The cube has many interesting mathematical properties and has been known to people since ancient times. Representatives of some ancient Greek schools believed that the elementary particles (atoms) that make up our world have the shape of a cube, and mystics and esotericists even deified this figure. And today, representatives of paranoscopy attribute amazing energy properties to the cube.
The cube is an ideal figure, one of the five Platonic solids. Plato's body is
regular multifaceted figure satisfying three conditions:
1. All its edges and faces are equal.
2. The angles between the faces are equal (in a cube, the angles between the faces are equal and are 90 degrees).
3. All the vertices of the figure touch the surface of the sphere described around it.
The exact number of these figures was called by the ancient Greek mathematician Teetet of Athens, and the student of Plato Euclid in the 13th book of the Beginnings gave them a detailed mathematical description.
The ancient Greeks, inclined with the help of quantitative quantities to describe the structure of our world, gave Platonic solids a deep sacred meaning. They believed that each of the figures symbolizes universal principles: a tetrahedron - fire, a cube - earth, an octahedron - air, an icosahedron - water, a dodecahedron - ether. The sphere described around them symbolized perfection, the divine principle.
So, the cube, also called the hexahedron (from the Greek. "Hex" - 6), is a three-dimensional regular geometric figure. It is also called a regular quadrangular prism or rectangular parallelepiped.
The cube has six faces, twelve edges and eight vertices. Other regular polyhedra can be entered into this figure : a tetrahedron (a tetrahedron with faces in the form of triangles), an octahedron (octahedron) and an icosahedron (twenty-sided).
A diagonal of a cube is a segment connecting two vertices symmetric with respect to the center. Knowing the length of the edge of the cube a, we can find the length of the diagonal v: v = a 3.
As mentioned above, a sphere can be inscribed in a cube, while the radius of the inscribed sphere (denoted by r) will be equal to half the length of the edge: r = (1/2) a.
If the sphere is described around the cube, then the radius of the described sphere (we denote it by R) will be: R = (3/2) a.
A fairly common question in school tasks: how to calculate the area
cube surface? It is very simple, just visualize a cube. The surface of the cube consists of six square-shaped faces. Therefore, in order to find the surface area of the cube, you first need to find the area of one of the faces and multiply by their number: S
p = 6a
2.Similar to how we found the surface area of the cube, we calculate the area of its side faces: S b = 4a 2.
From this formula it is clear that the two opposite faces of the cube are the bases, and the other four are the side surfaces.
There are other ways to find the surface area of a cube. Considering the fact that the cube is a rectangular parallelepiped, we can use the concept of three spatial dimensions. This means that the cube, being a three-dimensional figure, has 3 parameters: length (a), width (b) and height (c).
Using these parameters, we calculate the area of the full surface of the cube: S p = 2 (ab + ac + bc).
To calculate the area of the side surface of the cube, the perimeter of the base must be multiplied by the height: S b = 2c (a + b).
The volume of a cube is a product of three components - height, length and width:
V = abc or three adjacent edges: V = a 3.