Ptolemy’s Circumference of the Earth (TOPOI – Towards a Historical Epistemology of Space)

The relationship between the determination of the circumference of the Earth and the geographical mapping performed by Ptolemy in his Geography is discussed. A simple transformation of the Ptolemaic coordinates to the circumference of the Earth measured by Eratosthenes, based on the assumption that the metrical values of the stadion used by both Ptolemy and Eratosthenes are equivalent, drastically improves the positions of the locations given in Ptolemy’s catalogue at least for a great part of the oikoumenē. Comparing the recalculated positions of the identified localities with their actual positions, it turns out that the distances extracted by Ptolemy from ancient sources are remarkably precise. This in turn confirms the high precision of Eratosthenes’s result for the circumference of the Earth. It is shown that many distortions of Ptolemy’s world map can be explained as pure mathematical consequences of a mapping onto the surface of a sphere of wrong size

Astronomical Orientation of the Pyramids and Stellar Alignments

The remarkable degree of accuracy with which some of the Old Kingdom pyramids are oriented towards the cardinal directions is one of the most challenging problems in the history of science. The progressive deviation of the orientation of the 4th Dynasty pyramids from true north was long understood to be a consequence of the pyramids having been aligned to a star whose celestial position changed due to the effect of the general precession of the rotational axis of the Earth. Instead of a single star, recent proposals considered a possible orientation towards some notable vertical or horizontal stellar configurations. The main idea behind these recent attempts at explanation was to justify the gradual deviation of the pyramid alignments by way of the selected target stellar configuration exhibiting a similar azimuthal trend. Considering conventional Egyptian chronologies of this period to be only relative, and the astronomically determined data to be fully reliable, the researchers tried to make the two trends match perfectly by shifting the conventional Old Kingdom chronologies by some, often significant, number of years. Too little attention, however, was paid to allowing for systematic and random errors in the surveying of stars and in the orientation of pyramids towards the observed asterism, which may obfuscate the real accuracy of the methods and conceal the actual targets of observations. In this text, we consider recent proposals and analyze their errors. We propose and discuss two new solutions whose systematic errors are minimal among all the known proposals: one based upon the horizontal alignment of Alioth and Mizar, and another one upon the vertical alignment of Kochab and ζ UMi. In contrast to other methods, the latter pair has the advantage that it could have been observed at lower altitudes. Both variants show an impressive degree of agreement with the trend in the orientation of the pyramids for von Beckerath’s (lower estimates) as well as for Baines and Malek’s chronologies of the period. It appears to us that the preserved Egyptian astronomical diagrams are fully consistent with our new proposals

Properties of the "Orgamax" osteoplastic material made of a demineralized allograft bone

We investigated properties of the “Orgamax” osteoplastic material, which was produced from a demineralized bone, in the treatment of extensive caries, in particular chronic pulpitis of the permanent teeth with unformed roots in children. The “Orgamax” osteoplastic material consists of demineralized bone chips, a collagen additive, and antibiotics. The surface morphology of the “Orgamax” osteoplastic materialis macroporous, with the maximum pore size of 250 [mu]m, whereas the surface morphology of the major component of “Orgamax”, demineralized bone chips, is microporous, with a pore size of 10-20 [mu]m. Material “Orgamax” is used in the treatment of complicated caries, particularly chronic pulpitis of permanent teeth with unformed roots in children. “Orgamax” filling a formed cavity exhibits antimicrobial properties, eliminates inflammation in the dental pulp, and, due to its osteoconductive and osteoinductive properties, undergoes gradual resorption, stimulates regeneration, and provides replacement of the defect with newly formed tissue. The dental pulp viability is completely restored, which ensures the complete formation of tooth roots with root apex closure in the long-term period

UMBRELLA TYPE SURFACE FOR A SPORTS CENTER

The practical examples of umbrella-type shells and domes, methods of their genesis are given in the article, the prospects for future application are considered. Two innovational umbrella type surfaces of six equal elements, proposed for adaptation by Strength of materials department of PFUR, their application illustrated by the sports center roof