Abstract
Multidimensional simplices, special cases of which are tetrahedrons and triangles, are widely used both in science and in technical applications. The considered theorems are a generalization to n-dimensional simplices of some statements and theorems for triangles and tetrahedra, which are, respectively, two-dimensional and three-dimensional simplices. The definition of the angle of an n-simplex is given, which is understood as the angle between its two faces. An idea ofthe orientation of the elements of n-simplices relative to each other is introduced. A rule is given for deter- mining the sequence of consideration of vertices in the analytical description of the faces of an n-simplex. A number of theorems have been proved for n-simplices, incl. the cosine theorem, the Pythagorean theorem, the projection theorem, etc. The above theorems are also valid for n-simplices whose order is lower than the order of the space in which they are considered.
Keywords
n-simplex, cosine, projection, tetrahedron, triangle.
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