PAGES

**3**

WORDS

**656**

"Has been a lifesaver so many times!"

- Catherine Rampell, student @ University of Washington

"Exactly the help I needed."

- Jennifer Hawes, student @ San Jose State

"The best place for brainstorming ideas."

- Michael Majchrowicz, student @ University of Kentucky

Claudius Ptolemaeus, also known as Ptolemy, was a Greek/Egyptian scientist, astronomer, geographer, and mathematician during the second century. Ptolemy made many points throughout his years of studies which were used and relied upon for the next 1300 years. Although some of his theories have been proven incorrect, many others haven't and are still used today in mathematics.

Born in Egypt and living from about AD 100 to 170, Ptolemy was one of the greatest astronomers and geographers of all ancient times. Ptolemy was famous for making many astronomical, geographical, and mathematical contributions. He mainly studied mathematics during his life time to help with the geography and astronomy he was working on. Ptolemy has also written a large number of books based on his studies. Among his greatest are the Almagest, Geography, Optics, Analemma, Planisphearium, and Tetrabibles.

While living in Alexandria, Egypt for a period of his life, Ptolemy made many astronomical observations. This data was put together into a thirteen series book entitled Mathematical Composition, also referred to as the System of Mathematics. Mathematical Composition became one of the greatest books ever written during Ptolemy's time and was so well admired that it was given the term "Almagest" meaning "greatest". The Almagest stated that gravity is all forced to the center of the earth. It introduced the idea that the earth was motionless and the moon and sun rotated around it. Also, according to Ptolemy, stars didn't move in the atmosphere.

Ptolemy's major mathematical contribution was stating the motions of each planet in the solar system, in the Almagest. To find the motions of the sun, moon, Earth, and other planets, Ptolemy used geometric models to estimate their positions. The Almagest also contains a star catalog. Two of its books mathematically describe the arrangement of 1,022 stars in space. Each star was given a latitude and longitude number to find its location in space, and they were grouped in 48 different groups.

Not only did the Almagest tell the location of stars and movement of the planets, but it also introduced formulas relating the sines and cosines of triangles and the differences of their angles. A sine is the ratio of the side opposite an acute angle in a right triangle to the hypotenuse. A cosine is the ratio of the side adjacent to the acute angle to the hypotenuse. Ptolemy came up with a theorem that said if a quadrilateral is inside a sphere, then the sum of products of opposite sides is equal to the product of diagonals. The Almagest also contained information about the beginning stages of spherical trigonometry, studying triangles located on the surface of circles.

Aside from studying mathematics and astronomy to write the Almagest, Ptolemy also wrote an eight volume book called Geography. This book had stated scientific facts about geography. Ptolemy had made the first ever attempt to research it. Geography showed how the system of latitudes and longitudes worked. However, having listed over 8,000 places on earth with their latitude and longitude, Ptolemy had made some extremely inaccurate measurements.

Almost all of the mathematical, astronomical, and geographical theories Ptolemy had created, such as the motions of the earth and sun and the latitude and longitude measurements, were proved wrong around the 1400s and 1500s. Up until then, everyone had taken Ptolemy's word for what he had stated in his books. Finally, in 1543 Nicolaus Copernicus, a Polish astronomer, proved differently. Copernicus stated that the earth moved along with other planets and the sun did not move at all. He also proved that many of Ptolemy's other theories had been incorrect. His math contributions about sines, cosines and other minor things were the only theories not proven incorrect and are still used today.

Ptolemy spent his life researching mathematics, astronomy, and geography, and compiling what he knew into many famous books. He was not only a famous mathematician, but a famous person who was well respe