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Pythagoras contribution in mathematics
Pythagoras contribution in mathematics
Pythagoras contribution in mathematics
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For the Greeks philosophy wasn’t restricted to the abstract it was also their natural science. In this way their philosophers were also their scientist. Questions such as what is the nature of reality and how do we know what is real are two of the fundamental questions they sought to answer. Pythagoras and Plato were two of the natural philosophers who sought to explain these universal principles. Pythagoras felt that all things could be explained and represented by mathematical formulae. Plato, Socrate’s most important disciple, believed that the world was divided into two realms, the visible and the intelligible. Part of the world, the visible, we could grasp with the five senses, but the intelligible we could only grasp with our minds. In their own way they both sought to explain the nature of reality and how we could know what is real.
Pythagoras held that an accurate description of reality could only be expressed in mathematical formulae. “Pythagoras is the great-great-grandfather of the view that the totality of reality can be expressed in terms of mathematical laws” (Palmer 25). Based off of his discovery of a correspondence between harmonious sounds and mathematical ratios, Pythagoras deduced “the music of the spheres”. The music of the spheres was his belief that there was a mathematical harmony in the universe. This was based off of his serendipitous discovery of a correspondence between harmonious sounds and mathematical ratios. Pythagoras’ philosophical speculations follow two metaphysical ideals. First, the universe has an underlying mathematical structure. Secondly the force organizing the cosmos is harmony, not chaos or coincidence (Tubbs 2). The founder of a brotherhood of spiritual seekers Pythagoras was the mo...
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...ch one of us has a star that our soul is associated with. Our task as human is to try to live a good live so that when we reincarnate we can return to our associated star. In their own way they both sought to explain the nature of reality and how we could know what is real.
Works Cited
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Maddox, Bruno. "Blinded by Science The Math Behind Beauty." Discover Magazine. 01,06,2011: n. page. Web. 9 Nov. 2011.
Palmer, Donald. Looking at Philosophy. 5th. New York,NY: McGrae-Hill, 2010. 25,67. Print.
Tubbs, Robert. What is a Number? Mathematical Concepts and Their Origins. Baltimore, Md: The Johns Hopkins University Press, 2009. 2,10,24. Print
185-196. Dillon, Mathew, and Garland, Lynda. Ancient Greece: Social and Historical Documents from Archaic Times to the Death of Socrates. Routledge International Thompson Publishing Company, 1994, pp. 179-215 Lefkowitz, Mary.
Plato, and G. M. A. Grube. "Phaedo." Five Dialogues. Indianapolis, IN: Hackett Pub., 2002. 93-
Marra, James L., Zelnick, Stephen C., and Mattson, Mark T. IH 51 Source Book: Plato, The Republic, pp. 77-106. Kendall/Hunt Publishing Company, Dubuque, Iowa, 1998.
One of the main points of Plato’s philosophy was that he believed that people should not so easily trust their senses. In “The Allegory of the Cave”, Plato argues that what we perceive of the world through our sense does not give us the entire picture of what is really there. He states that what we can see is only shadows of what is true, but since we are born believing what we see, we don’t know that there is anything missing at all. Plato believed that in the “knowable realm”, the form of the good, the ultimate truth, is the last thing that we can see, which requires more effort that simply perceiving it. This ultimate truth can only be found through being able to not only perceive, but to be dragged out of the cave, or to be able to think. He likely believed this because through education, he felt that there was an ordering occurring in the mind that allowed for thoughts to become more focused, and clearer. As these thoughts became clearer, s...
"Plato." The Norton Anthology of World Masterpieces, Volume I. 6th ed. NY: W.W. Norton and Co., 1992. 726-746.
Plato, like Pythagoras, believes that knowledge of pure Forms and of “Being” is the direct path to someone living a life of salvation and of the highest quality. Plato, like Pythagoras, also believed that all of the forms are geometric figures and mathematical in nature. Also, Plato, like Heraclitus, believed that our world is constantly changing, or in a constant flux. Plato, also agreed with Parmenides, who believed that the real world is not the same as the world of our experience.
Dodds, E. R., The Ancient Concept of Progress and Other Essays on Greek Literature and Belief, London. Oxford University Press, 1973.
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.
How do we explain the world around us? How can we get to the truth? Plato and Aristotle began the quest to find the answers thousands of years ago. Amazingly, all of philosophy since that time can be described as only a rehashing of the original argument between Plato and Aristotle. Plato and Aristotle's doctrines contrast in the concepts of reality, knowledge at birth, and the mechanism to find the truth.
Plato. "Gorgias.” Voices of Ancient Philosophy. Ed. Julia Annas. New York: Oxford, 2001. 305-318. Print.
The mathematicians of Pythagoras's school (500 BC to 300 BC) were interested in numbers for their mystical and numerological properties. They understood the idea of primality and were interested in perfect and amicable numbers.
The Scientific Revolution was sparked through Nicolaus Copernicusí unique use of mathematics. His methods developed from Greek astr...
Euclid of Alexandria was born in about 325 BC. He is the most prominent mathematician of antiquity best known for his dissertation on mathematics. He was able to create “The Elements” which included the composition of many other famous mathematicians together. He began exploring math because he felt that he needed to compile certain things and fix certain postulates and theorems. His book included, many of Eudoxus’ theorems, he perfected many of Theaetetus's theorems also. Much of Euclid’s background is very vague and unknown. It is unreliable to say whether some things about him are true, there are two types of extra information stated that scientists do not know whether they are true or not. The first one is that given by Arabian authors who state that Euclid was the son of Naucrates and that he was born in Tyre. This is believed by historians of mathematics that this is entirely fictitious and was merely invented by the authors. The next type of information is that Euclid was born at Megara. But this is not the same Euclid that authors thought. In fact, there was a Euclid of Megara, who was a philosopher who lived approximately 100 years before Euclid of Alexandria.
Burton, D. (2011). The History of Mathematics: An Introduction. (Seventh Ed.) New York, NY. McGraw-Hill Companies, Inc.
The history of math has become an important study, from ancient to modern times it has been fundamental to advances in science, engineering, and philosophy. Mathematics started with counting. In Babylonia mathematics developed from 2000B.C. A place value notation system had evolved over a lengthy time with a number base of 60. Number problems were studied from at least 1700B.C. Systems of linear equations were studied in the context of solving number problems.