What are Euclid's axioms and Euclid's Postulates?

Question

Who is Euclid? what are Axioms and Postulates? Is any one going to find out? :-/

Answer 1

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.
In geometry, the parallel postulate, also called Euclid's fifth postulate since it is the fifth postulate in Euclid's Elements, is a distinctive axiom in what is now called Euclidean geometry. It states that:

If a line segment intersects two straight lines forming two interior angles on the same side that sum to less than two right angles, then the two lines, if extended indefinitely, meet on that side on which the angles sum to less than two right angles.

Euclidean geometry is the study of geometry that satisfies all of Euclid's axioms, including the parallel postulate. A geometry where the parallel postulate cannot hold is known as a non-euclidean geometry. Geometry that is independent of Euclid's fifth postulate (i.e., only assumes the first four postulates) is known as absolute geometry (or, in some places, neutral geometry).