Point, line, plane and space

Point, line, plane and space are the notionsprimitive gives Geometry. These objects have no definition, but they must exist to support the geometric definitions. Although it is not possible to define these objects, it is possible to discuss their characteristics, properties and their uses for Geometry.

Point

O Score it has no shape or dimension. This means the point is an object. dimensionless. One of the most important uses of the point refers to the localizationgeographic. You points they are the objects that best represent locations because they offer precision. If, instead of a period, we used a square, where in the square would the location be precisely?

straight

At straight are sets of points that do not curve. They are infinite for both directions. As these points are not in the same place, it is possible to measure the distance between them. However, as the stitches still don't have dimension or shape, it is not possible to measure its width. Therefore, we say that the line has only one dimension or that it is one-dimensional.

The following figure shows trying to draw a square over a straight. Note that most of the square “does not fit” on the line. For this reason, it is necessary to define a new location where it can be drawn.

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Flat

O flat it is a set of aligned lines and therefore it is also a set of points. The object formed by this alignment of straight it is a flat surface that does not curve and is infinite in all directions.

On a plane, it is possible to draw figures that, in addition to length, have width. The figure below shows a cube about a plan. Note that the base of the cube, which is a square and has two dimensions, fits perfectly into the plan. However, the depth of this solid is not contemplated.

Space

O space it's the place where all known geometry up to high school takes place. It is formed by the alignment of plans, which are placed side by side until filling the entire space. It is infinite in all directions and contains all flat and three-dimensional geometric shapes and shapes.

As it is formed by planes, the space involves the thirddimension, needed to contain the entire cube of the previous figure. It is in the third dimension that figures that have width, length and depth are constructed.

By Luiz Paulo Moreira
Graduated in Mathematics

Would you like to reference this text in a school or academic work? Look:

SILVA, Luiz Paulo Moreira. "Point, straight, plane and space"; Brazil School. Available in: https://brasilescola.uol.com.br/matematica/ponto-reta-plano-espaco.htm. Accessed on June 27, 2021.