MATHEMATICAL MODELS IN EUCLIDEAN GEOMETRY. THE MATHEMATICAL MODEL FOR DETERMINING THE COORDINATES OF GERGONNE'S POINT. THE MATHEMATICAL MODEL OF DETERMINING THE EQUATION OF THE ADAMS CIRCLE
MATHEMATICAL MODELS IN EUCLIDEAN GEOMETRY. THE MATHEMATICAL MODEL FOR DETERMINING THE COORDINATES OF GERGONNE'S POINT. THE MATHEMATICAL MODEL OF DETERMINING THE EQUATION OF THE ADAMS CIRCLE

Summary/Abstract: Mathematics has been, is and will remain a fascinating subject. Learning mathematics using modern means of information technology, pedagogical approaches specific to the challenges of the 21st century, are issues that will be addressed in this article. We live in an era of information explosion, of an accelerated and revolutionary technical progress, that is why it is imperative, obligatory to ask questions, to evaluate the risks, to modify methodologies, concepts and the creation of new learning situations. It is our responsibility to prepare the future, which today means the class of students, instilling in them models of attitudes and behaviors, transmitting to them the knowledge necessary for a world in a continuous change worldwide. Software solutions in eLearning require the existence of a complex online teaching and learning system, through advanced technologies (laptops, smartphones, tablets, e-learning platforms, internet), providing access to different levels of study, depending on user needs. Experimental mathematics continues to gain increasing importance in the engineering sciences, in this sense, computerization and simulation playing increasingly important roles, providing clarity and accuracy in the technique of the act of teaching-experimentation-evaluation. The triangle Gergonne - Euler - Soddy, is a broad topic, which is why in this article we propose the analytical and graphical treatment of determining the coordinates of GERGONNE's point and the equations of parallel lines taken to the sides of the contact triangle, drawing the circle of ADAMS, and through Specialized software is developed a graphical application, highlighting their unique characteristics and properties in Euclidean geometry. Graphic modeling of the triangle ABC, the inscribed circle and its tangent points with the sides of the triangle, determining the coordinates of GERGONNE's point, drawing parallel lines with the sides of the contact triangle, drawing the circle of ADAMS was done with Graph 4.3 software.

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