THE dimension is related to the possibility of obtaining measurements on objects defined within a space. It is possible that some objects cannot be defined in certain spaces because of the number of dimensions what they need and what is offered by these spaces. For the construction of an object to be possible, it must have a number of dimensions equal to or less than space.
Realize that the word space is not just used for the spacethree-dimensional, but for any “place” that is large enough to construct objects. So, the dimensions of space and the spaces themselves are as follows:
One-dimensional space and first dimension
When we say that a space, or object, has only one dimension, we are saying that it is only possible to perform one type of measurement in this space or object. One-dimensional space is the straight.
As straight lines are sets of aligned points that do not curve, are infinite and do not have spaces between the points, so there is no possibility of measuring their width. Thus, it is only possible to measure lengths of parts of them, called straight segments.
Thus, the line is the space which has only one dimension. The objects that can be built in this space are:
1 – Point;
2 – Segmentsinstraight;
3 – Semi-straights and
4 – Other straight lines.
Suppose it is necessary to build a rectangle. This geometric figure has width and length, which are two perpendicular measurements. Note that if we place one side of the rectangle over the one-dimensional space, everything else will be out of space. To build this geometric figure, it will be necessary that there is another space that also includes its width.
rectangle on the straight
Two-dimensional space and second dimension
When the space é two-dimensional, the objects that can be defined in it have up to two dimensions. In this type of space, it is possible to build figures that have length and width. Two-dimensional space is the plane.
Some of the geometric figures that can be defined in the plan are:
1 – Point;
2 – straight, segments in straight and semi-straight;
3 – Polygons generally;
4 – circles and circles.
Thus, the rectangle of the previous image can be defined in the flat, which is the two-dimensional space. Plane geometry is based on the spacetwo-dimensional, therefore, everything that is studied in this discipline is built on a plan.
Now imagine a plane on which one of the bases of a prism. The base of the prism can be defined in the plan, but the rest of the geometric solid, do not. For the prism to be completely built, a space in which there is the possibility of building objects with depth is necessary.
prism about the plan
three-dimensional space and third dimension
O spacethree-dimensional is composed of what we know only as space. This space is infinite in all directions, and in it all geometric figures and solids that are commonly studied during high school can be defined.
In this way, it is possible to define in the spacethree-dimensional all geometric figures that have length, width and depth. In other words, all figures that have three dimensions or less.
fourth dimension
Any object that is included in a spacethree-dimensional where time also counts as a measure, in reality it is in a space with four dimensions. O time is the measure responsible for fourthdimension.
It is possible to say that the dimensions they are infinite (there are also the fifth, sixth, seventh etc.), but they cannot be perceived by the human senses. Therefore, they are not represented geometrically or do not gain a representation as evident as the others.
By Luiz Paulo Moreira
Graduated in Mathematics
Source: Brazil School - https://brasilescola.uol.com.br/o-que-e/matematica/o-que-sao-as-dimensoes-espaco.htm