Saturday, November 25, 2017

Important Figures

Claudius Ptolemy 85-165 AD

Not much is known for sure about Ptolemy. It is believed that he lived in Alexandria, Egypt, but his first name suggests Greco-Roman heritage, meaning his family probably earned Roman citizenship from a ruler at some point. Ptolemy’s contributions to astronomy date from 127-141 AD. There is strong evidence that he trained under Theon of Smyrna, an observer and mathematician whose work in astronomy dealt with conjunctions, eclipses, occultations, and transits. Today as we examine works of Theon we realize he was most likely not a very effective mentor, as many of his hypotheses are inaccurate and he did not seem to have a firm grasp on many astronomical ideas. Fortunately for Ptolemy, the city of Alexandria prided itself on its academics and had many distinguished resources available, for example at its libraries. Many of Ptolemy’s early works are also dedicated to an individual called Syrus who was probably another mentor of Ptolemy, but no record remains of him.

Ptolemy is best known for writing The Almagest, a complete textbook in mathematical astronomy that was translated into at least four different languages and used as a standard guide in the field for about 1400 years.

Written around 150 AD, The Almagest is broken up into 13 chapters and documents Ptolemy’s most revolutionary work, such as his geocentric (with the Earth in the middle) model of the solar system and diagrams to explain planetary motion. Ptolemy begins The Almagest by explaining the mathematics of his observations and theories. Ptolemy then explains the procedures for his astronomical observations and how to work out his mathematical models of the sun, moon, and planets. It is characteristic of the book to teach the reader to perform its observations for themselves. The book includes tables and star charts demonstrating Ptolemy’s data and suggests alternate methods of finding it and ways to improve technique. The Almagest has also helped preserved mathematics done by Hipparchus, as much of Ptolemy’s work in it takes influences Hipparchus’s work in trigonometry.


A page of the Almagest demonstrating
spherical geometry.














An image representing Ptolomey's model of planetary 
retrograde motion. In it, planets are thought to follow 
smaller orbits within their orbit around Earth.




Aristotle 384-322 BC

Born in 384 BC in Stagira, Chalcidice, Aristotle was the son of the aristocratic medical doctor Nichomachus, who is known for having attended to king Amyntas of Macedonia. Aristotle and Amnytas’s son Philip were childhood friends. Traditionally in ancient Greece, medicine was a family profession, so originally Aristotle had begun to be trained as a doctor. By the time he was ten years old, both Aristotle’s parents had passed and had to be raised by his uncle (or possible family friend) Proxenus. Proxenus taught Aristotle Greek, rhetoric, and poetry which helped him complete his medical training. When he was 17 he was taught by Plato at his academy. Plato was a prominent influence to Aristotle. Aristotle was a close follower of Plato and worked at the academy for about 20 years. In 355 BC, after the death of Plato and his failure to take over the academy, Aristotle founded his own academy in Athens called the Lyceum where he did most of his studies that are still very influential to Western thought today. He studied medicine, physics, philosophy, psychology, logic, biology, zoology and many other subjects as well.

How Aristotle developed his spherical Earth hypothesis.

Aristotle was among the first astronomers to propose the idea of a spherical Earth. His hypothesis came from a few different observations. For one, he knew the moon is illuminated by light from the sun and that moon phases are caused by shadows the Earth casts on it. He noted these shadows were curved and realized only spherical objects can cast circular shadows. Second, Aristotle observed the stars as he traveled north to south and noticed they changed. Different constellations are visible on different parts of the planet. He also noticed certain areas were home to similar species of animals, so hypothesized that they could not be that far apart. For example, Morocco and India both had elephants so they must be in similar locations.


Pythagoras 560-480 BC


Often considered the first pure mathematician, Pythagoras led a secretive life as the head of a strict, half religious, half scientific society called the mathematikoi. Much of what we know about him is from external biographies written by authors that often portray him to have god-like powers. Pythagoras was born on the island of Samos and spent much of his childhood traveling with his father, Mnesarchus, who was a merchant. He was taught by Thales and his pupil Anaximander primarily in Egypt. Pythagoras went on to found his own religious/philosophical school in Croton where he assembled the mathematikoi. The mathematikoi were not mathematicians in the modern sense that worked out problems and formulas with numbers, but rather thought of numbers and equations as notions, like the concept of a geometric shape or the abstract idea of a proof.


While Pythagoras is most commonly associated with the Pythagorean Theorem today, Pythagoras only may have been the first to prove the equation; the Babylonians had known about it for about 1000 years before him, but in this Pythagoras began a tradition of mathematical proof. In astronomy, Pythagoras made some relatively accurate observations, however his reasoning tends to be philosophical. Pythagoras was the first intellectual to claim the Earth and planets were spherical, his reasoning being that all in the heavens is perfect and the sphere is the most perfect shape. The Pythagoreans were also some of the first to propose a type of non-geocentric universe, as they believed Earth orbited a sort of “central fire” in the universe, as the fire was the most important thing in the universe over us and must dwell in the most important position of the universe - the center. They realized this motion of the sphere orbiting the central fire was what caused night and day. Pythagoras also was the first to observe that the morning star and the evening star are both the same planet: Venus.



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