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Pythagoras and his contributions
Pythagoras and his contribution to math
Pythagoras and his contribution to math
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1) The connection between Mesopotamia and the development of civilization is the Sumerian tribe that arrived to that land. They were the first to read and write, and city-states rumored to have civilizations evolve around them are found surrounding Mesopotamia. Additionally, many of the first creation stories include Mesopotamia as the birthplace of civilization.
2) The debate regarding Pythagoras and his theorem is very strong because not much is known of him since neither he nor his pupils left many writings, thus we only know some facts from contradicting accounts written two centuries after his death. However, it is now known that he did not discover the Pythagorean Theorem nor the connection established between musical intervals and simple
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numbers. 3) According to medieval theologians, the clear and original meaning of the account of creation in the Genesis is that chaos is a condition in which there are no things; a world where whatever exists does not have a name.
It is the naming that makes the separation if chaos into cosmos, when things with names begin to exist. Medieval theologians imposed on this creation story the concept that the world was created ex nihilo (out of nothing).
4) Atomism tells us that everything in the universe is fashioned out of small invisible and eternally existing particles called atoms. Certain qualities of atoms explain why different substances have different attributes.
5) According to Plato, geometrical shapes relative to the Pythagorean philosophy apply to our world by existing in the Platonic world. For example, the motion of the heavens can be described as circular and in Pythagorean philosophy the circle is the perfect, idealized shape. As well, planets were also presumed to follow a spherical orbit. Another philosophy inherited from Pythagoras is that cosmos is a place of order and goodness.
6) The clash between their interests was that Plato based his idea of nature and life on mathematical evidence and scientific proof, while Aristotle made conclusions about the world based his vague observations, lacking any concrete verification of his
ideas. 7) Aristotle’s philosophy differs from Plato’s in that it emphasizes human perception of how the world appears to be over investigation of how the world actually is. Meanwhile, Plato would prove his assertions and theories with actual experimentation and mathematics, employing principles that originated from Pythagoras’ time. Furthermore, for Aristotle the world of change happened between the Earth and the Moon. Overall, both Plato and Aristotle were interested in planets and astronomy. 8) At the time of Muhammad, the West rediscovered classical knowledge and there was a boom of knowledge and information in the Arab world. This outburst of knowledge became inaccessible to the world for a long time. 9) Humanism was surprisingly integrated into Christianity and became known instead as humanistic Christianity. One of the Greek understandings of love changed to “platonic” to explain the love between Man and God. Humanism made Christianity focus more on rational thinking and observation. 10) Ptolemy was similar to Aristotle because he placed the Earth and mankind itself at the center of his cosmology and the spiritual world, and his ideas were also quite vague and lacking proof. They were based on assumptions. 11) Copernicus was fearful of his colleagues’ reactions to his word and wished to find more proof before presenting his theories. Additionally, his partaking in so many fields of study made him a busy man. 12) In Aristotle’s cosmos, Earth was the bottom of the universe, the place to which earthly objects fell. The heavens are to be found at and beyond where the moon is; a region that is unchanging and spotless. 13) Galileo disproved some of Aristotle’s cosmologies by gathering more data using his newly invented telescopes. He made the cosmology in want of more elaboration when he discovered the sun’s spots and the mountains on the moon’s surface. This discredited the idea that both these stellar objects are supposed to be “perfect”. 14) Tycho Bache was famous for his accuracy in astronomical observations, an attribute which Aristotle’s cosmology majorly lacked. Other than that, most of his cosmology aligned with Aristotle’s ideas. 15) The Church slows down a lot of the progress that science can otherwise gain, since it refuses to accept many novel theories unless they truly function for other phenomena and situations. Simultaneously, by doing so, it challenges the scientific world to further its study and evolve the theories it proposes, actually acting as a catalyst for better scientific explanations.
Mesopotamia was the first primordial, and influential cradle of civilization. Nestled in the valleys of the vehement Tigris-Euphrates Rivers around the time of the Lower Paleolithic period
Before the beginning of history, people from across the land gradually developed numerous cultures, each unique in some ways while the same time having features in common. Mesopotamia and Egypt are important to the history of the world because of religious, social, political and economic development. Mesopotamia was the first civilization, which was around 3000 B.C., and all other countries evolved from it. Mesopotamia emerged from the Tigris and Euphrates Rivers. The soil was rich and agriculture was plentiful. The Semitic nomads occupied the land around Akkad. The Sumerians established the city-states. Villages became urban centers. Because of the formation of the city-states everything flourished. However, Mesopotamian agriculture lacked stones; therefore mud brick became their major building block. Their diet consisted of fish from the rivers. The rivers were flooded frequently destroyed the cities. Mesopotamians made their living from crops and pottery.
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.
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.
Thirdly, Plato and Aristotle hold contrasting views on the mechanism of finding the truth. Plato relied on the ability to reason in his attempt to explain the world. He produced his ideal world based on reason since such a world lies beyond the realm of the five senses. Plato ignored his senses because he believed his senses only revealed the imperfect forms of the ordinary world.
Around 700 BC, the poet Hesiod’s Theogony wrote the first cosmogony, or origin story, of Greek mythology. The poet tells the story of the universe’s journey from nothingness to being, and details a family tree of gods and goddesses who evolved from Chaos and descended from Earth, Sea, Sky and the Underworld.
Thesis statement: In this research, I will investigate the basic concepts of the Egyptian mythology and its gods.
Egyptians were an astounding set of people woe helped shaping their culture and the rest of the world with the lack of modernized tools. This is translated through their arts, architecture and culture, thus guiding and building the foundation for contemporary society. In terms of history, Egyptians were and still are filled with a vast amount of history which has also contributed with the development unique and diverse society. Their development of religion and culture can be dated back to ancient times and is seen through their various ways of storytelling which has been passed onto generations. These forms of storytelling can be seen ancient Egyptians mythology. Mythology played an important role in ancient Egyptian history because it provided
The Classical mythology contains tales and epics of the ancient Greek and roman literatures and myths. On the other hand, Homer’s two epic poems, the Iliad relates to the events of the Trojan War while the Odyssey details Odysseus expedition after the war. Homer’s epic poems, the Odyssey and the Iliad present a major part of ancient history as modern fictional heroic stories. In ancient Greek, heroes were humans who were depicted to possess superhuman abilities. A key example in the classical mythology is Akhilles who is later known in Homer’s Iliad as Achilles. Achilles is he greatest hero of the Iliad whereas Odysseus is the greatest hero of the Odyssey. The greatest heroes from classic mythology and the modern fictional hero’s stories are mortal, and subject to death. The Odyssey and the Iliad marks the beginning of modern fictional literature.
Plato's first argument for his idea that Forms are universals uses mathematics and the sciences to explain his theory. According to Plato, science is the 'body of universal and necessary truths' (Jones 125). Jones also pointed out Plato's view that since math is a science, 'there must be forms to be the objects of mathematical knowledge.' "Nothing other than eternal, unchanging forms can qualify to be the objects of scientific knowledge." (Jones 125) Plato also described mathematical objects as being universals and separate substances (Cherniss 180).
Aristotle and Plato were both great thinkers but their views on realty were different. Plato viewed realty as taking place in the mind but Aristotle viewed realty is tangible. Even though Aristotle termed reality as concrete, he stated that reality does not make sense or exist until the mind process it. Therefore truth is dependent upon a person’s mind and external factors.
Around 190 B.C, Greek thoughts were dominated by Aristotelian cosmology. However, when the Greek mathematician and astronomer Hipparchus calculated the heliocentric system, it contradicted Aristotle’s idea of the orbits being perfectly circular. Hipparchus abandoned his work because Aristotle's cosmological was believed to be mandated by the science of the time, even though, Aristotle's model was questioned by certain observations such as changes in the brightness of the planets. Nonetheless, this did not stop Hipparchus’s curiosity in Astronomy. Using the Chaldean and Babylonian astronomical knowledge and techniques, many of his discoveries were widely accepted and proven to be right. Not only did he contribute to Greek Astronomy, he is
Greek mythology is a body of myths and teachings that belong to the ancient Greeks concerning Titans, gods, and heroes. According to Alan Dundes, a myth is a sacred narrative explaining how the world and humankind assumed their present form (Dundes 1). Though now it may be referred to as mythology, to the ancient Greeks it was an aspect of their religion. Like many other pre-Christian societies, the ancient Greeks deemed things that were important in their lives, such as fire, water, air, and lightning to be gods which govern the world. The gods of the ancient Greeks had a complicated genealogy with many generations of gods and goddesses. The tales of these gods were woven into an immense variety of fables. The fables of the Greek gods were handed down through word of mouth, from one generation to another, long before written logs were used (History). The fables that were passed down show that the Greeks used the tales to give answers to the questions, such as where do we come from? How did we get here? Why are we here? Questions like these are human nature and the basis of all religions.