The World of Trigonometry

The World of τριγωνομετρία

τριγωνομετρία (Greek)

τριγωνομετρία = trigonometria = trigonometry τριγώνου = Trigó̱nou = trigonon = triangle μέτρηση = métri̱si̱ = metria = measurement Hence, trigonometry = triangle measurement

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….

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

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

Greece 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.

Proof of Law of Cosines using Ptolemy’s Theorem

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 (4th-5th 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.

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 (10th C.E.), Persian Mathematician and Astronomer’s work had Muslim Mathematicians using all six trigonometric functions.

China Contributions in Spherical Trigonometry

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.

Europe In the 17th century, Isaac Newton and James Stirling developed the general Newton–Stirling interpolation formula for trigonometric functions.

Sir Isaac Newton (1642 – 1747) English physicist, mathematician, astronomer, alchemist and theologian

James Stirling (1692 - 1770) Scottish mathematician

The World of Trigonometry

TODAY The World of Trigonometry Watch out for the Triangles!

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 12th, 2012 from http://en.wikipedia.org/wiki/History_of_trigonometry Behera, A (2008). “The World of Trigonometry” Retrieved on from March 8th, 2012 from http://www.youtube.com/watch?v=Ah9NxAGzlDc&feature=related