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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.
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).
Ancient Greece's philosophers and mathematicians have made contributions to western civilizations. Socrates believed that a person must ask questions and seek to understand the world around them. Aristotle, another famous philosopher, is known for believing that if people study the origin of life, they will understand it more. Reasoning is what makes human beings unique. Hippocrates was a mathematician and a doctor. He created the Hippocratic oath. The oath states that Hippocrates will treat his patient to the best of his abilities that he will refuse to give deadly medicine. This oath is still used by doctors today. Another Greek mathematician was Euclid. His ideas were the starting point of geometry, which is still studied around the world today.
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...
One of the most well known contributors to math from Greece would be Archimedes. He
Euclid Of Alexandria may be the best-known mathematician of the world, he is best known for his work on mathematics The Elements. The fact that his work has survived so long, 2000 years in fact, is a tribute to his mathematical genius, however very little of him is known. Three theories abound as to the true nature of this historical figure. Not all historians agree that Euclid was in fact a historical figure, some argue that the school in Alexandria took up the name Euclid to publish their works. But the more accepted theories are that Euclid was in fact a real historical figure who may have been the leader of a team of mathematicians.
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
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.
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.
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.
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
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.
Of the people to influence Dirichlet, Ohm, the mathematician known for Ohm’s law, was Dirichlet’s teacher and influenced him greatly in inspiring Dirichlet to pursue mathematic developments and studies. Not only did Ohm have a relatively influential grasp on Dirichlet; the mathematician, Guass, did as well. One book in particular is said to have been placed under Dirichlet’s pillow every night, Disquisitiones Arithmeticae, by Guass. This book was treasured by Dirichlet and worshiped as some might worship the bible.
The simplest forms of equations in algebra were actually discovered 2,200 years before Mohamed was born. Ahmes wrote the Rhind Papyrus that described the Egyptian mathematic system of division and multiplication. Pythagoras, Euclid, Archimedes, Erasasth, and other great mathematicians followed Ahmes (“Letters”). Although not very important to the development of algebra, Archimedes (212BC – 281BC), a Greek mathematician, worked on calculus equations and used geometric proofs to prove the theories of mathematics (“Archimedes”).
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 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.