Yevhen Adoniev, Viktor Vereshchaga. Technique of B-functions algebraic generation

Natural Sciences / Mathematics / Applied Geometry

Submitted on: Sep 29, 2017, 07:08:10

Description: The article presents a unique technology of generating B-functions for B-curves which run through three points, and also demonstrates a possibility to create their infinite set. The basis of the point BN-calculus is the ratio of geometric figures or their properties. Formation of ratio that are the basis of point forms requires the use of B-functions (functions of Baliuba). It is known that B-functions are functions that, if pre-set values of the parameter, are equal to one or zero. The values of parameters for which a zero or one is required are selected from the original geometric figure. There are many ways to define such functions, in particular, the use of geometric schemes that take certain values for the given parameters, but they all have certain drawbacks. The technique proposed by the authors for the algebraic formation of B-functions for any intermediate values of the parameter t can be successfully applied to create a broad class of B-curves. The results of B-function generations for different t parameter values are summarized in this article.