Analytic geometry

Analytic geometry studies geometric figures by representing points with coordinates and describing shapes and relationships with algebraic equations.

Cartesian coordinate system: A coordinate system that locates points using signed distances along perpendicular axes. Its axes assign ordered number pairs to points in the plane.
Slope: A measure of a line's steepness, expressed as vertical change divided by horizontal change. Coordinate differences determine a line's direction and parallelism.
René Descartes: A French philosopher and mathematician whose work helped establish coordinate methods in geometry. His name became attached to the coordinate system central to the subject.
Linear algebra: The study of vectors, linear equations, and transformations represented by matrices. It extends coordinate geometry to higher dimensions and systematic transformations.
Synthetic geometry: Geometry developed through axioms and geometric constructions rather than coordinate equations. It proves properties directly from geometric relations instead of translating them into algebra.
Coordinate geometry: The use of coordinates and algebra to represent and solve geometric problems. It is the broader practice that includes analytic geometry.
Equation of a line: An algebraic relation whose solutions are precisely the points on a line. It is the basic equation-based representation of a geometric figure.
Pierre de Fermat: A French mathematician who developed methods relating equations to geometric curves. His independent work helped form analytic geometry.
Calculus: The branch of mathematics concerned with change, limits, derivatives, and integrals. Coordinate curves let calculus quantify slopes, areas, and motion.
Projective geometry: The study of geometric properties preserved by projection, including incidence and cross-ratio. It extends coordinate methods to include points at infinity and projection.

Linked from 23 pages