
06513069
j
2016a.00590
Berglund, Jorgen
Taylor, Ron
Bisections and reflections.
Math. Mag. 87, No. 4, 284290 (2014).
2014
Mathematical Association of America (MAA), Washington, DC
EN
G40
bisections
reflections
polygons
cyclic quadrilaterals
doi:10.4169/math.mag.87.4.284
Summary: We consider the process of reflecting a point on the side of a polygon across successive angle bisectors. As we iterate this process, we find an interesting and sometimes periodic pattern. In particular, we show that for any polygon with an odd number of sides, a point on any side is returned to its original position by a finite number of reflections that is either one or two times the number of sides. Additionally, for a polygon with an even number of sides, a point is guaranteed to return to its original position as soon as possible or not at all.