Geometry

Geometry is the branch of mathematics that studies shapes, sizes, positions, and spatial relationships. Its ideas range from properties of flat figures to the structure of space itself.

Point: A point is an exact position with no dimensions. Points mark positions and serve as the basic elements from which geometric figures are built.
Euclidean geometry: Euclidean geometry studies figures and spatial relationships under Euclid’s parallel postulate. It is the classical framework for familiar flat-plane geometry.
Non-Euclidean geometry: Non-Euclidean geometry studies consistent geometries that reject Euclid’s parallel postulate. Its alternatives to Euclidean parallelism show that familiar spatial rules are not inevitable.
Trigonometry: Trigonometry relates angles to side lengths and functions of angles, especially in triangles. It converts geometric relationships between angles and lengths into practical calculations.
Line: A line is a straight, one-dimensional path extending infinitely in both directions. Lines express straightness and alignment, central relations in geometric constructions and proofs.
Coordinate geometry: Coordinate geometry represents geometric points and relationships using numbers and algebraic equations. Coordinates translate spatial questions into equations that can be computed and proved.
Hyperbolic geometry: Hyperbolic geometry is a non-Euclidean geometry in which multiple lines through a point can be parallel to a given line. It provides one precise alternative to Euclidean geometry’s unique parallel line.
Descriptive geometry: Descriptive geometry represents three-dimensional objects through precise two-dimensional projections. It provides geometric methods for translating spatial forms into technical drawings.
Angle: An angle is the figure formed by two rays sharing an endpoint, or a measure of their relative direction. Angles quantify turning and determine many relationships among intersecting lines and shapes.
Geometric transformation: A geometric transformation maps points or figures to new positions, often preserving selected properties. Transformations reveal which features remain unchanged when a figure moves or changes scale.

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