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1. Which shapes pack tightly and completely fill space? Which shapes do not? 2D tiling activity

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2. For shapes that do not completely fill space, is there an optimum arrangement that is most dense? (i.e., leaving the smallest percentage of open space) What is the percentage coverage? 2D tiling activity

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3. Are there any shapes that, when in their most dense packing, do not form a periodic pattern? 2D tiling activity

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4. For an asymmetric shape, like a cork, a trapezoid or spoon, what type of structures can form if you try alternative arrangements? 2D tiling activity

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1. With the help of gravity and agitation, do straws arrange into a lattice? What is the geometry? (photograph it; draw it) straws in container activity

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2. Are there any defects in the lattice? (photograph it; draw it) straws in container activity

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3. Does the shape or the dimensions of the container affect the perfection of the lattice? straws in container activity

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1. Add floating objects of a specific shape one-by-one to a pan of water. As you do so, agitate by tapping the side of the pan. How does the object shape influence the geometry of the structures that form? floating objects

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2. Describe the geometry and symmetry of the structures that form? Are they periodic or random? floating objects

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3. Are the structures that form stable? For a given shape, is there a most stable structure? floating objects

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1. Add identically oriented magnets one- by-one to a pan of water. What pattern forms? magnets glued in floating bottle caps

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2. Add alternately oriented magnets one- by-one to a pan of water. What pattern forms? magnets glued in floating bottle caps

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3. Repeat this experiment with bare magnets on a table top. Do you get a similar result? magnets glued in floating bottle caps

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