Geometry: An Interactive Journey to Mastery

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,QWKLVVHULHVRISUREOHPVDEDOOLVVKRWDWDƒDQJOHIURPWKHWRSOHIWFRUQHURIDQn × m billiards table. The

ball traverses the diagonals of the individual squares marked on the table, bouncing off the sides of the tables at

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fall into if it entered that corner.

)LJXUH shows the beginning of the path of a ball on a 5 × 9 table.

 Trace the motion of the ball in the diagram, and verify that the ball eventually falls into the

bottom-right corner.

 Draw examples of 3 × 5, 5 × 9, and 7 × 3 tables. Does a ball shot from the top-left corner land in the

bottom-right corner in each case?

 Must a ball on a 103 × 5001 table also land in the bottom-right corner? Explain. Is this the case for all

odd × odd tables?

Problems

Figure 27.5