  Three different representation of the proper Euclidean geometry are
considered. They differ in the number of basic elements, from which the
geometrical objects are constructed. In E-representation there are three basic
elements (point, segment, angle) and no additional structures. V-representation
contains two basic elements (point, vector) and additional structure: linear
vector space. In sigma-representation there is only one basic element and
additional structure: world function \sigma =\rho^{2}/2, where \rho is the
distance. The concept of distance appears in all representations. However, as a
structure, determining the geometry, the distance appears only in the
sigma-representation. The sigma-representation is most appropriate for
modification of the proper Euclidean geometry. Practically any modification of
the proper Euclidean geometry turns it into multivariant geometry, where there
are many vectors Q_0Q_1, Q_0Q_1^{\prime},..., which are equal to the vector
P_0P_1, but they are not equal between themselves, in general. Concept of
multivariance is very important in application to the space-time geometry. The
real space-time geometry is multivariant. Multivariance of the space-time
geometry is responsible for quantum effects.
