Point Equation, Line Equation, Plane Equation etc and Point Solution, Line Solution, Plane Solution etc —Expanding Concepts of Equation and Solution with Neutrosophy and Quad-stage Method

Abstract

The concepts of equations and solutions are constantly developed and expanded. With Neutrosophy and Quad-stage method, this paper attempts to expand the concepts of equations and solutions in the way of re- ferring to the concepts of domain of function, the geome- try elements included in domain of function, and the like; and discusses point equation, line equation, plane equa- tion, solid equation, sub-domain equation, whole-domain equation, and the like; as well as point solution, line solu- tion, plane solution, solid solution, sub-domain solution, whole-domain solution, and the like. Where: the point so- lutions may be the solutions of point equation, line equa- tion, plane equation, and the like; similarly, the line solu- tions may be the solutions of point equation, line equa- tion, plane equation, and the like; and so on. This paper focuses on discussing the single point method to deter- mine "point solution". Also, the concepts of equations and solutions are con- stantly developed and expanded. From the historical per- spective, these developments and expansions are mainly processed for the complexity of variables, functional rela- tionships, operation methods, and the like. For example, from elementary mathematical equations develop and ex- pand into secondary mathematical equations, and advanced mathematical equations. Again, from algebra equations develop and expand into geometry equations, trigonomet- ric equations, differential equations, integral equations, and the like. With Neutrosophy and Quad-stage method, this paper considers another thought, and attempts to expand the con- cepts of equations and solutions in the way of referring to the concepts of domain of function, the geometry elements included in domain of function, and the like; and discusses point equation, line equation, plane equation, solid equa- tion, sub-domain equation, whole-domain equation, and the like; as well as point solution, line solution, plane solu- tion, solid solution, sub-domain solution, whole-domain solution, and the like. Where: the point solutions may be the solutions of point equation, line equation, plane equa- tion, and the like; similarly, the line solutions may be the solutions of point equation, line equation, plane equation, and the like; and so on.