Definition

Noun: - A branch of mathematics: Analytic geometry is the study of geometry using a coordinate system and the principles of algebra. It involves representing geometric shapes as equations and using algebraic operations to solve geometric problems.

Usage

Analytic geometry provides a powerful link between algebra and geometry. It is used to describe points, lines, curves, and shapes using numerical coordinates and algebraic formulas. - Analytic geometry is a fundamental subject for students of mathematics and physics. - The problem was solved efficiently using the methods of analytic geometry.

Examples

• In a sentence as a subject:
  • Analytic geometry was pioneered by René Descartes.
  • Analytic geometry allows the precise description of a circle's location and size.
• In a sentence as an object:
  • The engineer applied analytic geometry to design the component.
  • We studied analytic geometry in our first-year calculus course.

Advanced Usage

• "the tools of analytic geometry": Refers to the specific methods (like coordinate systems and equations) used in this field.
  • Using the tools of analytic geometry, we can find the intersection of two lines.
• "principles of analytic geometry": Refers to the foundational concepts of the subject.
  • The solution relies on the basic principles of analytic geometry.

Variants and Related Words

• Coordinate geometry: A direct synonym for analytic geometry.
• Cartesian geometry: Another term for analytic geometry, named after René Descartes.
• Analytical: (Adjective) Relating to or using analysis or logical reasoning. While related, this is a broader term not specific to geometry.

Synonyms

• Coordinate geometry
• Cartesian geometry

Related Phrases

• "algebraic geometry": A more advanced field of mathematics that uses abstract algebraic techniques to study geometric objects. It is related to but distinct from analytic geometry.
• "vector analysis": A field that often uses coordinate systems and is built upon the foundation of analytic geometry.

Noun

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