Knowing the definitions of various objects in geometry is the key to correctly and successfully solving many problems. We will devote this article to answering the questions of what a pyramid is from a geometric point of view and which pyramid is called correct.
Pyramid figure
Hearing the name of this spatial figure, many people recall the great pyramid of Cheops. Indeed, it belongs to the class of geometric objects under consideration. However, the concept of a pyramid is broader. In geometry, a volumetric object is considered under it, which is a polyhedron and consists of one n-gon of arbitrary type and n-triangles intersecting at one point. This point is the top of the pyramid.
To construct the figure in question, it is enough to take an n-gon in the plane and connect all its vertices with a single point selected in space. It is easy to guess that this point will be the top of the pyramid, the n-gon will be its base, and the resulting triangles form a side surface. The figure below shows a quadrangular pyramid.
Types of the pyramid
Before giving a definition of which pyramid is called correct, consider the possible types of this figure.
Depending on how many sides (angles) the base of the pyramid has, triangular, quadrangular and other n-angular figures are distinguished. We will say right away that each of them can be both right and wrong.
An important classification division of the pyramids is the relative position of their top and bottom. If the perpendicular that connects the base with the vertex passes exactly through the center of the n-gon, then such a figure will be a straight pyramid, and the length of the perpendicular is its height. If the base does not cross the perpendicular at its geometric center, then they speak of an inclined figure.
The geometric center of the n-gon was mentioned above. By it is meant such a point of the plane of the polygon, which is the center of its mass, if the polygon is made of a sheet of solid homogeneous material. So, the geometric center of any convex quadrangle is the intersection point of the diagonals, for a triangle it is the intersection point of the medians.
There is another type of classification of pyramids, the knowledge of which is the key to answering the question of which pyramid is called correct. This is a type of polygonal base. It can be right and wrong. Consider this issue later in the article.
Polygons are regular and irregular
In planimetry, a planar convex polygon is called correct, all sides of which are equal to each other and all angles are the same. If at least one of the above conditions is not satisfied, then the polygon is already considered incorrect.
The simplest regular polygon is a triangle with the same sides. The equality of its parties is a reliable criterion for its correctness. The next regular polygon is a square. He is the only one who has his own name. Next are the regular pentagon, which is difficult to find in natural structures, and the hexagon. The shape of a regular hexagon is possessed by some atomic planes in the crystal lattices of metals, bee honeycombs and some other objects in nature. Regular polygons of a higher order are practically not found in nature in any structure.
Which pyramid is called correct?
Above, we examined a number of questions that were intended to prepare you for understanding the answer to the main question of the article. So, when they ask: “Explain which pyramid is called correct,” you should answer that this is such a pyramid in which the base is a regular polygon, and the figure itself is straight.
According to this definition, two criteria for the correctness of the pyramid can be distinguished:
- The right foundation.
- Straight figure.
If you fix the number of sides of the polygon, then with its help you can build an infinite number of pyramids, while changing their height. On the contrary, fixing the height, you can build an infinite number of regular pyramids, increasing the number of sides of the base. Note that if the number of these sides approaches infinity, then the pyramid itself will be transformed into a straight circular cone.
The most famous regular pyramid
Of course, this is the stone giant mentioned in the beginning of the article in Egyptian Giza. The Cheops pyramid in geometry is called regular quadrangular. Its base is a square, the side of which is 230.363 meters. The height of the structure was originally 14.60 meters (currently 136.86 meters). The Cheops pyramid consists of four side faces, which are isosceles triangles with side ribs about 213 meters long. The construction covers an area of 53,000 square meters, that is, 5.3 hectares.
The accuracy of the machining of multi-ton stone blocks from which the structure is made, as well as the accuracy of their adjustment to each other, are still not explained in modern science.