Claudius Ptolemy

By: Ray Zimmerman

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Not much is known about Ptolemy’s life. He lived so long ago that most of the records on him have probably been lost or destroyed. Other details about his life are not accurate or verified. What we do know are the questions he raised, and the mathematical improvements he made.


Claudius Ptolemy was born in Egypt around the year AD 41, but nobody is exactly sure where. Theodore Meliteniotes claimed that Ptolemy was born in Hermiou Egypt, but this is most likely untrue. We do know that Ptolemy made astronomical observations from Alexandria Egypt. It is thought that his teacher was Theon of Smyrna. Not much else is known about Ptolemy’s early life because of the lack of records due to how long ago he lived.


Ptolemy dedicated the rest of his life to the study of astronomy and mathematics. Perhaps one of the most important of Ptolemy’s works is his book entitled, Almagest, which means, “The Mathematical Compilation.” Ptolemy writes mostly on astronomy and trigonometry. Ptolemy first talks about his description, and Aristotle’s description of the earth centered universe. This was the geothentric theory.(http://tinyurl.com/yfj4fcj)


Next Ptolemy moves on to the subject of pi. Ptolemy approximated that pi was equal to 3.14166, which is very accurate for his time period. At that time to find pi was a very complicated process. First he would start with a square. Next, he would draw another square around the first, but turned on its side so that the middle of every edge was touching the angles of the other. Then he had to find the average of the two. This process would be repeated, but next a hexagon would be used so that he would get closer to a circle. This process would be repeated, each time getting closer to a perfect circle. It was a very tedious process. Aristotle was able to get to a polygon with 96 sides, an amazing feat.



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The rest of the book goes into many of his other theories. It focuses on mainly astronomy. He talks about his theory of the sun. He explains his theory for the moon. Ptolemy also begins to write about eclipses. Ptolemy wrote about fixed stars, and how he believed that they never changed position relative to one another. Ptolemy also catalogued over 1000 stars in the night sky. (http://tinyurl.com/yfj4fcj)


Lastly Ptolemy goes into planetary theory. He explains using mathematics the very complicated movements of the planets. Ptolemy also mingled in geography. His book “Guide to Geography” contained maps of many areas. Sadly these maps were not to scale and highly inaccurate. He created Ptolemy’s Theorem, and Ptolemy’s inequality. Other of Ptolemy's accomplishments include work on solstices and equinox, and optics. Using his work on Solstices and Equinoxes, Ptolemy was able to find the length of the seasons. He also proposed a model for the sun. [[(http://tinyurl.com/yheqerz)]] Optics is the study of light and its behavior and properties. Ptolemy wrote a book on optics in which he discussed color, refraction, reflection and many other subjects. Ptolemy’s Theorem is explained below.



Ptolemy’s Theorem


"Let a convex quadrilateral ABCD be inscribed in a circle. Then the sum of the products of the two pairs of opposite sides equals the product of its two diagonals. In other words,


AD·BC + AB·CD = AC·BD


(http://tinyurl.com/yhhln6w)

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Explanation: In Ptolemy's theorem a circle must be drawn. The circle has to be almost perfect to ensure maximum accuracy. Next a convex quadrilateral is drawn inside of the circle. A convex quadrilateral means a four sided shape which goes outward. To clarify, an example of a quadrilateral that is not convex would be:

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If the previous steps were completed correctly, the following equation (Ptolemy's Theorem) will hold true.


AD·BC + AB·CD = AC·BD"

"The sum of the products of the two pairs of opposite sides equals the product of its two diagonals." Example: Say that AD=60 BC=45 AB=45, and CD=60. After plugging in these values, the equation should read 5400=AC·BD. If the other side of the equation is solved, the equation will read 5400=5400, proving Ptolemy's Theorem. The diagram of this problem is shown below:

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Ptolemy probably died around AD 150. Again the exact date or year is not known. He is best known as an Astronomer and Mathematician who raised many difficult questions. Ptolemy was constantly correcting the work of others. He proposed different theories about his understandings of astronomy. Ptolemy is remembered as an innovative thinker, problem solver, influential philosopher, and most of all as a great mathematician.

Most Interesting Fact: In 1492 when Christopher Columbus sailed to North America, and in 1519 when Magellan began to sail around the world, they both used Ptolemy's map he created, which was innacurate.