Generalization and analogy in geometry
In the world of study the Generalization and Analogy may open "windows" for the student's mind and give the possibilities of discovering new things, results and concepts. The Generalization and Analogy have played an important role in the history of Geometry, and have a deep impact in examination of mathematical ideas. ^ As an example of generalization and analogy in geometry, starting from a well-known relation involving the weight center of the triangle, we will extend the expression in the general case for an arbitrarily interior point of the triangle in synthetic geometry, vector geometry and coordinates geometry. Moreover, will be given the analogous in 3-D, where in the place of a triangle it will be considered a tetrahedron, in synthetic geometry, vector geometry and coordinates geometry. ^ Building analogies and generalizations is an excellent support for inductive reasoning, often concur in solving problems and is a great benefit for high school and college students in exploring the ways in which mathematicians viewed Geometry. ^ The mathematical contribution of this thesis is the finding of generalization and analogy from a particular geometrical problem. The mathematical results presented are new and they are supported by methodological considerations. ^
Agut, Ioana Ecaterina, "Generalization and analogy in geometry" (2007). ETD Collection for University of Texas, El Paso. AAI1444105.