Euclidean geometry

Euclidean geometry studies points, lines, angles, and figures in flat space, using principles traditionally organized around Euclid’s postulates.

Point (geometry): A point is an exact location with no dimensions. Points mark the locations from which Euclidean figures and constructions are defined.
Euclid's postulates: Euclid’s postulates are five foundational assumptions about constructing and reasoning with geometric objects. They state the rules from which classical Euclidean geometry is derived.
Euclidean distance: Euclidean distance is the length of the straight line segment joining two points in a Euclidean space. It gives the standard geometric meaning of distance between points.
Non-Euclidean geometry: Non-Euclidean geometry studies geometries in which Euclid’s parallel postulate does not hold. Its alternatives show that Euclidean geometry is not the only consistent account of space.
Euclid: Euclid was an ancient Greek mathematician associated with the systematic exposition of geometry in the Elements. His name became attached to the geometry organized in his influential text.
Line (geometry): A line is a straight, one-dimensional path extending without end in both directions. Euclid’s geometry builds figures from straight lines and their intersections.
Parallel postulate: The parallel postulate asserts, in one formulation, that exactly one parallel can pass through a point outside a given line. This distinctive postulate separates Euclidean geometry from non-Euclidean geometries.
Pythagorean theorem: The Pythagorean theorem states that a right triangle’s hypotenuse squared equals the sum of its legs’ squares. It converts perpendicular side lengths into straight-line distances.
Hyperbolic geometry: Hyperbolic geometry is a non-Euclidean geometry in which multiple parallels pass through a point outside a given line. It replaces Euclid’s unique-parallel rule with a geometry of negative curvature.
Elements (Euclid): The Elements is Euclid’s thirteen-book mathematical work, presenting geometry and number theory through definitions, postulates, and proofs. It preserved and organized the propositions that became classical Euclidean geometry.

Linked from 137 pages