   #copyright

Euclid

2007 Schools Wikipedia Selection. Related subjects: Mathematicians

   CAPTION: Euclid

   Justus van Ghent's 15th-century depiction of Euclid. No likeness or
   description of Euclid's physical appearance made during his lifetime
   survives.
   Justus van Ghent's 15th-century depiction of Euclid. No likeness or
   description of Euclid's physical appearance made during his lifetime
   survives.
   Born c. 325 BC
   Died c. 265 BC
   Nationality Greek
   Field Mathematics
   Known for Euclid's Elements

   Euclid (also referred to as Euclid of Alexandria) ( Greek: Εὐκλείδης)
   (c. 325–c. 265 BC), a Greek mathematician, who lived in Alexandria,
   Hellenistic Egypt, almost certainly during the reign of Ptolemy I ( 323
   BC– 283 BC), is often considered to be the "father of geometry". His
   most popular work, Elements, is thought to be one of the most
   successful textbooks in the history of mathematics. Within it, the
   properties of geometrical objects are deduced from a small set of
   axioms, thereby founding the axiomatic method of mathematics.

   Although best-known for its geometric results, the Elements also
   includes various results in number theory, such as the connection
   between perfect numbers and Mersenne primes, the proof of the
   infinitude of prime numbers, Euclid's lemma on factorization (which
   lead to the fundamental theorem of arithmetic, on uniqueness of prime
   factorizations), and the Euclidean algorithm for finding the greatest
   common divisor of two numbers.

   Euclid also wrote works on perspective, conic sections, spherical
   geometry, and possibly quadric surfaces. Neither the year nor place of
   his birth have been established, nor the circumstances of his death.

The Elements

   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. In addition to providing some
   missing proofs, Euclid's text also includes sections on number theory
   and three-dimensional geometry. In particular, Euclid's proof of the
   infinitude of prime numbers is in Book IX, Proposition 20. The
   geometrical system described in Elements was long known simply as "the"
   geometry. Today, however, it is often referred to as Euclidean geometry
   to distinguish it from other so-called non-Euclidean geometries which
   were discovered in the 19th century. These new geometries grew out of
   more than two millennia of investigation into Euclid's fifth postulate,
   one of the most-studied axioms in all of mathematics. Most of these
   investigations involved attempts to prove the relatively complex and
   presumably non-intuitive fifth postulate using the other four (a feat
   which, if successful, would have shown the postulate to be in fact a
   theorem).

Other works

   In addition to the Elements, 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, except Euclid's
       work characteristically lacks any numerical calculations.
     * Phaenomena concerns the application of spherical geometry to
       problems of astronomy.
     * Optics, the earliest surviving Greek treatise on perspective,
       contains propositions on the apparent sizes and shapes of objects
       viewed from different distances and angles.
     * Catoptrics, which concerns the mathematical theory of mirrors,
       particularly the images formed in plane and spherical concave
       mirrors.

   All of these works follow the basic logical structure of the Elements,
   containing definitions and proved propositions.

   There are four works credibly attributed to Euclid which have been
   lost.
     * Conics was a work on conic sections that was later extended by
       Apollonius of Perga into his famous work on the subject.
     * Porisms might have been an outgrowth of Euclid's work with conic
       sections, but the exact meaning of the title is controversial.
     * Pseudaria, or Book of Fallacies, was an elementary text about
       errors in reasoning.
     * Surface Loci concerned either loci (sets of points) on surfaces or
       loci which were themselves surfaces; under the latter
       interpretation, it has been hypothesized that the work might have
       dealt with quadric surfaces.

Tributes

     * 4354 Euclides is an asteroid named after Euclid
     * A lunar crater Euclides (7.4S, 29.5W, 12km dia, 1.3 km depth) is
       named after him
     * In the 1998 film π (or Pi: Faith in Chaos) the main character's
       computer is called Euclid

   Retrieved from " http://en.wikipedia.org/wiki/Euclid"
   This reference article is mainly selected from the English Wikipedia
   with only minor checks and changes (see www.wikipedia.org for details
   of authors and sources) and is available under the GNU Free
   Documentation License. See also our Disclaimer.
