Analytical geometry

Analytic geometry is a share of mathematics, which with the help of algebraic means explores the geometric objects based on entered coordinates and coordinate systems.

It is built on the possibility of geometric objects (points, does, crooked, plains, surfaces) to be matched numbers, which distinguish them from each other. Each geometric object is considered as locus of points, T.e. set of all points satisfying a certain condition expressed in formula type.

Analytical geometry

For example, if a coordinate system is introduced in a given plane, then every point of the plane can be represented in a unique way as ordered pair from real numbers relative to the origin and axes of this coordinate system. Every line in the plane is represented by a singular an equation {\displaystyle ax+by+c=0} ({\displaystyle a,b,c} – real numbers), i.e. the line consists of all points whose pairs of coordinates satisfy the equation.

Or another example: the geometric description of the district is the set of points equidistant from a given point. Algebraically, this condition is expressed by the equation {\displaystyle x^{2}+y^{2}=1}, which is satisfied by all points of the circle with coordinates the ordered pair {\displaystyle (x,y)}. Analytic geometry thus gives the tools of geometric objects to map algebraic objects. Te (ordered pairs of numbers, equations) and to investigate their properties.

Analytical geometry

The foundations of this mathematical discipline are posted by René Descartes (1596 – 1650) and Pierre de Fermat (1601 – 1665), and developed in detail by Leonard Euler (1707 – 1783). Initially Johann Bernoulli (1667 – 1748) called this part of mathematics "Cartesian geometry" (in his work of 1692), and the term "analytic" was introduced by Isaac Newton (1643 – 1727) in his work of 1671, published posthumously in 1736.

Analytic geometry served as the basis for new branches of mathematics, such as differential geometry, in which the toolkit of mathematical analysis, and algebraic geometry, where the theory of is applied algebraic systems.