The Dial of the Circular Complementarity of the Designated and Antidesignated Pairs

Abstract

“Let None But Geometers Enter Here” – that was a motto of Platonic Academy. The founder of the higher geometry chair in Sorbonne M. Chasles said that the geometry “is considered as a basis of mathematical sciences, and the best thinkers of all times considered it, as an excellent exercise in the logics, extremely suitable for development of great minds” [17, p. 515]. Lobachevsky's works have focused scientists’ attention on the problem of the relationship between various geometrical constructions. “When analyzing formation of a principle of compliance in the history of geometry, usually the value of ideas of N.I. Lobachevsky for identification of relationship between Euclidean and not Euclidean geometry is appreciated” [12, p. 234].