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http://dx.doi.org/10.7468/jksmee.2018.32.3.257

On the Isoperimetric Problem of Polygons: the mathematical reasoning and proof with the Geometer's Sketchpad  

Choi, Keunbae (Dept. of Math. Edu., Teachers College, Jeju National University)
Publication Information
Communications of Mathematical Education / v.32, no.3, 2018 , pp. 257-273 More about this Journal
Abstract
In this paper, we deal with the isoprimetric problem of polygons from the point of view of learning materials for elementary gifted students. The isoperimetric problem of the polygon of odd degree can be solved by E-transformation(see Figure III-1) and M-transformation(see Figure III-3). But in the case of even degree's polygon, it is quite difficult to solve the problem because of the connected components of diagonals (here we consider the diagonals forming triangle with two adjacent sides of polygon). The primary purpose of this paper is to give an idea to solve the isoperimetric problem of polygons of even degree using the properties of ellipse. This idea is derived from the programs of the Institute of Science Education for Gifted Students in the Jeju National University.
Keywords
isoprimetric problem; polygon; mathematisation; ellipse;
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