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 -