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.
Mathematics and astronomy are very closely related. It is the mathematical procedures which help define time and space. However, Greek culture plays a role too. With a Greek mindset one would be restricted to believing that the universe is composed of perfect circles. This idea is rooted in Plato and Aristotle’s work. Plato believed that the celestial bodies were godly because their motion was consistent, whereas the Earth is always changing. Plato believed that the Earth was at the centre of the universe and all the celestial bodies orbited around it on perfect uniform circular paths. He chose a circular path because circles have no corners or edges. They are continuous like the motion of the planets (Cassidy, 9).
Similarly, Aristotle believed that the circle was a symbol of continuity. He applied this idea of continuity to the notion of time, which has no beginning or end. (Aristotle, IV) He also said that the circle is “the perfect, first, most beautiful form.” (Wikipedia, Perfection)
Ptolemy lived from approximately 90 A.D. to 168 A.D (Wikipedia, Ptolemy) and grew up in Alexandria, Egypt. Throughout his life time he studied astronomy and worked a great deal on astrology, g...
... middle of paper ...
...co.uk/ptolemy.html
Lahanas, M.Astronomy of ptolemy. Retrieved March 1, 2011, from http://www.mlahanas.de/Greeks/PtolemyAstronomy.htm
Professor Craig Fraser. (February 14, 2011). HPS390 class
Retrograde motion. (2010). Retrieved March 1, 2011, from http://www.lasalle.edu/~smithsc/Astronomy/retrograd.html
Swerdlow, N., & Neugebaur, O. (1984). Mathematical astronomy in copernicus's de revolutionibus. New York: Springer-Verlag.
Wikipedia. (2011). Almagest. Retrieved March 1, 2011, from http://en.wikipedia.org/wiki/Almagest
Wikipedia. (2011). Inferior and superior planets. Retrieved March 1, 2011, from http://en.wikipedia.org/wiki/Inferior_and_superior_planets
Wikipedia. (2011). Perfection. Retrieved March 1, 2011, from http://en.wikipedia.org/wiki/Perfection
Wikipedia. (2011). Ptolemy. Retrieved March 1, 2011, from http://en.wikipedia.org/wiki/Ptolemy
In his book, Repcheck recounts how a Catholic Church cleric invented a highly complicated theory of the heavens’ architecture. Copernicus made a breakthrough by solving a significant astronomical problem. Everybody except the astronomers had earlier accepted Aristotle’s concept that heavenly objects revolved around the earth in perfectly circular orbits. The astronomers were opposed to this notion since their calculations could not work according to it. Repcheck introduces Ptolemy who described a cosmos in which the earth positioned itself somewhat off-center and other heavenly bodies revolved in one circular orbit inside a second ideal circle at changeable speeds. Even though Ptolemy’s model was rather complicated, astronomers found it to be reasonable in their calculations. Astronomers were still using this new concept even 1500 years later. In this regard, the author starts to bring Copernicus into the picture.
The surest foundation for the origin of science in its practical form is to be found in the ìco–rdination and standardization of the knowledge of common sense and of industry.î[1] One of the first occurrences of this co–rdination can be traced back to 2500 BCE in the form of edicts from the ancient Babylonian rulers, who issued royal standards of length, weight and capacity. Non-Semitic Sumerians also laid down the elements of mathematics and geometry at that time, making use of fractions, decimals, circles and radial angles. But knowledge as we know it today was tightly woven with magical notions, and as both spread westward they instilled in European thought a reverence for ìspecial numbers, their connections to the gods and the application of geometrical diagrams to the prediction of the future.î[2] As well, the ancient Babylonians were fascinated by the heavens. They were the first to make a map of the stars and associate them with animals like the Ram, Crab and Scorpion, names that we still use to this day. They also realized the periodicity and reliability of astronomical movement and phenomena, and were soon able to predict many of them. Tablets have been found dating to the sixth century BCE that predicted the relative positions of the sun and moon, as well as forecasted the occurrences of eclipses.[3] Out of all this knowledge the Babylonians built up a fantastic system of astrology, through which the starsówhich were thought to fix and foretell the course of human affairsówould give up their secrets.
He used mathematics and observations to develop his understanding of the universe. This was key, because it showed how science could explain things instead of the church. As stated in (Document C) Ptolemy was a Roman astronomer who lived in Alexandria, Egypt, shortly after the time of Jesus. He developed a theory of the universe that was adapted by most scholars during the Middle Ages. Catholicism was the main view point of the way the world worked. Also that many different people had their own theories of the universe and the way the world
Clarke, Leonard W.‘Greek Astronomy and Its Debt to the Babylonians' The British Journal for the History of Science, Vol. 1, No. (Cambridge University Press. 1962)
Galilei, Galileo, and Stillman Drake. Discoveries and Opinions of Galileo: Including the Starry Messenger (1610), Letter to the Grand Duchess Christina (1615), and Excerpts from Letters on Sunspots (1613), the Assayer (1623). New York: Anchor, 1990. Web
One of the most well known contributors to math from Greece would be Archimedes. He
Copernicus’s theory showed the earth and other planets revolving around the sun in a circular motion. At the same time, the moon is rotating around the earth as well. Like Ptolemy, Copernicus believed that the stars occupied the region farthest from the sun. Copernicus, however, never stated whether or not these stars were in a fixed sphere around the universe or if they were scattered throughout space. Unlike Ptolemy’s motionless earth, Copernicus said the earth rotates around itself daily, causing night and ...
Plato was born in Athens, Greece around 427 B.C. He was always interested in politics, until he witnessed his mentor and teacher, Socrates, death. After learning of the callousness of politics, Plato changed his mind and eventually opened up The Academy, which is considered if not the first, one of the first Universities. Students at the Academy studied many different fields of science, including biological and astronomical. The students also studied many other fields, such as math. Plato developed many views that were mathematical in nature. He expressed these views through his writings. According to Dr. Calkins of Andrew University, "Timaeus is probably the most renowned of Plato's thirty-five dialogues. [In it] Plato expresses that he believes that the heavenly bodies are arranged in perfect geometric form. He said that because the heavens are perfect, the various heavenly bodies move in exact circles." (Calkins 1). Of course that is a much summarized view of what Plato discusses in Timaeus, but still a solid view on Plato's beliefs about cosmology. Cosmology can be loosely defined as everything being explained and in its place or beautiful. The cosmos is beautiful because everything is perfect. Plato understood that when he defined the most perfect geometric design as the circle. In a circle one line is always equidistance from one point. In Plato's universe there are two realms, eternity and time. The factor that creates "time" out of the chaos of "eternity" is the Demiurge. Plato's Demiurge can be defined as an architect creator theological entity. The importance of the Demiurge in this paper is to compare and contrast him with Boethius's God in The Consolation of Philosophy.
While there he studied theology, philosophy, mathematics, and astronomy. After his intellectual abilities became well known he was offered a professorship in Graz, Styria. One of his responsibilities was to make astrological predictions, and after his predictions of a cold winter and the Turks invading came true he was promoted. One day, while teaching a class, he observed that his drawing of circles and triangles could explain the solar system. He strongly believed in the Copernican system and with much examining he found that the solar system was three dimensional, not two dimensional.
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.
The concept of impossible constructions in mathematics draws in a unique interest by Mathematicians wanting to find answers that none have found before them. For the Greeks, some impossible constructions weren’t actually proven at the time to be impossible, but merely so far unachieved. For them, there was excitement in the idea that they might be the first one to do so, excitement that lay in discovery. There are a few impossible constructions in Greek mathematics that will be examined in this chapter. They all share the same criteria for constructability: that they are to be made using solely a compass and straightedge, and were referred to as the three “classical problems of antiquity”. The requirements of using only a compass and straightedge were believed to have originated from Plato himself. 1
Geometry, a cornerstone in modern civilization, also had its beginnings in Ancient Greece. Euclid, a mathematician, formed many geometric proofs and theories [Document 5]. He also came to one of the most significant discoveries of math, Pi. This number showed the ratio between the diameter and circumference of a circle.
Aristarchus lived from about the year 310 B.C. to about 230 B.C. Aristarchus was the first Greek philosopher and mathematician to make sense of the solar system. Others before him thought that the Earth is a sphere and that it moves, but he was the first to understand the heliocentric theory, which states that the sun is in the middle. In 288 or 287 B.C. he followed Theophrastus as the head of the Peripatetic School established by Aristotle.
Astronomy is a very important field in science. Ancient Greece, China, and India all contributed to our everyday ideas and uses of astronomy. Ancient Greece was the most influential because the Indian’s based most of their astronomy off of Greece. The Greeks created calendars that were based off of the eclipse cycle, which they called by two different names, Hellenic Calendars and Lunisolar Calendars. Because of Ancient Greece, we now have calendars to keep us on track every day. The Greeks observed a celestial object passing through the eastern and western morning sky. After a long time of observations, they came to a realization that it was a planet and now that is the planet is well known as Venus. (Sarton, 75) Plato and Aristotle’s theories were incredible contributions on us today. Both of their theories were all about the behavior and life of the planets, such as their theory that the earth is spherical. (Sarton, 421). Ancient Greece als...
Physics began when man first started to study his surroundings. Early applications of physics include the invention of the wheel and of primitive weapons. The people who built Stone Henge had knowledge of physical mechanics in order to move the rocks and place them on top of each other. It was not until during the period of Greek culture that the first systematic treatment of physics started with the use of mechanics. Thales is often said to have been the first scientist, and the first Greek philosopher. He was an astronomer, merchant and mathematician, and after visiting Egypt he is said to have originated the science of deductive geometry. He also discovered theorems of elementary geometry and is said to have correctly predicted an eclipse of the sun. Many of his studies were in astronomy but he also observed static electricity. Phythogoras was a Greek philosopher. He discovered simple numerical ratios relating the musical tones of major consonances, to the length of the strings used in sounding them. The Pythagorean theorem was named after him, although this fundamental statements of deductive geometry was most likely first an idea from Egyptian methods of measurements. With the help of his followers he discovered that the earth was a sphere, but he did not believe it revolved around the sun.