The Minimum Distance Energy for Polygonal Unknots
نویسندگان
چکیده
This paper investigates the energy UMD of polygonal unknots. It provides equations for finding the energy for any planar regular n-gon and for any m-gon, where the vertices lie on the vertices of a regular m 2 -gon and on the midpoints of each edge. In addition, we show that a regular 4-gon minimizes the energy for any quadrilateral. Finally, this paper includes a proof showing that if we have a regular n-gon, Rn, inscribed in a circle and can move only one vertex of Rn, v, along the circle between its two adjacent vertices, then the UMD is minimized when v is a vertex on Rn.
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