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 Ratings
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| Reviewed: |
Apr 04, 2004 by Mathematics |
| Overview: |
This applet is designed as a discovery tool with which a student can determine a recursive relationship for a classic problem. |
| Learning Goals: |
This applet provides a visual representation of a classic problem in introductory discrete mathematics, the Tower of Hanoi. |
| Target Student Population: |
Students in an introductory Discrete Mathematics course. |
| Prerequisite Knowledge or Skills: |
The applet is self-explanatory. Knowledge of recursive sequences is required to develop an equation. |
| Type of Material: |
Simulation, animation, and exploration |
| Recommended Uses: |
Guided student experimentation. |
| Technical Requirements: |
Requires a "Java-enabled" browser. |
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| Strengths: |
This is a classic problem in Discrete Mathematics based on a myth of gold and Hindu priests and a world that would disappear when all the disks are relocated. The applet is discovery tool that encourages students to develop appropriate recursive relationships that model the situation.
The rules are to transfer all the disks one by one from the first pole to one of the others without placing a larger disk on top of a smaller one. For those who are beginning, three disks may be used. For those who are developing a strategy, as many as 12 disks are available. The actual classic problem uses 64 disks, too many to experiment with, but easy to determine once the recursive sequence is known. The applet challenges the user with the minimum number of moves required, a timer and the capability of restarting the problem. |
| Concerns: |
None |
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Potential Effectiveness as a Teaching Tool |
Rating:  |
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| Strengths: |
This applet allows the student to experiment. Without a manipulative tool, the student would be hand drawing the possibilities, unable to visualize the use of more than a few disks. With the applet the student is able to utilize additional disks and possibly determine the recursive relationship without assistance. The applet also allows the student to visualize variations on the classic problem of moving the disks from the left pole to the right pole. If a student completes the task but not in the minimal number of moves, the computer responds with, ?Done! Now try for the minimum number of moves.? Hence the student is encouraged to find the optimal solution. This applet is effective in exploring recursive sequences and proof by mathematical induction. |
| Concerns: |
None. |
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Ease of Use for Both Students and Faculty |
| Rating: |
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| Strengths: |
This applet is simple to use. A solution is provided and the speed of visualization is adjustable on a sliding scale. The user may select the number of disks from three to twelve. The use of subproblems to determine the solution of a larger problem is utilized in this applet.
For those who wish to experiment with similar problems,
the applet allows the user to move the disks to the center pole. The minimum number of moves is not calculated, but the user has the ability to experiment without having a solution presented. |
| Concerns: |
None |
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