Tower of Hanoi Set With Four Pegs
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Every Year, My Former Honors Precalculus Teacher Presents A Tower Of Hanoi Demonstration To Her Class. Consisting Of Sets Wooden Base, Wooden Pegs, And Metal Washers, The Set Was Unnecessarily Large And Heavy For One Teacher To Carry. In Addition, The Wooden Pegs And Base Eventually Deformed, Causing Many Pegs To Become Loose. As A Result, I Created A 3D Printed Tower Of Hanoi Set For Her, Mitigating The Problems Associated With Weight, Size, And Durability. This Tower Of Hanoi Set Is Slightly Different Than Most, Having Four Pegs Instead Of The Traditional Three. This Is For My Former Precalculus Teacher'S Class To Determine The Algorithm For The Minimum Number Of Moves Required To Move All Of The Washers From One Side To Another. The Algorithm For Three Pegs Is (2^N) - 1, And Thus Scales With Logarithm Base Two. The Fourth Peg Is There To Show That The Base Of The Logarithm Is Equal To 1 Less Than The Number Of Pegs, Or In This Case With Four Pegs, The Algorithm Using All Four Pegs Scales With Logarithm Base Three. Throughout The Creation Of This Product, I Went Through Various Iterations Of Both The Base And The Washers. Initially, The Base And Pegs Were Separate, Staying Connected With The Power Of Friction. However, This Was Determined To Be Unnecessary And Ineffective, So The Pegs Were Printed With The Base As One Piece. A Small Fillet Was Made Where The Peg And Base Connect To Strengthen That Area. Meanwhile, Washers Were Edited Multiple Times In Order To Have Different Shaped Designs Between Adjacent Washers, And Washers Were Made In An Increasing Radius For Students To Easily Figure Out Where Each Washer Goes.
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