Euclid (Greek: . ), fl. 300 BCE, also known as Euclid of Alexandria, is often referred to as the Father of Geometry. He was a Greek mathematician, and is believed to have been active in Alexandria during the reign of Ptolemy I (323 BCE–283 BCE). His Elements is the most successful textbook in the history of mathematics. In it, the principles of what is now called Euclidean geometry are deduced from a small set of axioms. Euclid also wrote works on perspective, conic sections, spherical geometry, and rigor.
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Known as the "Father of Geometry," Euclid lived during the reign of Ptolemy in ... Euclid Blogs. Fermat's Last Theorem: Euclid of Alexandria ...www.mahalo.com/EuclidEuclid (Greek: . ), fl. 300 BCE, also known as Euclid of Alexandria, is often referred to as the Father of Geometry. He was a Greek mathematician, and is believed to have been active in Alexandria during the reign of Ptolemy I (323 BCE–283 BCE). His Elements is the most successful textbook in the history of mathematics. In it, the principles of what is now called Euclidean geometry are deduced from a small set of axioms. Euclid also wrote works on perspective, conic sections, spherical geometry, and rigor.
Biographical knowledge
Little is known about Euclid other than his writings. What little biographical information we do have comes largely from commentaries by Proclus and Pappus of Alexandria. Euclid was active at the great Library of Alexandria and may have studied at Plato's Academy in Greece. The date and place of Euclid's birth and the date and circumstances of his death are unknown.
Some writers in the Middle Ages confused him with Euclid of Megara, a Greek Socratic philosopher who lived approximately one century earlier.
The Elements
main: Euclid's Elements image:Oxyrhynchus papyrus with Euclid's Elements.jpg and dated to circa AD 100. The diagram accompanies Book II, Proposition 5.]]Although many of the results in Elements originated with earlier mathematicians, one of Euclid's accomplishments was to present them in a single, logically coherent framework, making it easy to use and easy to reference, including a system of rigorous mathematical proofs that remains the basis of mathematics 23 centuries laterFact: date=July 2008.
Although best-known for its geometric results, the Elements also includes number theory. It considers the connection between perfect numbers and Mersenne primes, the infinitude of prime numbers, Euclid's lemma on factorization (which leads to the fundamental theorem of arithmetic on uniqueness of prime factorizations), and the Euclidean algorithm for finding the greatest common divisor of two numbers.
The geometrical system described in the Elements was long known simply as geometry, and was considered to be the only geometry possible. Today, however, that system is often referred to as Euclidean geometry to distinguish it from other so-called Non-Euclidean geometries that mathematicians discovered in the 19th century.
Other works
In addition to the Elements, at least five works of Euclid have survived to the present day.
- Data deals with the nature and implications of "given" information in geometrical problems; the subject matter is closely related to the first four books of the Elements.
- On Divisions of Figures, which survives only partially in Arabic translation, concerns the division of geometrical figures into two or more equal parts or into parts in given ratios. It is similar to a third century AD work by Heron of Alexandria.
- Catoptrics, which concerns the mathematical theory of mirrors, particularly the images formed in plane and spherical concave mirrors. The attribution to Euclid is doubtful. Its author may have been Theon of Alexandria.
- Phaenomena is a treatise on spherical Astronomy, it survives in Greek and is quite similar to "On the Moving Sphere", by Autolycus of Pitane, who flourished around 310 BC.
- Optics is the earliest surviving Greek treatise on perspective. In its definitions Euclid follows the Platonic tradition that vision is caused by discrete rays which emanate from the eye. One important definition is the fourth: "Things seen under a greater angle appear greater, and those under a lesser angle less, while those under equal angles appear equal." In the 36 propositions that follow, Euclid relates the apparent size of an object to its distance from the eye and investigates the apparent shapes of cylinders and cones when viewed from different angles. Proposition 45 is interesting, proving that for any two unequal magnitudes, there is a point from which the two appear equal. Pappus believed these results to be important in astronomy and included Euclid's Optics, along with his Phaenomena, in the Little Astronomy, a compendium of smaller works to be studied before the Syntaxis (Almagest) of Claudius Ptolemy.
