Geometry
Geometry existed in 3000 B.C. in the ancient civilizations of Babylon and Egypt. However, it was merely a nameless mathematical system. Historians are unsure as to which of them first discovered Geometry. These ancient Indian civilizations also had records of the earlier versions of geometry. The geometry universally used today is referred to as the Euclidean Geometry. In 300 B.C.,Euclid gathered the most general concepts of geometry in his time and added his own original theorems as well. He saved all his hard work in a book knows as The Elements of Geometry. This important book contains what are known today as common notions and the fundamental geometric principles.
Euclid of Alexandria authored the earliest extant axiomatic presentation of Euclidean geometry and number theory. An axiomatic system is a set of axioms used to derive theorems. What this means is that for every theorem in math, there exists an axiomatic system that contains all the axioms needed to prove that theorem. An axiom is a statement that is considered true and does not require a proof. It is considered the starting point of reasoning. Axioms are used to prove other statements. Many axiomatic systems were developed in the nineteenth century, including non-Euclidean geometry.
Geometry is divided into two separate branches, Euclidean and Non-Euclidean. Non-Euclidean geometry came into being in the 19th century as a problem with several of Euclid’s claimed surfaced. They both have different postulates, theorems, and proofs. Euclidean Geometry deals mostly with two-dimensional figures, while Non-Euclidean geometry is a consistent system of definitions, assumptions, and proofs that describe such objects as points, lines and planes. The main difference between Euclidean and a Non-Euclidean is the assumption of how many lines are parallel to another. Euclidean states that there саn be οnlу one line through a point whісh іѕ іn thе same plane аѕ thе line, and it саnnοt bе intersected. The two most common Non-Euclidean geometries are spherical geometry and hyperbolic geometry. In spherical geometry there are no such lines. In hyperbolic geometry there are at least two distinct lines that pass through the point and are parallel to (in the same plane as and do not intersect) the given line.