3. WHO IS EUCLID ?
Euclid is the a famous ancient greek mathematician
who lived in the greek city of alexandria in egypt during
the 3rd CENTURY BCE.
4. ABOUT HIS LIFE
Very few original references to Euclid survive, so little is known
about his life. He was likely born c. 325 BC, although the place and
circumstances of both his birth and death are unknown and may only
be estimated roughly relative to other people mentioned with him. He
is rarely mentioned by name by other Greek mathematicians
from Archimedes (c. 287 BC – c. 212 BC) onward, and is usually
referred to as "ὁ στοιχειώτης" ("the author of Elements").[6] The few
historical references to Euclid were written centuries after he lived,
by Pappus of Alexandria c. 320 AD and Proclus c. 450 AD.
5.
6. EUCLID’S ELEMENTS
The Elements is a mathematical treatiseconsisting of 13 books
attributed to the ancient Greek
mathematician Euclid in Alexandria, Ptolemaic Egypt c. 300 BC. It is
a collection of definitions, postulates, propositions
and mathematical proofs of the propositions. The books cover plane
and solid Euclidean geometry, elementary number theory,
and incommensurable lines. Elements is the oldest extant large-scale
deductive treatment of mathematics. It has proven instrumental in
the development of logic and modern science, and its logical rigor
was not surpassed until the 19th century.
Euclid's Elements has been referred to as the most successful and
influential textbook ever written.
7. GEOMETRY
Euclidean space, the two-dimensional plane and three-dimensional space
of Euclidean geometry as well as their higher dimensional generalizations
Euclidean geometry, the study of the properties of Euclidean spaces
Non-Euclidean geometry, systems of points, lines, and planes analogous to
Euclidean geometry but without uniquely determined parallel lines
Euclidean distance, the distance between pairs of points in Euclidean
spaces
Euclidean ball, the set of points within some fixed distance from a
center point .
8.
9. NUMBER THEORY
Euclidean division, the division which produces a quotient and a remainder
Euclidean algorithm, a method for finding greatest common divisors
Extended Euclidean algorithm, a method for solving the Diophantine
equation ax + by = d where d is the greatest common divisor of a and b.
Euclid's lemma: if a prime number divides a product of two numbers, then
it divides at least one of those two numbers.
Euclidean domain, a ring in which Euclidean division may be defined,
which allows Euclid's lemma to be true and the Euclidean algorithm and the
extended Euclidean algorithm to work .
![EUCLID[THE GREATEST
MATHEMATICIAN]](data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7)