Part: Analytic Geometry

Analytic geometry is a mathematical discipline describing geometrical figures using equations and numbers. The figures (e.g. points, circles, parables, planes, straight lines, etc.) are interpreted as sets of points in a coordinate system. Depending on the number of dimensions of the coordinate system, every point can be described using one, two, three or more coordinates. Usually, the study is focused on two or three dimensions and the corresponding subdisciplines are called planar analytic geometry, respectively spacial analytic geometry.

The sets of points forming the figures in the coordinate systems turn out to be solutions of some types of equations. In this sense, each type of these equations corresponds to some specific type of a geometric figure. In this sense, analytic geometry is able to "translate" geometric phenomena into the language of algebra and vice versa.

  1. Definition: Points in a Coordinate System - Number Spaces
  2. Definition: Points vs. Vectors in a Number Space
  3. Definition: Describing a Straight Line Using Two Vectors
  4. Lemma: Equivalence of Different Descriptions of a Straight Line Using Two Vectors
  5. Theorem: Existence and Uniqueness of a Straight Line Through Two Points
  6. Proposition: Presentation of a Straight Line in a Plane as a Linear Equation
  7. Definition: Hyperplane of a Number Space

Theorems: 1

Thank you to the contributors under CC BY-SA 4.0!