Study of Overlapped Triangles with the Maximal Overlapped Area under Translation and Rotation
Date:
In 2015, Poom Lertpinyowong, Krittamed Lengrugsa, and I contucted the math project together. The project has been presented in Thaiand’s YSC (Young Scientist Competition) 2015 and the Kolmokorov readings in 2016. The advisors of this work were Professors Sittichoke Som-am from Mahidol Wittayanusorn School and Wacharin Wichiramala from Chulalongkorn University. permalink: /talks/2015-04-01-talk-6
Abstract
Problems about overlapped area are also one of the problems that many mathematicians have studied for decades. In this research, the maximal overlapped area of two arbitrary triangles under translation and rotation are studied. Reflection is not allowed during the process of research. First, we observed that the arrangement of two arbitrary triangles that maximized the overlapped area by using the Geometer’s Sketchpad (GSP) and madw some conjectures. The results showed that the maximal overlapped area of two triangles that one cannot cover another one occurs when one side of each triangle lies on the same line, overlapping each other, or when two triangles form a star-shaped. In the first case, we could find the unique position of the triangles that gives the maximal overlapped area. However, in the second case, it might require more tools to find the desired position.
Here is the link to our paper Study of Overlapped Triangles with the Maximal Overlapped Area under Translation and Rotation, and here to the poster that we used in Thailand’s YSC conference 2015.
More high school project:
Upon my high school graduation, I was required to give a seminar presention on any math paper that I liked. I chose to study Joe DeMaio’s “Which Chessboards have a Closed Knight’s Tour within the Cube?.” Here is the slides of my presentation.
Reference: Which Chessboards have a Closed Knight’s Tour within the Cube?