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Euclid of Alexandria “The Element”
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.
Many mathematicians established the theories found in The Elements; one of Euclid’s accomplishments was to present them in a single, sensibly clear framework, making elements easy to use and easy to reference, including mathematical evidences that remain the basis of mathematics many centuries later. The majority of the theorem that appears in The Elements were not discovered by Euclid himself, but were the work of earlier Greek mathematician such as Hippocrates of Chios, Theaetetus of Athens, Pythagoras, and Eudoxus of Cnidos. Conversely, Euclid is generally recognized with ordering these theorems in a logical ...
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...discrete, because the radius may be indefinitely small.
Obviously Euclid’s The Elements is by far the most famous mathematical work of classical antiquity, and also has the distinction of being the world’s oldest continuously used mathematical textbook. Very little information is known about the author, beyond knowing the fact he lived in Alexandria around 300 BCE. Subjects of works includes geometry, proportion and number theory.
Euclid proved his concepts logically, using definitions, axioms, and postulates. Proclus Diadochus wrote a commentary on Euclid's Elements that kept Euclid's works in circulation. It is believed that Euclid set up a private school at the Alexandria library to teach Mathematical enthusiasts like himself. There are other theories that suggest that Euclid went on to help these students write their own theories and books later in life.
The Aeneid In the Aeneid, the author Virgil outlines the significance of authority by reiterating the need for Aeneas to fulfill his destiny in relation to pietas, devotion to family and country, as the central Roman virtue in the underworld. Virgil successfully uses the underworld to capture and dramatize the importance of authority by allowing Aeneas to see the future Rome due to his leadership through many forms and histories of Roman authority. Once the Trojans were on the shores of Italy, Aeneas had yet another duty to fulfill: a visit to the underground, where he met Sibyl, the "holy prophetess (pg. 149)." After the God Delian (pg.149) breathed "visionary might" into Sibyl, she and Aeneas were able to visit the Earth's hidden world. In this world, he learned what happens to the souls of the dead. Most likely, it served as a future lesson for Aeneas (especially after being guilty of neglecting his duty for his true love of Italy while indulging with Dido) which is still believed and practiced today: the kind of life that we lead; the way we die, self - inflicted or not; and how we are buried after death are all of great significance - that all good deeds in life deserve the goodness of heaven, and all bad deeds deserve the pain and the punishment of hell. "Philgyas in extreme of misery cries loud through the gloom appeals warning to all mankind: Be warned, learn righteousness; and learn to scorn no god (pg.
Euclid propositions can be called theorems in common language. In the Book I Euclid main considerations was on geometry. He began with a long list of definitions which followed by the small number of basic statements to take the essential properties of points, lines, angles etc. then he obtained the remaining geometry from these basic statements with proofs. (Berlinghoff, 2015, p.158).
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.
Hippocrates taught in Athens and worked on squaring the circle and also worked on duplicating the cube. He grew far in these areas and although his work is not lost, it must have contained much of what Euclid later included in Books One and Two of the Elements.
One of the most well known contributors to math from Greece would be Archimedes. He
In “Oedipus the King” by Sophocles, Oedipus, the king of Thebes finds out that he kills his father and that his wife is his mother. Oedipus is very concerned for his kingdom and his people. He wants to “drive the corruption from the land” (Sophocles 109) by finding Laius’s murderer and killing him. Through his curiosity, Oedipus finds out that the man he kills long ago is Laius, who is his father, and that his wife is his mother—all in accordance with Oedipus’ prophecy. After coming on this realization as well, Jocasta, Oedipus’ wife, commits suicide, and Oedipus gouges out his eyes as a result of this. In his search for the murderer, Oedipus strives to be a fair king. Ironically, he often is not fair to the people he sees or things that are essential to him. This play demonstrates the theme of justice through Oedipus’ denial of justice in three situations—Oedipus’ meeting with Tiresias, Oedipus’ gouging out of his eyes, and Creon’s asking of Oedipus to adjudicate fairly
Euclidean distance was proposed by Greek mathematician Euclid of Alexandria. In mathematics, the Euclidean distance or Euclidean metric is the distance between two points, which is shown as a length of a line segment and is given by the Pythagorean theorem. The formula of Euclidean distance is a squ...
Archimedes was a Greek mathematician who created multiple inventions, formed new mathematical techniques, and made advances in geometry that we use in everyday mathematics. Regarded as one of the utmost mathematicians of all time (“Archimedes c.287 B.C.-212 B.C.”), he is responsible for improving the arithmetical meaning of infinity and how we use mathematical models in the real world (Noel, 28). He opened many doors in the world of geometry and math, making very important contributions to our lives today. In 287 B.C, Archimedes was born in Syracuse, Sicily, where he grew up and lived all of his life. In the Greek times he grew up in, math was considered as a fine art (“Archimedes c.287 B.C.-212 B.C.”).
This source provided a lot of background information on Euclid and his discoveries. This source gave details about the many geometrical theories of Euclid, as well as his practical geometrical uses. This source also explained how geometry helped Greece a long time ago, and how it is used by many people everyday.
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
By the time Euclid's Elements appeared in about 300 BC, several important results about primes had been proved. In Book IX of the Elements, Euclid proves that there are infinitely many prime numbers. This is one of the first proofs known which uses the method of contradiction to establish a result. Euclid also gives a proof of the Fundamental Theorem of Arithmetic: Every integer can be written as a product of primes in an essentially unique way.
He published two books called “Mirror” and “ The Phaenomena”, which took him a year for both books to be completed and revised by other astronomers. The works were lightly criticized, in the light of strong knowledge, by the intellectual astronomer Hipparchus two centuries later; however, they were pioneering compendia and was proved useful. Several verbatim quotes were given by Hipparchus in his commentary on the phenomenal poem of Aratus, which drew on Eudoxus and was entitled phenomena. Another book called “Disappearances of the Sun”, may have been worried with the eclipses, and perhaps with increasing s and settings as well. He composed an astronomical poem that may result in confusion with Aratus although a genuine Astronomia in hexameters, in tradition, is a probability. Nowadays, the mathematical labor of Eudoxus is not particularly well known to the public due to the fact that he did not leave anything behind that could ensure that he had posthumous fame. He left no important theorem as the Pythagoras, nor mathematical assumptions like Euclid. Eudoxus main contribution was the theory of proportions that helped in the involvement of Pythagorean geometry, which did not contain any source of
Even though Aristotle’s contributions to mathematics are significantly important and lay a strong foundation in the study and view of the science, it is imperative to mention that Aristotle, in actuality, “never devoted a treatise to philosophy of mathematics” [5]. As aforementioned, even his books never truly leaned toward a specific philosophy on mathematics, but rather a form or manner in which to attempt to understand mathematics through certain truths.
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.
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...