Geometry is a word that results from the Greek terms "geo" (earth) and "metron" (measure), whose general meaning is to designate properties related to the position and shape of objects in space.
Geometry is the area of Mathematics dedicated to issues related to shape, size, relative position between figures. or properties of space, dividing into several sub-areas, depending on the methods used to study their problems.
This segment of mathematics covers the laws of figures and the relationship of measurements of geometric surfaces and solids. Measurement relationships such as angle amplitudes, solid volumes, line lengths, and surface areas are used.
There are several types of geometry, such as the descriptive geometry, which studies the representation of spatial objects in a plane, and the plane geometry, a geometry of the two-dimensional scope, as it is defined on a plane. THE geometry of flat figures it is also known as planimetry, while that of geometric solids is known as stereometry.
Learn more about geometric shapes.
Spatial Geometry
THE spatial geometry is defined in a three-dimensional space and therefore aims to study three-dimensional figures. Thus, through spatial geometry it is possible to calculate the volume of a solid.
analytic geometry
THE analytic geometry is a branch of mathematics that uses algebra and mathematical analysis processes and makes a investigation in relation to geometric figures, such as curves and surfaces, and they are represented by equations. A straight line, for example, can be represented by a linear equation of two variables. One of the first scholars of analytic geometry was Descartes.
Know what the Cartesian Plan.
Euclidean geometry
Euclidean (classical) geometry is dedicated to the study of plane or space based on the postulates of Euclid of Alexandria:
- given two distinct points, there is a single straight line connecting them;
- a line segment can be extended indefinitely to build a line;
- given any point and any distance, a circle can be constructed with the center at that point and with a radius equal to the given distance;
- all right angles are the same;
- if a straight line cuts two other straight lines so that the sum of the two interior angles on the same side is less than two straight lines, then these two straight lines, when sufficiently long, intersect on the same side as these two angles.
The fifth postulate was the most controversial throughout history and is equivalent to the axiom of parallels: through a point outside a line, only another line passes parallel to the given line.
Lobachevsky and Riemann (among others) proposed alternatives to the fifth postulate. Lobachevsky postulates that at least two parallel lines pass through a point outside a line, Riemann postulates that through a point outside a line there are no parallel lines.
From Lobachevsky's alternative was born the hyperbolic geometry, from the Riemann alternative was born the Elliptical Geometry or Spherical.
See too:
- Polygon
- Types of triangles