Varying scales of spatial distance, as known from redshift, are applied to time and analyzed by means of physical action and quantized scaling. This consideration leads to a modified Planckian constant ℎ/c as a force as well as to purely mathematically justified unit scale values for space and for time. The relationships between the special and general theories of relativity are described by means of irreducible basic mathematical building blocks. Relationships between algebra and geometry/topology are applied to both theories of relativity. Thus, the relationships of the special theory of relativity, in contrast to the Minkowski diagram, are geometrically mapped as space and time proportions on the invariant unit circle. The proportions are complementary and dimensionless. The Schwarzschild equation of general relativity, which describes the effect of a central mass, can be reduced to a hyperbola substantially. The presented geometric representation of the general theory of relativity leads to a connection between differential amendment of the spatial distance proportion and the differential amendment of the time proportion. Fundamental for this is the definition of proper time by means of a guide field according to Max von Laue and a variable speed of light. The lemniscate, as an inversion of a hyperbola on the unit circle, is interpreted physically. By inversion, the interior and exterior of the unit circle can be mapped to itself as a transformation via reciprocal radii. The inversion circle itself becomes the event horizon. The interior of the unit circle becomes a black hole with a potential field, the center of which is without change of state, without time and without space. The present as an infinitesimal state change and time direction are discussed.weiterlesen