Plane geometry

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Plane geometry is a branch of geometry dedicated to the study of two-dimensional figures, that is, those that are graphed on a plane.

Plane geometry analyzes elements as one-dimensional such as the line, ray, and segment. Similarly, angles and polygons are part of this field of study.

This branch of geometry often implies the simplification of the world that surrounds us in a plane, so that not all the characteristics of the objects can be studied. For example, you could not analyze all the dimensions of a box, but each of its faces that are quadrilateral.

Plane geometry has its origins in antiquity, its main antecedent being the work The Elements of the Greek mathematician Euclid, dating from the 4th century BC. This is considered one of the most influential texts in history and collects basic notions of elements such as lines and polygons, and we can even find the famous Pythagorean theorem.

Elements of plane geometry

The elements studied by plane geometry are:

  • Straight: It is a one-dimensional element made up of an infinite series of points that go to a single direction, that is, it does not present curves.
  • Ray: Like the line, it is a one-dimensional element that consists of a sequence of points, but it is not indefinite, but rather has an origin and extends to infinity. It can also be defined as the portion of a line defined from a cut-off point.
  • Segment: It is a one-dimensional element made up of points that go in only one direction, but, unlike the ray, it is bounded by an origin point and an end point.
  • Angle: It is the arc that is formed from the intersection or origin of two two-dimensional elements, whether they are straight lines, rays or segments.
  • Polygon: It is a two-dimensional figure formed by a finite series of non-collinear segments (they are not part of the same line), so that they form a closed space. Some examples are squares, rectangles, rhombuses, triangles, or octagons. Polygons can be classified into:
    • Regular: When all its sides and interior angles have the same measure.
    • Irregular: When not all its sides and interior angles are identical.
  • Circumference: It is a flat and closed geometric figure that is characterized because all the points that constitute it are located at the same distance from the center. This constant distance is called the radius. The circumference is also defined as the perimeter of the circle.

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