TY - JOUR

T1 - Periodic orbits on a 120-isosceles triangle, 60-rhombus, 60-90-120-kite, and 30-right triangle

AU - Baer, Benjamin R

AU - Gilani, Faheem

AU - Han, Zhigang

AU - Umble, Ronald

PY - 2022/7/1

Y1 - 2022/7/1

N2 - A periodic orbit on a frictionless billiard table is a piecewise linear path of a billiard ball that begins and ends at the same point with the same angle of incidence. The period of a primitive periodic orbit is the number of times the ball strikes a side of the table as it traverses its trajectory exactly once. In this paper we find and classify the periodic orbits on a billiard table in the shape of a 120-isosceles triangle, a 60-rhombus, a 60-90-120-kite, and a 30-right triangle. In each case, we use the edge tessellation (also known as tiling) of the plane generated by the figure to unfold a periodic orbit into a straight line segment and to derive a formula for its period in terms of the initial angle and initial position.

AB - A periodic orbit on a frictionless billiard table is a piecewise linear path of a billiard ball that begins and ends at the same point with the same angle of incidence. The period of a primitive periodic orbit is the number of times the ball strikes a side of the table as it traverses its trajectory exactly once. In this paper we find and classify the periodic orbits on a billiard table in the shape of a 120-isosceles triangle, a 60-rhombus, a 60-90-120-kite, and a 30-right triangle. In each case, we use the edge tessellation (also known as tiling) of the plane generated by the figure to unfold a periodic orbit into a straight line segment and to derive a formula for its period in terms of the initial angle and initial position.

UR - https://www.pme-math.org/journal/issues.html

M3 - Article

SN - 0031-952X

VL - 16

SP - 321

EP - 331

JO - Pi Mu Epsilon Journal

JF - Pi Mu Epsilon Journal

IS - 6

ER -