Four dogs, A, B, C, and D are located at the vertices of a square. They start to run at the same time and at the same speed. A runs toward B, B runs toward C, C runs toward D, and D runs toward A.
Eventually they all meet in the center of the square. Why?
What are the paths followed by the four dogs?
What is the length of the path followed by each dog?
How many times does the path of each of the dogs cross a diagonal of the square? at what angle?
Suggestion: Implement the animation on a GSP sketch. Vary the speed of the animation to obtain different configurations. One GSP Sketch.EXTENSIONS:
How is the problem changes it there are 3 dogs beginning at the vertices on an equilateral triangle?
What if there are 5 dogs beginning at the vertices of a regular pentagon?
What if there are 4 dogs beginning at the vertices of a rectangle that is n ft by 2n ft?
Reference:
Steinhaus, H. (1969) Mathematical Snapshots. Third American Edition. Originally published in 1950. New York: Oxford University Press.