A Few Problems for the Intellectual Development of Students in High Schools and Community Colleges
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It is a truism that mathematics is about relations. In this article we are considering few problems related to the Viviani’s and Routh’s Theorems. All Problems are connected by the relation which exists between the distances of the point inside the triangle to it sides. We show how reasoning about the relations could lead the student’s problem solving process and give easy to understand solutions of the problems. Among the problems being considered are the proof of the Converse to Viviani’s Theorem, the formulas for areas of all figures formed by the sides of triangle and its cevians.
Abstract
It is a truism that mathematics is about relations. In this article we are considering few problems related to the Viviani’s and Routh’s Theorems. All Problems are connected by the relation which exists between the distances of the point inside the triangle to it sides. We show how reasoning about the relations could lead the student’s problem solving process and give easy to understand solutions of the problems. Among the problems being considered are the proof of the Converse to Viviani’s Theorem, the formulas for areas of all figures formed by the sides of triangle and its cevians.
참고문헌 (4)
- Halford, G. S., "The properties of representations used in higher cognitive processes: Developmental implications. in: The Development of Mental Representation: Theories and Applications", pp.147~168 (1999), Erlbaum
- Chen, Zhibo, "The Converse of Viviani’s Theorem", The College Mathematics Journal, 37(5), pp.390~391 (2006)
- Cook, R. J., "Feynman’s Triangle", Mathematical Gazette, 88, pp.299~302 (2004)
- Man, Y.-K., "On Feynman’s Triangle problem and the Routh Theorem", Teaching Mathematics and its Applications: An International Journal of the IMA, 28(1), pp.16~20 (2009)