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Counting, Coloring and Computing: Lessons from the Kindergarten
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International Society of Arts, Mathematics and Architecture: Proceedings of the First International Conference (ISAMA)
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The University of the Basque Country, San Sebastian, Spain
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Symmetry, Permutations, Kindergarten method, Frederic Froebel, Polya’s Theorem of Counting, Shape studies
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A systematic inquiry into some of the geometric possibilities inherent in Frederick Froebel's kindergarten method. A series of studies pertaining to counting, coloring and computing issues is proposed. The Froebel building gifts are used as samples for this approach. The symmetry groups and subgroups of these building blocks are identified and their conjugacy classes are established. The cycle indices of the permutation groups of the blocks are used within Polya's theorem of counting to provide all non-equivalent perfect coloring schemes for the blocks. A catalogue of all n-colorings of the blocks for n≤3 is provided as well and its application within a specific computational framework is suggested in the end.
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