"In mathematics, analytic geometry, also known as coordinate geometry or Cartesian geometry, is the study of geometry using a coordinate system."
The branch of Mathematics that deals with the relationship between algebraic equations and geometric shapes.
Coordinates: Understanding the coordinate system, Cartesian plane, and polar coordinates.
Lines and Slopes: Basic concepts of lines and slopes, including parallel and perpendicular lines.
Conic Sections: Understanding parabolas, ellipses, and hyperbolas.
Transformations: How to translate, rotate, and reflect geometric shapes.
Vectors: Fundamental principles of vectors and vector operations.
Matrices and Determinants: Introduction to matrices and determinants and how they related to geometry.
Three-Dimensional Geometry: Introduction to geometric concepts in three dimensions.
"This contrasts with synthetic geometry."
"Analytic geometry is 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 circles, often in two and sometimes three dimensions."
"Geometrically, one studies the Euclidean plane (two dimensions) and Euclidean space."
"As taught in school books, analytic geometry can be explained more simply: it is concerned with defining and representing geometric shapes in a numerical way and extracting numerical information from shapes' numerical definitions and representations."
"That the algebra of the real numbers can be employed to yield results about the linear continuum of geometry relies on the Cantor–Dedekind axiom."
"Analytic geometry is used... in aviation, rocketry, space science, and spaceflight."
"Analytic geometry... 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 circles, often in two and sometimes three dimensions."
"Analytic geometry is used in physics and engineering..."
"Analytic geometry is the foundation of most modern fields of geometry, including algebraic, differential, discrete, and computational geometry."
"It is concerned with defining and representing geometric shapes in a numerical way and extracting numerical information from shapes' numerical definitions and representations."
"Analytic geometry is used... in rocketry, space science, and spaceflight."
"Analytic geometry is used in... engineering..."
"Usually, the Cartesian coordinate system is applied to manipulate equations..."
"usually in two and sometimes three dimensions."
"One studies the Euclidean plane (two dimensions) and Euclidean space."
"That the algebra of the real numbers can be employed to yield results about the linear continuum of geometry relies on the Cantor–Dedekind axiom."