Definition

Noun: * Analytical Geometry: A branch of mathematics that uses algebraic methods and a coordinate system to study and solve problems related to geometric figures and their properties. It establishes a connection between algebraic equations and geometric curves or shapes.

Usage

Analytical geometry is used to describe geometric shapes with equations, calculate distances and angles, and prove geometric theorems using algebraic manipulation. * The course on analytical geometry covers conic sections like circles, ellipses, and parabolas. * In analytical geometry, a line can be represented by the equation y = mx + b. * The problem was solved using principles of analytical geometry.

Advanced Usage

• "to apply analytical geometry": To use the methods of coordinate geometry to solve a problem.
  • We can apply analytical geometry to find the intersection point of these two lines.
• "foundations of analytical geometry": The fundamental principles and concepts upon which the subject is built.
  • Descartes and Fermat are credited with laying the foundations of analytical geometry.

Variants and Related Words

• Coordinate Geometry: A direct synonym for analytical geometry.
• Cartesian Geometry: Another synonym, named after the philosopher and mathematician René Descartes.
• Analytic (adj): Pertaining to analysis or analytical methods. (Note: "Analytic geometry" is a common variant spelling of "analytical geometry").

Synonyms

• Coordinate Geometry
• Cartesian Geometry

Related Phrases

• Coordinate System: The framework (like the x-y plane) used in analytical geometry to define the position of points.
• Algebraic Representation: The expression of a geometric figure using an equation.

Noun

1. the use of algebra to study geometric properties; operates on symbols defined in a coordinate system