In the area of analytical geometry, the concept of locus involves specifying or determining the surface created on a coordinate axis from a given equation. This means that each mathematical equation has a concrete graphic representation, which can be a line, a curve, a parabola or any other figure.
Like any other mathematical idea, the concept of locus is abstract. Mathematical abstraction is based on two basic units: the number and the point. The first is used to make algebraic calculations and the second to understand geometric space. In this sense, loci are sets of points that share the same property.
This proposal allows a better understanding of the space
If we take as a reference a circumference with a radius of one meter, this geometric figure is the locus of points on the plane that are at an equal distance from another specific point, the center of the circumference. In other words, the common distance between all the points that make up the locus is the radius of the circumference.
Analytical geometry studies geometric figures, but this is done through mathematical equations. It is a tool that allows to represent all kinds of situations, make decisions, explain phenomena or know the basic characteristics of a given situation. Ultimately, the shape that expresses a locus helps to describe all kinds of spatial realities.
Analytic geometry in the history of mathematics
Euclidean geometry was developed by the Greek mathematician Euclid in the third century BC. C and focuses on the study of geometric figures and their properties. Analytical geometry comes to be a fusion between classical geometry and algebra.
The founder of this discipline was Descartes, a French philosopher and mathematician of the 17th century. His new vision of geometry was developed in his famous work "The Discourse of Method". For Descartes, mathematics was not properly a science, but a method for understanding science itself. It could be said that with mathematics it was already possible to explain the why of things,
The Cartesian axes (the word Cartesian comes from the name of Descartes in Latin) are the traditional coordinates of any study of analytic geometry. In this sense, an abstract expression of algebraic type is translatable in a certain image, for example a parabola.
Analytic geometry deals with the set of algebraic curves: the ellipse, the circumference, the parabola, the hyperbola or the hyperboloid.
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