Hipparchus, Menelaus, Ptolemy and Greek Trigonometry Essay

Hipparchus, Menelaus, Ptolemy and Greek Trigonometry Essay

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Hipparchus of Nicaea (c. 190 – c. 120 B.C.) was a Greek astronomer, geographer, and mathematician of the Hellenistic period. Many credit him as the founder of trigonometry. Hipparchus was born in Nicaea, Bithynia (now Iznik, Turkey) and most likely died on the island of Rhodes. He flourished during 162 to 127 B.C. as a working astronomer and is considered by many to be the greatest ancient astronomical observer and, by some, the greatest overall astronomer of antiquity. Utilizing the observations and mathematical techniques accumulated over the centuries by the Babylonians and other Mesopotamians, he was the first person whose quantitative and accurate models for the motion of the Sun and Moon still survive to this day. He developed trigonometry, constructed trigonometric tables, and solved several problems of spherical trigonometry. He may have been the first to develop a reliable method to predict solar eclipses, compiled the first comprehensive star catalog of the western world, and possibly invented the astrolabe and armillary sphere. He is most famous for his incidental discovery and measurement of Earth’s procession (Wikipedia). It is also believed that Hipparchus introduced Greece to the concept of the division of a circle into 360 degrees and Theon of Alexandria credits Hipparchus with a twelve-book treatise on chords. However, this work has been lost to history. It is believed Ptolemy’s famous table of chords was based on a Hipparchus’ treatise (History of Mathematics 175-177).

Menelaus
Menelaus of Alexandris (c. 70 – 140 A.D) was a Greek mathematician and astronomer. Little is known of Menelaus’s life. After spending his youth in Alexandria, he most likely moved to Rome. Both Pappus of Alexandria and Proc...


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...own. The function sin x is equivalent to ½ (chord 2x) and cos x is equivalent to ½ chord(180 – 2x). The Almagest also contains trigonometric theorems equivalent to the present day law of sines and compound-angle and half-angle identities. Hipparchus probably knew of these and even possible invented them (The Beginning of Trigonometry).


























References
An Introduction to the History of Mathematics. 6th ed. Pacific Grove: Brooks/Cole, 1990. Print
Hipparchus. (n.d.). Retrieved from http://en.wikipedia.org/wiki/Hipparchus
Hunt, J. (n.d.). The Beginnings of Trigonometry. Retrieved from http://www.math.rutgers.edu/~cherlin/History/Papers2000/hunt.html
Menelaus of Alexandria. (n.d.). Retrieved from http://en.wikipedia.org/wiki/Menelaus_of_Alexandria
Ptolemy. (n.d.). Retrieved from http://en.wikipedia.org/wiki/Ptolemy

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