**The Four-dimensional Plane Binary
Model and the Explanation of the False Elements of the Euclid Plane**

The elements of the complex plane
C^{2} including the mentioned plane are considered as the R^{2}
real Euclid plane geometric false elements. These elements do not belong to
R^{2}. To obtain the explanation of these elements in R^{2},
first it is considered the isomorphic representation of C^{2} plane on
the four-dimensional space R^{4} and then the binary projective
representation of the space R^{2} on the R^{2} plane.

It has been proved that the simplest
explanation is obtained in the case, when the images of the cyclic points of the
C^{2} plane are considered to be projecting centres in the space
R^{4}.