Euclid also known as Euclid of Alexandria, was a Greek mathematician who flourished in Alexandria, Egypt, almost certainly during the reign of Ptolemy 1 between 323 and 283 BC. Neither the year nor the place of his birth has been established, and the circumstances of his death remain a mystery. Little is known about Euclid other than his writings, the little information known about Euclid comes from commentaries by Proclus and Pappus of Alexandria. Euclid attended the great library of Alexandria and may have studied at Plato's Academy in Greece. Euclid's life span is unknown and he was often confused with Euclid of Megara, who was a Greek Socratic philosopher who live about a century earlier. His elements is the most successful textbook in the history of mathematics. The principles of geometry are deduced from a small set of axioms. Euclid's method of proving mathematical theorems by logical reasoning from accepted first principles continues to be the backbone of mathematics and is responsible for that field's characteristics rigor. Elements is best-known for its geometric results, but it also includes many results in number theory, for example the connection between perfect numbers and Mersenne primes, the proof of the infinitude of prime numbers, Euclid's lemma on factorization this leads to the fundamental theorem of arithmetic on uniqueness of prime factorizations, and the Euclidean algorithm for discovering the greatest common divisor of two numbers. Many of the results in Elements originated with earlier mathematicians so one of Euclid's accomplishments was to present them in a single, logically coherent framework, including a system of rigorous mathematical proofs that remains the basis of mathematics twenty-three centuries later. Euclid's text also includes section on three dimensional geometry and treating plane geometry. The geometrical system presented in the Elements was known simply as geometry and was thought to be the only geometry...

...Geometry (Greek γεωμετρία; geo = earth, metria = measure) arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modernmathematics, the other being the study of numbers (arithmetic).
Classic geometry was focused in compass and straightedge constructions. Geometry was revolutionized by Euclid, who introduced mathematical rigor and the axiomatic method still in use today. His book, The Elements is widely considered the most influential textbook of all time, and was known to all educated people in the West until the middle of the 20th century.[1]
In modern times, geometric concepts have been generalized to a high level of abstraction and complexity, and have been subjected to the methods of calculus and abstract algebra, so that many modern branches of the field are barely recognizable as the descendants of early geometry.
Early geometry[edit]
The earliest recorded beginnings of geometry can be traced to early peoples, who discovered obtuse triangles in the ancient Indus Valley (see Harappan Mathematics), and ancient Babylonia(see Babylonian mathematics) from around 3000 BC. Early geometry was a collection of empirically discovered principles concerning lengths, angles, areas, and volumes, which were developed to meet some practical need in surveying, construction, astronomy, and various crafts. Among these were some surprisingly sophisticated principles, and a...

...History of mathematics
A proof from Euclid's Elements, widely considered the most influential textbook of all time.[1]
The area of study known as the history of mathematics is primarily an investigation into the origin of discoveries in mathematics and, to a lesser extent, an investigation into the mathematical methods and notation of the past.
Before the modern age and the worldwide spread of knowledge, written examples of new mathematical developments have come to light only in a few locales. The most ancient mathematical texts available arePlimpton 322 (Babylonian mathematics c. 1900 BC),[2] the Rhind Mathematical Papyrus (Egyptian mathematics c. 2000-1800 BC)[3] and the Moscow Mathematical Papyrus (Egyptian mathematics c. 1890 BC). All of these texts concern the so-calledPythagorean theorem, which seems to be the most ancient and widespread mathematical development after basic arithmetic and geometry.
The study of mathematics as a subject in its own right begins in the 6th century BC with the Pythagoreans, who coined the term "mathematics" from the ancient Greekμάθημα (mathema), meaning "subject of instruction".[4]Greek mathematics greatly refined the methods (especially through the introduction of deductive reasoning andmathematical rigor in proofs) and expanded the subject matter of mathematics.[5] Chinese...

...Week 5
Final Exam
Continuous schedule from Friday , November 1st. 9am until Saturday , November 2nd., 23:59pm.
Monday, November 4, 2013
20%
100%
To obtain the opportunity to take your final exam you should have delivered at least 6 activities.
Please keep this Agenda at hand so that you can deliver you assignments on time.
Greetings,
Blanca Alanís
Posted by: BLANCA HILDA ALANIS PENA
Posted to: CEL.HI09107V.343.13320 Inglés VII
Bibliography
Posted on: Thursday, October 3, 2013
Hello guys,
The books we are going to use are:
Text book:
Richards, Jack C. & Sandy, Chuck (2009). Passages 2 (2nd ed.). New York, N.Y. Cambridge University Press.
ISBN 978-0-521-68391-3
Workbook:
Richards, Jack C. & Sandy, Chuck (2009). Passages 2 (2nd ed.). New York, N.Y. Cambridge University Press.
ISBN 978-0-521-68393-7
Make sure they are the 2nd. edition, because the 1st. edition is completely different.
In your course, in the Bibliography Section you have a link of a bookstore where you can buy the books. You can try other bookstores in your city, of course, but they don't usually have the book in stock.
Greetings,
Blanca Alanís
Posted by: BLANCA HILDA ALANIS PENA
Posted to: CEL.HI09107V.343.13320 Inglés VII
Grading in the courseWeek 5
Final Exam
Continuous schedule from Friday , November 1st. 9am until Saturday , November 2nd., 23:59pm.
Monday, November 4, 2013
20%
100%
To...

...concrete model.
Looking on the locality of the paper, I highly acknowledge the fact that the researchers described the current state of math education in the Philippines. They emphasized the fact that we are more focused on procedural knowledge rather than the more desired conceptual knowledge. That is our disadvantage because we usually train students to perform math without understanding or making connections on what they are doing. By mentioning this, the readers would really have an idea that the paper itself could be a solution to the problem mentioned. Moreover, it makes the thesis more realistic.
To sum up everything that was tackled, I could say that the thesis served to have an important purpose in the current state of Mathematics Education in the Philippines. It is very informative and feasible. Since it is a small study because it only involved 6 average students, we could propose more studies rooting from this which would have a bigger scope such as implementing the same study but now comparing it to the results gathered from high and low performing students....

...HISTORY OF MATHEMATICS
The history of mathematics is nearly as old as humanity itself. Since antiquity, mathematics has been fundamental to advances in science, engineering, and philosophy. It has evolved from simple counting, measurement and calculation, and the systematic study of the shapes and motions of physical objects, through the application of abstraction, imagination and logic, to the broad, complex and often abstract discipline we know today.
From the notched bones of early man to the mathematical advances brought about by settled agriculture in Mesopotamia and Egypt and the revolutionary developments of ancient Greece and its Hellenistic empire, the story of mathematics is a long and impressive one.
Prehistoric Mathematics
The oldest known possibly mathematical object is the Lebombo bone, discovered in the Lebombo mountains of Swaziland and dated to approximately 35,000 BC. It consists of 29 distinct notches cut into a baboon's fibula. Also prehistoric artifacts discovered in Africa and France, dated between 35,000 and 20,000 years old, suggest early attempts to quantify time.
The Ishango bone, found near the headwaters of the Nile river (northeastern Congo), may be as much as 20,000 years old and consists of a series of tally marks carved in three columns running the length of the bone. Common interpretations are that the Ishango bone shows either the earliest known...

...Euclid is considered by many as the “Father of Geometry.” A Greek mathematician, Euclid is believed to have lived around 300 BC. He is most known for his contributions to geometry and immaculate proofs. His magnum opus, The Elements, is one of the greatest mathematical works in history, with its use in education still existent until the 20th century.
His areas of math ranged from geometry, algebra, number theories, irrational numbers, and solid geometry. Then, after he was done teaching, he wrote his best work, The Elements. It was based on the works of mathematicians that came before him, who he had much respect for, and his own thoughts and theories. The Elements consists of thirteen books, all written by Euclid and based on methods and beliefs before him. Books 1-6 are all on focused on plane geometry, books 7-9 consist of number theories, and book 10 deals with Exodus's theory of irrational numbers, and books 11-13 deal with solid geometry. It is "remarkable for the clarity with which the theorems and problems are selected and ordered" (Albaugh, 1972). At the time of its introduction, Elements was the most comprehensive and logically rigorous examination of the basic principles of geometry. It survived the eclipse of classical learning, which occurred with the fall of the Roman Empire, through Arabic translations. Elements was reintroduced to Europe in 1120 C.E. when Adelard of Bath translated an Arabic version into Latin....

...Pros of Earning an Online High School Diploma
Convenience
You can study and take classes from anywhere that you have a computer and an Internet connection. This is particularly useful for students who live in remote areas or travel frequently for athletics or other extracurricular activities.
Flexible Scheduling
Although some online courses do require students to attend live meetings in real-time, much of your studying can be done asynchronously or on your own schedule. This offers another major advantage for young people whose lives are too busy for traditional school.
Safety
Bullying, whether it involves physical threats or social isolation, is a growing problem at U.S. high schools. Students who suffer from extreme bullying may feel safer completing high school diploma programs from the safety of their homes.
Finishing Early
Some online high school programs allow students to complete work at an accelerated pace. This may be beneficial for students who are ready to move on to college or the workplace.
Quality Materials
According to the U.S. Department of Education, many online high school programs are able to offer students access to higher quality learning materials. The quality of your teachers and materials in an online program will not be limited by the quality of your local public schools, which can vary widely from region to region.
Cons of an Online High School Diploma Program
Social Isolation
While being away from peers may be a...

480 Words |
2 Pages

Share this Document

{"hostname":"studymode.com","essaysImgCdnUrl":"\/\/images-study.netdna-ssl.com\/pi\/","useDefaultThumbs":true,"defaultThumbImgs":["\/\/stm-study.netdna-ssl.com\/stm\/images\/placeholders\/default_paper_1.png","\/\/stm-study.netdna-ssl.com\/stm\/images\/placeholders\/default_paper_2.png","\/\/stm-study.netdna-ssl.com\/stm\/images\/placeholders\/default_paper_3.png","\/\/stm-study.netdna-ssl.com\/stm\/images\/placeholders\/default_paper_4.png","\/\/stm-study.netdna-ssl.com\/stm\/images\/placeholders\/default_paper_5.png"],"thumb_default_size":"160x220","thumb_ac_size":"80x110","isPayOrJoin":false,"essayUpload":false,"site_id":1,"autoComplete":false,"isPremiumCountry":false,"userCountryCode":"US","logPixelPath":"\/\/www.smhpix.com\/pixel.gif","tracking_url":"\/\/www.smhpix.com\/pixel.gif","cookies":{"unlimitedBanner":"off"},"essay":{"essayId":33098692,"categoryName":null,"categoryParentId":null,"currentPage":1,"format":"text","pageMeta":{"text":{"startPage":1,"endPage":1,"pageRange":"1-1","totalPages":1}},"access":"premium","title":"Mathematics and Euclid","additionalIds":[],"additional":[],"loadedPages":{"html":[],"text":[1]}},"user":null,"canonicalUrl":"http:\/\/www.studymode.com\/essays\/Mathematics-And-Euclid-114941.html","pagesPerLoad":50,"userType":"member_guest","ct":10,"ndocs":"1,500,000","pdocs":"6,000","cc":"10_PERCENT_1MO_AND_6MO","signUpUrl":"https:\/\/www.studymode.com\/signup\/","joinUrl":"https:\/\/www.studymode.com\/join","payPlanUrl":"\/checkout\/pay","upgradeUrl":"\/checkout\/upgrade","freeTrialUrl":"https:\/\/www.studymode.com\/signup\/?redirectUrl=https%3A%2F%2Fwww.studymode.com%2Fcheckout%2Fpay%2Ffree-trial\u0026bypassPaymentPage=1","showModal":"get-access","showModalUrl":"https:\/\/www.studymode.com\/signup\/?redirectUrl=https%3A%2F%2Fwww.studymode.com%2Fjoin","joinFreeUrl":"\/essays\/?newuser=1","siteId":1,"facebook":{"clientId":"306058689489023","version":"v2.8","language":"en_US"}}