Derivation of the Lorentz transformation for determination of space contraction

The paper demonstrates the incompleteness of the relativistic space contraction formula for space-time coordinates transformation between inertial frames of reference in the existing normally acknowledged version of the theory of special relativity. The reason is the lack of a formula expressing the space contraction in terms of the cosines of the direction of an object’s movement. Thus a modified version of the special relativity theory has been presented through a natural extension of the Lorentz transformation to three dimensions of space. The new transformations are based on the same mathematical operation as the Lorentz transformation, and provide mathematical information similar to that of a single-axis movement. An expression for the new transformation between inertial frames, when there was simultaneous relative motion in three directions, was introduced. The presence of relative motion in three directions between a parallelepiped and an observer (were introduced) made it possible to obtain the formulas of the directions of the ends of the parallelepiped. In fact, the Lorentz transformation was interpreted, revealing transformation of space-time coordinates in three dimensions. This offers ample scope for finding the space contraction within moving frame of reference.