What is a pyramid?
When pronouncing the word "pyramid", the first thing that comes to mind is the images of the famous Egyptian tombs of the pharaohs. They are familiar to us as one of the oldest wonders of the world, monumental structures built by Egyptian architects thousands of years ago. Many secrets and riddles are inseparably associated with them, the solution and explanation of which scientists struggle to this day, giving rise to new versions, disputes and statements. But, despite the disagreements, everyone agrees to one thing, that the pyramid is one of the most important figures in geometry, which has interesting properties.
See also online calculator - Pyramid Surface Calculator.
A pyramid in mathematics is a special polyhedron, it has side faces and a base. A polygonal figure can act as the base of a figure: a square, a triangle, a p-gon. The role of the lateral faces is played by triangles with one beginning - the vertex. The number of corners of the base determines the name of the pyramids: triangular, quadrangular, n-angular.
However, this definition was not used at all times. For example, Euclid once suggested that the term "pyramid" be used to endow certain bodily figures that are limited by planes emanating from a common plane and converging to a single point. Like Heron, Euclid does not give an exact concept of "foundation", due to which there is no exact understanding of the term "pyramid".
Regular pyramids are the most common case of these geometric shapes, they are stable and are found in modern architecture, construction, mechanical engineering and other industries.
A regular one is a pyramid in which a regular polygon is the base, and the height is projected exactly to its center. An equilateral triangle lying at the base forms a tetrahedron, and a square forms a regular 4 sided pyramid, and so on.
To solve any problem involving the correct pyramids, remember that:
• its lateral faces are isosceles triangles, which are equal in area and in all features, base and lateral sides, which are simultaneously ribs;
• around and within the correct type of pyramid, you can describe and inscribe a sphere;
What is a pyramid in terms of mathematics?
• the lateral surface area of a regular pyramid is ½ of the product of the facet height and the perimeter of the figure base. Do not forget that in the correct pyramid are equal to each other, which greatly simplifies finding the answer to many problems;
• lateral faces with the base plane form angles of equal degree measure, therefore, knowing one of them, it is easy to make the necessary calculations.
• a regular triangular pyramid and a regular tetrahedron have significant differences. In the first case, the faces are an isosceles triangle, in the second - equilateral, which should be taken into account when solving a number of problems.