Hipparchus, Menelaus, Ptolemy and Greek Trigonometry Essay

Hipparchus, Menelaus, Ptolemy and Greek Trigonometry Essay

Length: 1139 words (3.3 double-spaced pages)

Rating: Strong Essays

Open Document

Essay Preview

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 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...

... middle of paper ...

...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).

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

Need Writing Help?

Get feedback on grammar, clarity, concision and logic instantly.

Check your paper »

Trigonometry: The Hipparchus Catalogue Essay

- ... Hipparchus catalogue was completed in about 129 BC, it had listed about 850 stars. He had spent most of his life in Rhodes in the observatories. Hipparchus was a powerful influence on Claudius Ptolemy who centuries later his works had considerable impact on the development of Western culture. Hipparchus was also one of the most influential astronomers of antiquity, yet very little information available about him still survives. Hipparchus did his studying in Alexandria in 146 BC and in Rhodes near the end of his career in 127 BC and 126 BC....   [tags: motion of the sun and moon]

Free Essays
571 words (1.6 pages)

Essay on Ptolemy’s Astronomy

- Greek mathematics began during the 6th century B.C.E. However, we do not know much about why people did mathematics during that time. There are no records of mathematicians’ thoughts about their work, their goals, or their methods (Hodgkin, 40). Regardless of the motivation for pursuing mathematical astronomy, we see some impressive mathematical books written by Hippocrates, Plato, Eudoxus, Euclid, Archimedes, Apollonius, Hipparchus, Heron and Ptolemy. I will argue that Ptolemy was the most integral part of the history of Greek astronomy....   [tags: Greek Mathematics, Culture]

Strong Essays
1010 words (2.9 pages)

Trigonometric Functions Essays

- Introduction to prepare for uses of trigonometric functions: The general trigonometric functions are sin, cos, tan functions only. The students uses trigonometric functions in problems to find the distance, length of the shadow, poles, height of the building, angles between the slopes, etc. The trigonometric functions are kept in the student’s curriculum in order to prepare them for a well defined practical application or experience of the problems that are used in applying in there day to day life....   [tags: Trigonometry]

Strong Essays
580 words (1.7 pages)

Ptolemy of Alexandria, the Influential Astronomer Essays

- Ptolemy of Alexandria, the Influential Astronomer Ptolemy of Alexandria was the most influential astronomer of the ancient world. The books and theories Ptolemy developed served as a major basis for future astronomers. It was during the Renaissance period that his work became thoroughly studied and revised. Ptolemy collected all ancient knowledge of astronomy and geography including it in his book Almagest around 140 A.D. It follows, he then wrote a four volume astrological study known as the Tretrabiblos....   [tags: Biography Biographies Essays]

Strong Essays
520 words (1.5 pages)

A Brief History of Clocks: From Thales to Ptolemy Essay

- A Brief History of Clocks: From Thales to Ptolemy The clock is one of the most influential discoveries in the history of western science. The division of time into regular, predictable units is fundamental to the operation of society. Even in ancient times, humanity recognized the necessity of an orderly system of chronology. Hesiod, writing in the 8th century BC., used celestial bodies to indicate agricultural cycles: "When the Pleiads, Atlas' daughters, start to rise begin your harvest; plough when they go down" ( Hesiod 71)....   [tags: Expository Essays Research Papers]

Free Essays
2924 words (8.4 pages)

Essay on Applications of Trigonometry in Music

- Trigonometry is the branch of mathematics that is based off on the study of triangles. This study help define the relations between the different angle measures of a triangle with the lengths of their sides. Even though trigonometry is the study of triangles, it is mostly used to study right angled triangles with the six functions: sine, cosine and tangent, and their reciprocals cosecant, secant, and cotangent. These functions are made by the corresponding points to the infinite number of angles that are present when continuously rotated in the unit circle....   [tags: Fourier Series, Recording Software]

Strong Essays
958 words (2.7 pages)

Essay on Greek Mythology And The Greek Society

- ... Aphrodite had children by gods and also humans. The ancient Greeks use this particular part of the myth to encapsulate their female counterparts. If the women have a man whom they belong to, then they will not be as promiscuous as the goddess of love, beauty, and pleasure. In another myth about the goddess Aphrodite, she is the daughter of Zeus and Dione. Zeus being the most supreme god that he can be, marries Aphrodite off to Hephaestus. He does this because his daughter is so beautiful he does not want the gods to fight over possessing her....   [tags: Greek mythology, Zeus, Aphrodite, Gaia]

Strong Essays
1001 words (2.9 pages)

Trigonometry in Daily Life Essay

- Introduction to Trigonometry in daily life Trigonometry is one of the branches of mathematical and geometrical reasoning that studies the triangles, particularly right triangles The scientific applications of the concepts are trigonometry in the subject math we study the surface of little daily life application. The trigonometry will relate to daily life activities. Let’s explore areas this science finds use in our daily activities and how we use to resolve the problem. Usages in daily life Trigonometry and vector in math to deal with progress through water/air currents....   [tags: Math ]

Free Essays
416 words (1.2 pages)

Essay about Greek Mythology And Greek Myths

- People wonder why the world is so obsessed with ancient Greek myths when there just stories that was told millenniums ago. Although if you looked at the number of Greek-themed books and movies today, people would see that the world is still dazzled by Greek myths even if they can’t explain why. People see something related to a Greek myth every day and they don’t even notice. These ancient myths gave us an inside look on how the Greek lived back in that time and how their minds worked. Not only did the Greeks give us things like the alphabet, the Greeks gave us interesting stories that make us think if these Greek myths were real or just fables....   [tags: Greek mythology, Zeus, Apollo, Homer]

Strong Essays
1011 words (2.9 pages)

Greek Mythology And Greek Gods Essay

- Many religions and gods were around at the time of Paul, two of which are Greek and Roman religions. Even though these were two countries with separate religions, the Roman religion came from the Greek gods. There were aspects, such as the names, that were different, but they still originated from the Greek gods. Greek gods were an important part of Greek mythology. They were around all the way back before Christ. Most of them still existed at the time of Paul. The highest Greek god was Zeus. He was the “Lord of the sky and supreme ruler of the gods”1, only after he overthrew his father, Cronus....   [tags: Zeus, Greek mythology, Hera, Apollo]

Strong Essays
1481 words (4.2 pages)