• Sunday August 7,2022

Analog Geometry

We explain to you what is the analytical geometry, its history, characteristics and most important formulas. In addition, its various applications.

The analytical geometry allows to graphically represent mathematical equations.
  1. What is the analytical geometry?

The analytical geometry is a branch of mathematics dedicated to the in-depth study of the geometric figures and their respective data, such as areas, distances, volumes, points of intersection, angles of inclination, etc. To do this, he uses basic techniques of mathematical and algebra analysis.

It uses a coordinate system known as the Cartesian Plane, which is two-dimensional and consists of two axes: one of abscissa (x axis) and another of ordinates (y axis). There you can study all the geometric figures that are of our interest, assigning to each point of the same a specific place of coordinates (x, y).

Thus, analytical geometry analyzes usually comprise the mathematical interpretation of a geometric figure, that is, the formulation of equations. Or it may be the opposite: the graphic representation of a mathematical equation. This equivalence is embodied in the formula y = f (x), where f is a function of some kind.

Analytical geometry is a fundamental field of mathematics that is usually part of the high school curriculum.

See also: Cartesian plane

  1. History of analytical geometry

The founder of this field of study is considered the French philosopher René Descartes (1596-1650), with the appendix entitled " La Geometrie " in his famous work Discourse on the method .

However, in the eleventh century, the Persian mathematician Omar Khayyam (c.1048-c.1131) employed similar ideas, which Descartes could hardly know. In other words, both probably invented them on their own.

Given the hermetic ideas of Descartes, the Dutch mathematician Franz van Schooten (1615-1660) and his collaborators expanded, developed and disseminated analytical geometry in the West. It used to be called "Cartesian geometry", to pay tribute to its creator, but that term today prefers to be used to refer only to the appendix written by Descartes.

  1. Applications of analytical geometry

Hanging bridges can be designed thanks to the analytical geometry.

The analytical geometry is one of the most useful conceptual tools of humanity, and today its applications can be seen in, to name a few examples:

  • The suspension bridges . From the old wooden suspension bridges, to its modern versions with steel cables, the geometrical principle of the parabola applies to each of them.
  • The satellite dishes . Parabolic antennas to capture satellite information have the shape of a paraboloid, generated by its reflector that rotates on the axis, chasing the signal. Thanks to the reflection property of the parabola, the antenna disk can reflect the satellite signal to the power supply device.
  • Astronomical observation . Celestial bodies orbit in a path that describes an ellipse, as Johannes Kepler (1571-1630) deduced, and not a circumference, as Copernicus believed (1473-1543). These calculations were possible only using the Analytical Geometry.
  1. Analogue geometry formulas

The analytical geometry offers formulas for the geometric figures.

The geometry studies the geometric figures and obtains their basic equations, such as:

  • The lines are described by the formula ax + by = c .
  • The circles are described by the formula x 2 + y 2 = 4 .
  • The hyperbolas are described by the formula xy = 1 .
  • The parabolas are described by the formula y = ax 2 + bx + c .
  • Ellipses are described by the formula (x 2 / a 2 ) + (y 2 / b 2 ) = 1 .

Continue with: Trigonometry

Interesting Articles

Law of the Offer

Law of the Offer

We explain what the offer law is and what the supply curve is for. In addition, the law of demand and what factors determine it. The law of supply justifies the quantity of a product in the market. What is the law of supply? It is known as the law of the offer, an economic and commercial principle that justifies the quantity available in the market of a particular product (that is, its offer), based on its requirement



We explain what spermatogenesis is and the phases in which this process is divided. In addition, what is azoospermia and oogenesis? Spermatogenesis takes place in the male sex glands. What is spermatogenesis? It is called a spermatogenesis , or spermatocytogenesis , the process of generation or production of sperm , which takes place inside the male sex glands (test Circles), specifically in the seminiferous tubes, coiled ducts of about 30 to 60 cm

Olympic Games

Olympic Games

We explain to you what the olympic games are and what is their origin and history. In addition, we list all the Olympic disciplines. The Olympics date back to Greek antiquity (around the 8th century BC). What are the Olympic Games? The Olympic Games (Olympic Games) (or also the Olympic Games ) are the largest international sporting event in the world , in which athletes representing virtually all of the competitors compete



We explain what xenophobia is, what are its causes and examples. In addition, its relationship with racism and discrimination. The origin of the xenophobia could be assumed at the beginning of human civilization. What is xenophobia? It is called `` xenophobia '' to fear, contempt or hatred of people who come from a nation or a culture different from their own , that is, foreigners, including their cultural manifestations, their language or anything that can Associate with the foreign



We explain what mortality is, what is the mortality rate and what is birth. In addition, infant morbidity and mortality. It is known that human mortality is higher in men than in women. What is mortality? Human beings are mortal, that is, we are going to die, and therefore we have a particular relationship with mortality



We explain to you what a saying is and some short sayings spread in the Spanish language. In addition, some popular sayings. Some sayings offer a solution to deal with dilemmas or complicated moments. What is a refrain? A saying is a saying or phrase that expresses a teaching or moral , often formulated with a rhyme or some other literary figure