The concepts of semi-straight, semi-plane and half space are closely linked with the concepts of straight, flat and space and they can be quite useful in Geometry to explain some special cases and properties. Note these concepts and some of their most important properties.
semi-rectal
One straight it is an infinite, unlimited set of points, which does not curve at all and has no “holes”. One semi-straight is a portion of a line that starts at any point and goes in one of its directions. We can say that a point divides a line into two semi-straight. The following figure shows this division performed by a point.
At semi-straight above are represented by the capital letter S and an index, formed by the starting point of the ray and the point to which it is directed. So we have the ray SBA and SBC. Note that point A belongs to the entire straight, but does not belong to semi-straight sBC. Point C belongs to the entire line, but it is not on the ray SBA.
Semi-plane
You plans they are infinite and limitless surfaces and also do not curve. You
half planes are obtained when a straight divides a plan into two parts. This means that the plan will begin but not end. One of its properties is the following: if two points A and B are in the same semi-plane, all points of segmentinstraight AB are also on this demiplane.Likewise, if two points A and B are at half planes distinct, the straight which contains A and B is concurrent to the line that divided the plane.
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The following figure shows a part of a flat which was split into two semi-planes and the property discussed above.
You half planes can be used to define convex polygons. To do so, it is enough that the entire polygon be in the same semi-plane formed by each of its sides. See an example of a convex polygon.
Half space
O space is the set of all plans. It is infinite and unlimited for all directions and contains all geometric shapes and figures. It is formed by everything around us.
When a line divides space into two parts, those parts are called half spaces. Imagine that a shoebox is a small portion of space. If this box is halved by a plane, the two halves represent the half spaces. A schematic of this comparison can be seen in the following figure:
You half spaces can be used to determine polyhedra convex. If each face of a polyhedron is in a flat which determines two semi-spaces and the entire polyhedron is contained in one of these semi-spaces, this polyhedron is convex. See an example of a non-convex polyhedron, as one of its faces determines distinct semiplanes that both contain points of the polyhedron.
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. "Semi-rectal, semi-plane and semi-space"; Brazil School. Available in: https://brasilescola.uol.com.br/matematica/semirreta-semiplano-semiespaco.htm. Accessed on June 27, 2021.
