Euclid

Euclid (/ˈjuːklɪd/; Greek: Εὐκλείδης, Eukleidēs Ancient Greek: [eu̯.klěː.dɛːs]; fl. 300 BCE), sometimes called Euclid of Alexandria to distinguish him from Euclid of Megara, was a Greek mathematician, often referred to as the "father of geometry". He was active in Alexandria during the reign of Ptolemy I (323–283 BCE). His Elements is one of the most influential works in the history of mathematics, serving as the main textbook for teaching mathematics (especially geometry) from the time of its publication until the late 19th or early 20th century. In the Elements, Euclid deduced the principles of what is now called Euclidean geometry from a small set of axioms. Euclid also wrote works on perspective, conic sections, spherical geometry, number theory and rigor.

Euclid is the anglicized version of the Greek name Εὐκλείδης, which means "renowned, glorious".

Life

Very few original references to Euclid survive, so little is known about his life. The date, place and circumstances of both his birth and death are unknown and may only be estimated roughly relative to other figures mentioned alongside him. He is rarely mentioned by name by other Greek mathematicians from Archimedes onward, who usually call him "ὁ στοιχειώτης" ("the author of Elements"). The few historical references to Euclid were written centuries after he lived, by Proclus c. 450 AD and Pappus of Alexandria c. 320 AD.

Euclid's Elements

Euclid's Elements (Ancient Greek: Στοιχεῖα Stoicheia) is a mathematical and geometric treatise consisting of 13 books written by the ancient Greek mathematician Euclid in Alexandria, Ptolemaic Egypt c. 300 BC. It is a collection of definitions, postulates (axioms), propositions (theorems and constructions), and mathematical proofs of the propositions. The thirteen books cover Euclidean geometry and the ancient Greek version of elementary number theory. The work also includes an algebraic system that has become known as geometric algebra, which is powerful enough to solve many algebraic problems, including the problem of finding the square root of a number. The Elements is the second oldest extant Greek mathematical treatises after Autolycus' On the Moving Sphere, and it is the oldest extant axiomatic deductive treatment of mathematics. It has proven instrumental in the development of logic and modern science. According to Proclus the term "element" was used to describe a theorem that is all-pervading and helps furnishing proofs of many other theorems. The word 'element' is in the Greek language the same as 'letter'. This suggests that theorems in the Elements should be seen as standing in the same relation to geometry as letters to language. Later commentators give a slightly different meaning to the term 'element', emphasizing how the propositions have progressed in small steps, and continued to build on previous propositions in a well-defined order.

Alexandria

Alexandria (/ˌælɪɡˈzændrɪə/ or /ˌælɪɡˈzɑːndrɪə/;Arabic: الإسكندرية al-Iskandariyyah; Egyptian Arabic: اسكندرية Eskendereyyah; Coptic: Ⲣⲁⲕⲟⲧⲉ Rakotə) is the second largest city and a major economic centre in Egypt, extending about 32 km (20 mi) along the coast of the Mediterranean Sea in the north central part of the country. It is also the largest city lying directly on the Mediterranean coast. Its low elevation on the Nile delta makes it highly vulnerable to rising sea levels. Alexandria is Egypt's largest seaport, serving approximately 80% of Egypt's imports and exports. It is an important industrial center because of its natural gas and oil pipelines from Suez. Alexandria is also an important tourist destination.

Alexandria was founded around a small Ancient Egyptian town c. 331 BC by Alexander the Great. It became an important center of the Hellenistic civilization and remained the capital of Hellenistic and Roman and Byzantine Egypt for almost 1000 years until the Muslim conquest of Egypt in AD 641, when a new capital was founded at Fustat (later absorbed into Cairo). Hellenistic Alexandria was best known for the Lighthouse of Alexandria (Pharos), one of the Seven Wonders of the Ancient World; its Great Library (the largest in the ancient world; now replaced by a modern one); and the Necropolis, one of the Seven Wonders of the Middle Ages. Alexandria was the second most powerful city of the ancient world after Rome. Ongoing maritime archaeology in the harbor of Alexandria, which began in 1994, is revealing details of Alexandria both before the arrival of Alexander, when a city named Rhacotis existed there, and during the Ptolemaic dynasty.

Khan Academy

Khan Academy is a non-profit educational organization created in 2006 by educator Salman Khan with the aim of providing a free, world-class education for anyone, anywhere. The organization produces short lectures in the form of YouTube videos. In addition to micro lectures, the organization's website features practice exercises and tools for educators. All resources are available for free to anyone around the world. The main language of the website is English, but the content is also available in other languages.

History

The founder of the organization, Salman Khan, was born in New Orleans, Louisiana, United States to immigrant parents from Bangladesh and India. After earning three degrees from the Massachusetts Institute of Technology (a BS in mathematics, a BS in electrical engineering and computer science, and an MEng in electrical engineering and computer science), he pursued an MBA from Harvard Business School.

In late 2004, Khan began tutoring his cousin Nadia who needed help with math using Yahoo!'s Doodle notepad.When other relatives and friends sought similar help, he decided that it would be more practical to distribute the tutorials on YouTube. The videos' popularity and the testimonials of appreciative students prompted Khan to quit his job in finance as a hedge fund analyst at Connective Capital Management in 2009, and focus on the tutorials (then released under the moniker "Khan Academy") full-time.

Of Alexandria

related to Alexandria

of Alexandria