### Geometry graphical variationsof the circular conjugate problems

Pages 137-146

In civil engineering and architectural design the coupling of circular curves are of great importance. There are different requirements for their practical application, including the possibility of approximation of the curves of higher order. The present article contains a brief excursion into the axiomatic description of the properties and concepts uniting the geometric graphics of a circular, a direct and a point into various compositions. One of the main conjunction theorems is presented, which defines the position and properties of orthoelements of pairing and the sequence of mating arcs using symmetry. The content of the theorem is commented in the form of proof by contradiction, in the form of geometric graphical operations that are naturally consistent with the analytical results. The examples are given of the circular conjunctions closed into oval shapes with a slight difference in the algorithms of composition construction. A particular case of the present configuration is a linear model of squaring the circle, the circle when the medial conjunction coincides with the base circle squaring. Here, the rhomb figure is presented as a basic square and the four successively conjugated circles have their centers at the vertices of squaring, their area are equiareals. Then, the straight “tapered” circular number and variations of its geometry graphical construction are analyzed. The summary results of the considered material are as follows. The main qualitative, quantitative, and typical examples of the circular conjunctions allow competently and variably solving certain problems of geometry graphics in the design process of civil engineering, architecture and applied domestic objects, items and personal things.

DOI: 10.22227/1997-0935.2015.7.137-146

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