Can you explain me what is Euclid's geometry and it is necessary for exam???
Euclidean geometry is a mathematical system attributed to Greek mathematician Euclid. Euclid's method consists in assuming a small set of axioms, and deducing many other theorems from these. Euclid's work begins with plane geometry, still taught in secondary schools. It goes on to the solid geometry of three dimensions.
For more than two thousand years, the adjective "Euclidean" was unnecessary because no other sort of geometry had been conceived. Euclid's axioms seemed so intuitively obvious that any theorem proved from them was deemed true in an absolute, often metaphysical, sense. Today, however, many otherself-consistent non-Euclidian geometries are known, the first ones having been discovered in the early 19th century. An implication of Einstein's theory of general relativity is that physical space itself is not Euclidean, and Euclidian space is a good approximation for it only over short distances (relative to the strength of the gravitational field).
Euclidean geometry is an example of synthetic geometry, in that it proceeds logically from axioms describing basic properties of geometric objects such as points and lines, to propositions about those objects, all without the use of coordinates to specify those objects. This is in contrast to analytic geometry, which uses coordinates to translate geometric propositions into algebraic formulas.
A non-Euclidean geometry is a rethinking and redescription of the properties of things like points, lines, and other shapes in a non-flat world. Spherical geometry—which is sort of plane geometry warped onto the surface of a sphere—is one example of a non-Euclidean geometry.
Euclidean geometry is a mathematical system attributed to Greek mathematician Euclid. Euclid's method consists in assuming a small set of axioms, and deducing many other theorems from these. Euclid's work begins with plane geometry, still taught in secondary schools. It goes on to the solid geometry of three dimensions.
For more than two thousand years, the adjective "Euclidean" was unnecessary because no other sort of geometry had been conceived. Euclid's axioms seemed so intuitively obvious that any theorem proved from them was deemed true in an absolute, often metaphysical, sense. Today, however, many otherself-consistent non-Euclidian geometries are known, the first ones having been discovered in the early 19th century. An implication of Einstein's theory of general relativity is that physical space itself is not Euclidean, and Euclidian space is a good approximation for it only over short distances (relative to the strength of the gravitational field).
Euclidean geometry is an example of synthetic geometry, in that it proceeds logically from axioms describing basic properties of geometric objects such as points and lines, to propositions about those objects, all without the use of coordinates to specify those objects. This is in contrast to analytic geometry, which uses coordinates to translate geometric propositions into algebraic formulas.
A non-Euclidean geometry is a rethinking and redescription of the properties of things like points, lines, and other shapes in a non-flat world. Spherical geometry—which is sort of plane geometry warped onto the surface of a sphere—is one example of a non-Euclidean geometry.
