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Pythagoras
Pythagoras was born around 569 B.C. in Samos, Ionia, and died around 475 B.C. Pythagoras was a Greek philosopher, and mathematician. Pythagoras also developed the Pythagorean brotherhood. This was religious in nature, however it formulated principals that influenced the thoughts of Plato and Aristotle, and contributed to the development of mathematics and Western rational philosophy. Pythagoras not only developed the theorem of A2+B2=C2, but he was also the first to create the music scale of today. Unfortunately none of Pythagoras’s writings from this development time have survived to present day.
In the brotherhood that Pythagoras created, he was the head of the society with an inner circle of followers known as mathematikoi. The mathematikoi lived permanently with the society, had no personal possessions and were vegetarians. They were all taught by Pythagoras himself, and they had strict rules to abide by. Some of his rules ranged from; At its deepest level, reality is mathematical in nature, to that all brothers of the order should observe strict loyalty and ...
Antisthenes of Athens (445-360 B.C.) is remembered for being one of Socrates' older pupils. (1) In fact, he was old enough to have first studied under the sophists, before he met Socrates. (2) He thus stands straddling three important periods in the history of Greek philosophy. As a 5th century philosopher, he copied the rhetoric of Gorgias in his famous Ajax and Odysseus speeches and like the sophists, believed that virtue was teachable; surviving into the 4th century, he was taken seriously by Plato and Aristotle, composing essays in which he propounded an individual logical theory of his own; (3) and as precursor of Hellenistic Cynicism, he composed dialogues, teaching new ethical and social norms that resurfaced after his death in the teaching of Diogenes of Sinope and the Stoa. (4) In this paper, I would like to examine some aspects of Antisthenes' educational theory and his concept of paideia.
Through history, as said before, many philosophers have supported and developed what Pythagoras first exposed to the world. One of the most important philosophers to support Pythagoras’s ideas was Plato. In some of his writings he discusses the creation of the universe based on the musical proportions discovered by Pythagoras (Timaeus), and the explanation of the sound emitted by the planets, which is exposed in the “Myth of Er” in The Republic. It talks about a man who died and came back to life who narrates how he saw the space and how, in every “sphere,” there was a being singing constantly, each one in a different tone, so a perfect harmony was built. Nevertheless, not everyone agreed with this theory, being one of its most important critics Aristotle, who claimed that Plato’s arguments where false in his text On the Heavens. He acknowledges that it is a creative and innovative theory, but it is absurd to think that such music, which is imperceptible to us, exists in a harmonic way up in the heavens. I am not going to go deeper into that for it is not relevant for the text. As the years went on, many people continued developing this theory. Nevertheless, this philosophical theory, not truly explained until later on, was an inspiration for many artists and that is why not only philosophers but many other artists mention and base their works upon this theory.
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.
The rise of the Greeks was a revolutionary step away from this system. Although Greek society was also greatly influenced by their polytheistic religion, they took an intellectual approach to the study of the man-nature relationship. Instead of acce...
“Why Herodotus believed Culture is King” Herodotus believed preservation of culture had to be the dominant policy in maintaining, and controlling an empire, thus believing that “culture is king”, Herodotus celebrated the cultures, and achievements of humanity. In Herodotus he writes, “The actions of people shall not fade with time, so the great and admirable monuments produced by both Greeks and Barbarians shall not go unrenowned, and among other things, set forth the reasons why they waged war against each other. ””(Herodotus)” this quote sums up Herodotus’s view, that culture is something that needed to be preserved, and documented. Through his many journeys and travels, Herodotus documented everything, and wrote about many cultures, and societies. He made it a point to not only gather information, and the specific culture, but the reasoning behind the rituals.
The Ancient Greeks for many years in history have been critically acclaimed as a culture that emphasizes significantly on executing and maintaining perfection within its society. It is a culture popularly known for its significant advancements in areas such as; art, architecture, math, and philosophy. This constant need to improve seemed to be a trait that heavily lied within the Ancient Greeks and this is shown through their embodiment of perfectionism. All throughout history, the Greeks have been praised and looked upon greatly due to their significant lifestyle and historical achievement. Through extensive research of the Greeks, including the analyzation of their art, architecture, math and philosophy, I will be able to depict the true
Golden Mean was an important value in Ancient Greek culture because it taught people to be balanced
It is a commonplace of the western world’s recollection of the Greek civilization that the Greek loved things that are definite, that have clear definition and boundaries that really are what they appear to be. For the Greeks in general as for the cult of the Pythagoreans, the finite, the definite, the bounded are “good,” and the infinite, the ambiguous, the indefinite, the unbounded are “evil”. So much so that one of the most powerful Greek thinkers, Aristotle, equated Being with “identity.” To “be” and to “be one” are the same, Aristotle says. (citation, )
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.
Pythagoras was one of the first true mathematicians who was not only known for the famous Pythagorean theorem. His father was from Tyre while his mother was from Samos but when Pythagoras was born and growing up he spent most of his time in Samos but as he grew he began to spend a lot of time with his father. His father was a merchant and so Pythagoras travelled extensively with him to many places. He learned things as he went along with his father but the primary teacher known to be in his life was Pherekydes. Thales was also a teacher for himself and he learned some from him but he mainly inspired him. Thales was old when Pythagoras was 20 and so Thales told him to go to Egypt and learn more about the subjects he enjoyed which were cosmology and geometry. In Egypt most of the temples where the learning took place refused him entry and the only one that would was called Diospolis. He was then accepted into the priesthood and because of the discussions between the priests he learned more and more about geome...
Trigonometry is one of the branches of mathematical and geometrical reasoning that studies the triangles, particularly right triangles The scientific applications of the concepts are trigonometry in the subject math we study the surface of little daily life application. The trigonometry will relate to daily life activities. Let’s explore areas this science finds use in our daily activities and how we use to resolve the problem.
There are many people that contributed to the discovery of irrational numbers. Some of these people include Hippasus of Metapontum, Leonard Euler, Archimedes, and Phidias. Hippasus found the √2. Leonard Euler found the number e. Archimedes found Π. Phidias found the golden ratio. Hippasus found the first irrational number of √2. In the 5th century, he was trying to find the length of the sides of a pentagon. He successfully found the irrational number when he found the hypotenuse of an isosceles right triangle. He is thought to have found this magnificent finding at sea. However, his work is often discounted or not recognized because he was supposedly thrown overboard by fellow shipmates. His work contradicted the Pythagorean mathematics that was already in place. The fundamentals of the Pythagorean mathematics was that number and geometry were not able to be separated (Irrational Number, 2014).
Pythagoras was a mathematician and philosopher from Greece. Most people even say that he is the first real mathematician. He was born in 570 BC and died in 495 BC. Since Pythagoras was alive in a time period that was a very long time ago, there is not very much that historians know for certain about the mathematician. Pythagoras was born to father, Mnesarchus, and mother, Pythais, and he had about two or three brothers. When Pythagoras was young, he lived on the island of Samos. While living on Samos, he enjoyed to travel constantly. He traveled to places such as, Babylonia, Phoenicia, and Egypt. When he grew older he made his way to the city of Croton. Croton is located in southern Italy. This is where most of Pythagoras’ work occurred, and where he acquired many followers and people interested in his works. He died the city of Metapontum, Lucania, Italy. Pythagoras married a woman named, Theano. The two had two children....
The 17th Century saw Napier, Briggs and others greatly extend the power of mathematics as a calculator science with his discovery of logarithms. Cavalieri made progress towards the calculus with his infinitesimal methods and Descartes added the power of algebraic methods to geometry. Euclid, who lived around 300 BC in Alexandria, first stated his five postulates in his book The Elements that forms the base for all of his later Abu Abd-Allah ibn Musa al’Khwarizmi, was born abo...
Euclid, also known as Euclid of Alexandria, lived from 323-283 BC. He was a famous Greek mathematician, often referred to as the ‘Father of Geometry”. The dates of his existence were so long ago that the date and place of Euclid’s birth and the date and circumstances of his death are unknown, and only is roughly estimated in proximity to figures mentioned in references around the world. Alexandria was a broad teacher that taught lessons across the world. He taught at Alexandria in Egypt. Euclid’s most well-known work is his treatise on geometry: The Elements. His Elements is one of the most influential works in the history of mathematics, serving as the source textbook for teaching mathematics on different grade levels. His geometry work was used especially from the time of publication until the late 19th and early 20th century Euclid reasoned the principles of what is now called Euclidean geometry, which came from a small set of axioms on the Elements. Euclid was also famous for writing books using the topic on perspective, conic sections, spherical geometry, number theory, and rigor.