The guideline is that line, surface or volume that determines the generation of a geometric figure. This, when another line, surface or volume revolves around it, which is called the generatrix.
In other words, the generatrix moves around the directrix. For example, if the directrix is a circle and the generatrix is a line, a cylindrical surface will be formed (about which we will talk later).
The concept of a directrix is relevant when we define, for example, solids of revolution. These are geometric bodies that can be formed by rotating a flat surface as a function of a line called the axis.
It should be noted that the axis is different from the guideline. In the case of a sphere, for example, the axis is the invisible line that passes through the center of the figure, but the directrix is the circumference that constitutes its contour.
In the same way, it is important to mention that there is the particular case of the ruled surface. This is the one generated by a line of changing direction (the generatrix) that revolves around one or more curves (the guidelines).
Another point to keep in mind is that, as understood in the explanation of this article, the guideline is a concept of the geometry of space. That is, that branch of geometry that is characterized by studying three-dimensional figures.
Directrix in solids of revolution
Although we have already mentioned an example (that of the cylinder), we will detail what the guidelines of the solids of revolution are and how they are related to their generatrix:
- Cone: In the case of the cone, this would be the perimeter of the base of the figure, which is a circumference or an ellipse.
- Cylinder: In this case, it is the circumference that forms the base of the figure, the generatrix being a straight line that revolves around it. If the directrix and the generatrix are perpendicular, the cylinder is straight. Otherwise, the cylinder is oblique.
- Sphere: The directrix, in this case, is the circumference around which the semicircle, which is the generatrix, rotates.
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