how do you identify a plane in geometry
Two distinct but intersecting lines Two parallel lines
title: Plane (geometry) text: Plane (geometry) In mathematics, a plane is a flat, two-dimensional surface that extends infinitely far. A plane is the two-dimensional analogue of a point (zero dimensions), a line (one dimension) and three-dimensional space. Planes can arise as subspaces of some higher-dimensional space, as with a room's walls extended infinitely far, or they may enjoy an independent existence in their own right, as in the setting of Euclidean geometry. When working exclusively in two-dimensional Euclidean space, the definite article is used, so, "the" plane refers to the whole space. Many fundamental tasks in mathematics, geometry, trigonometry, graph theory, and graphing are title: Analytic geometry text: Analytic geometry In classical mathematics, analytic geometry, also known as coordinate geometry or Cartesian geometry, is the study of geometry using a coordinate system. This contrasts with synthetic geometry. Analytic geometry is widely used in physics and engineering, and also in aviation, rocketry, space science, and spaceflight. It is the foundation of most modern fields of geometry, including algebraic, differential, discrete and computational geometry. Usually the Cartesian coordinate system is applied to manipulate equations for planes, straight lines, and squares, often in two and sometimes in three dimensions. Geometrically, one studies the Euclidean plane (two dimensions) and Euclidean space (three title: Geometry text: some general concepts that are more or less fundamental to geometry. These include the concepts of points, lines, planes, surfaces, angles, and curves, as well as the more advanced notions of manifolds and topology or metric. Geometry has applications to many fields, including art, architecture, physics, as well as to other branches of mathematics. Contemporary geometry has many subfields: The earliest recorded beginnings of geometry can be traced to ancient Mesopotamia and Egypt in the 2nd millennium BC. Early geometry was a collection of empirically discovered principles concerning lengths, angles, areas, and volumes, which were developed to meet some practical title: Plane (geometry) text: performed in a two-dimensional space, or, in other words, in the plane. Euclid set forth the first great landmark of mathematical thought, an axiomatic treatment of geometry. He selected a small core of undefined terms (called "common notions") and postulates (or axioms) which he then used to prove various geometrical statements. Although the plane in its modern sense is not directly given a definition anywhere in the "Elements", it may be thought of as part of the common notions. Euclid never used numbers to measure length, angle, or area. In this way the Euclidean plane is not quite the same title: Plane (geometry) text: complex projective line. The projection from the Euclidean plane to a sphere without a point is a diffeomorphism and even a conformal map. The plane itself is homeomorphic (and diffeomorphic) to an open disk. For the hyperbolic plane such diffeomorphism is conformal, but for the Euclidean plane it is not. Plane (geometry) In mathematics, a plane is a flat, two-dimensional surface that extends infinitely far. A plane is the two-dimensional analogue of a point (zero dimensions), a line (one dimension) and three-dimensional space. Planes can arise as subspaces of some higher-dimensional space, as with a room's walls extended infinitely far,