Irrational Digits Walk

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Take a irrational digit walk by stepping in the direction given by each successive digit as represented in a chosen base. Compare your digit walk against a different irrational number or against the same number with different direction steps assigned to each digit. The area of the smallest enclosing rectangle for each walk is also presented. For paths with less than 100 steps the vertices along the path can be labeled with each successive digit. For fun, try to find the smallest or largest rectangle or rectangular prism that encloses the 2D or 3D digit walk for a particular irrational number.

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The "base" slider allows you to choose what base to represent the chosen irrational numbers and therefore determines the number of directions for the representation. The "number of digits" slider selects how many digits of the chosen irrational numbers to represent. If 3D is selected so that a three-dimensional representation is presented then the "3D method for directions" pull-down menu allows for a choice of two ways of determining the set of possible directions in 3D. Usually the default of "SpringEmbedding" is the best choice, but for some bases, such as 9, "SpringElectricalEmbedding" gives a better representation. When the base is less than 9 then permutations of the canonical ordering of the directions can be made with the "permutation of directions" slider.

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Contributed by: Noel Patson (March 2011)
Open content licensed under CC BY-NC-SA


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