Abstract. The results of extensive mathematical observations of the manifestation of astrometric-geodetic parameters of the Earth and the Moon in the parameters of rectangular triangles with legs 10 and 19, 3 and 4, 81 and 100, as well as in the English system of measures of length are described. The purpose of the description is to show the unknown numerical regularities of the space-time (s-t) values of the bodies of adjacent space, reflected in the ancient system of knowledge. Analysis of the composition of the numbers of angles and sides of three triangles made it possible to detect in them a compact manifestation of the principal s-t values of the Earth and the Moon.
In the first triangle, s-t values and their ratios in simple terms correspond with one of the royal cubits (measure of length) of Ancient Egypt with base value of 0.526315789 (real meter), or the reciprocal value of the number 1.9. This cubit is considered the standard of the sarcophagi of the First and Second pyramids of Giza. S-t values appear in the triangle so that their values correlate with a series of royal cubit numbers approaching its base value, which allowed using the cubit as one of the universal measures on the Earth. Together with the number of the cubit in the triangle, the Meton number (6939.63515) is displayed, as well as in the triangle 3 : 4 : 5 this number (6939.495) is found, which represents the time cycles of the Moon and the Earth and their ratios.
The second and third triangles are included as triangles of the apothem, respectively, into the Second and Third (smaller) pyramids of Giza. In the triangle of the apothem of the Second Pyramid, a parametric model of the orbital motion of the Moon and its synodic day was found, as in the adjacent triangles of the face and edge of the Second Pyramid, parametric models of the orbital motion of the Earth and its day were previously discovered. This establishes that the parameters of the time cycles of the Earth and the Moon are geometrically related to each other by the sector of the Second Pyramid, consisting of three adjacent right-angled triangles.
In the Third Pyramid, the apothem triangle with the legs 81 and 100 with its hypotenuse represents the ancient cosmic principle of yonilinga, expressed in terms of the product of the polar radius of the Earth and its angular rate of rotation. The length of the hypotenuse, which is 83.8 real meters, seems to be used as another universal measure on Earth. In the pyramid, a wide range of numbers representing the astrometric-geodetic parameters of the Earth, related to its axial rotation, to the motion along the orbit and the precession of the axis, to the spheroid of the Earth, as well as to the rotations of the Moon (around its axis and the Earth) is also found. In the parameters of the pyramid, numbers from the English system of measures of length appear numerically, which indicates the origin of this system of measures. The geometry of the apothem triangles, as well as edges and faces of the pyramid determine a number close to the value of the modern English foot, and this number of real meters can be considered a universal earthly measure of length.
It is still too early to talk about the complete and final decoding-recognition of the geometry of the pyramids of Giza, but on the basis of the studies carried out, it can be asserted that the choice of the pyramids’ geometry is due to certain relationships and interrelations of the s-t values of, first and foremost, the Earth and the Moon, the numbers of which form a definite astronomical numerical network, and it is studies precisely in the astrometric-geodesic direction that can result in complete decoding. In a preliminary way, we can point to the possible existence of a single cosmic concept of the three pyramids, consisting in the displayed in them principle of triplicity referred to space, time and their interaction, according to the model from Nothing. On the whole, it can be argued that a single key has been found for the recognition of the geometry of the Giza pyramidal complex and, as a consequence, for the recognition of the English system of measures. This recognition can mean not only a historical value and the fact of establishing contact with the preceding civilization. Detection of series of numbers of s-t values and their manifestation in the geometry of pyramids indicates the existence of certain fundamental laws of the world order, and these triangles, representing some of the initiating principles, can be fragments of the geometry of the model from Nothing. Superseries of the numbers of s-t values are also found.
Perceptions of numbers of cosmogenic and technogenic civilizations are compared. The conclusion is drawn that in the first case the numbers are perceived more in collectivistic and qualitative aspects, and in the second case in individualistic and quantitative aspects.
Keywords: right-angled triangle, astrometric parameter, geodesic parameter, Giza pyramidal complex, English system of length measures, astronomical series of numbers, astronomical numerical network, universal astronomical number, universal space-time measure, Meton cycle, cosmic principle of yonilinga, astrogeometronumerology, model from Nothing, the fetish of numbers.