHATA (4 th -5 th C.E.) Indian mathematician and astronomer, Aryabhatta, collected and expanded upon the developments of the Siddhantas in an important work called the “Aryabhatiya”. The Siddhantas and the Aryabhatiya contain the earliest surviving tables of sine values and versine (1 − cosine) values, to an accuracy of 4 decimal places.

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Persia and Arabia The Indian works were later translated and expanded in the medieval Islamic world by Muslim mathematicians of mostly Persian and Arab descent. Abū al-Wafā' al-Būzjānī (10 th C.E.), Persian Mathematician and Astronomer’s work had Muslim Mathematicians using all six trigonometric functions.

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China Shen Kuo or Shen Gua (1031–1095 C.E.) mathematician, astronomer, meteorologis, geologist, zoologist, botanist, pharmacologist and more… Guo Shoujing ( 1231–1316 C.E.) Chinese astronomer, engineer, and mathematician. Contributions in Spherical Trigonometry

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Europe In the 17th century, Isaac Newton and James Stirling developed the general Newton–Stirling interpolation formula for trigonometric functions. James Stirling (1692 - 1770) Scottish mathematician Sir Isaac Newton (1642 – 1747) English physicist, mathematician, astronomer, alchemist and theologian

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The World of Trigonometry TODAY The World of Trigonometry Watch out for the Triangles!

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Resources Adamek T., Penkalski K., Valentine G. (2005). ”The History of Trigonometry”. Retrieved on March 10th, 2012, from http://www.math.rutgers.edu/~mjraman/History_Of_Trig.pdf Anonymous (n.d.), “History of Trigonometry”. Retrieved on March 12 th, 2012 from http://en.wikipedia.org/wiki/History_of_trigonometry http://en.wikipedia.org/wiki/History_of_trigonometry Behera, A (2008). “The World of Trigonometry” Retrieved on from March 8 th, 2012 from http://www.youtube.com/watch?v=Ah9NxAGzlDc&feature=related

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Lesson 13.1: Trigonometry.

Lesson 13.1: Trigonometry.

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