A Study for Drawing a Regular Eleven Polygons at once with Geogebra using Hilton Pedersen Approximation

This study is the result of research with R&E students at Chungnam Science High School. We questioned whether it would be possible to accurately divide paper into thirds, and studied how to fold lines into equal parts. By expanding this, I was curious about whether it was possible to fold an angle into equal parts, and it was found that it was possible to divide an angle into thirds that could not be constructed by Hilton Pederson approximation. From the relational expression for the size of an exterior angle of a regular polygon, it was inferred that folding an angle into n equal parts is related to the regular n-gon folding problem. Pierpont said that the smallest regular n-gon that cannot be origami is a regular 11 polygon, and he deduced that an 11 polygon could be folded with an approximate folding method that is easier to access than multi-folds. Therefore, the purpose of the study was set as follows. First, by using the Fujimoto approximation method and the Hilton Pederson approximation method, we investigate how to fold an regular 11 polygon approximately, and examine the relationship between the two methods. Second, we look at how to actually implement regular 11 polygon approximation using two methods using GeoGebra. The researcher observed the R&E students through the assignment research guidance and found the following implications. First, it has significance in repeatedly repeating the interaction of asking, answering, arranging, and verifying questions between teachers and students. Second, Students had the experience of solving and generalizing the problem of dividing angles into thirds with a new method called origami. Third, through the experience of actually dividing an angle into 11 parts with origami and GeoGebra, it aroused curiosity in creating coding that reduces errors and solves problems more easily. Fourth, mathematical reasoning ability and problem-solving ability could be improved by experiencing the process of proving and inferring two approximate folds mathematically.