id: 06513069
dt: j
an: 2016a.00590
au: Berglund, Jorgen; Taylor, Ron
ti: Bisections and reflections.
so: Math. Mag. 87, No. 4, 284-290 (2014).
py: 2014
pu: Mathematical Association of America (MAA), Washington, DC
la: EN
cc: G40
ut: bisections; reflections; polygons; cyclic quadrilaterals
ci:
li: doi:10.4169/math.mag.87.4.284
ab: 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.
rv: