Mathematicians Identify

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Hexaflexagon

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A folded shape made from triangles that has multiple sides you can flip and fold.

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Möbius Strip

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A shape that has only one side and one edge, created by twisting a strip of paper and joining the ends.

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Reuleaux Triangle

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A shape that looks like a triangle but has rounded corners, maintaining the same width everywhere.

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Twisted Cylinder

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A shape made by twisting a strip of paper twice before joining the ends, making it hard to distinguish the inside from the outside.

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Fixed-width shapes

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Shapes that maintain the same width regardless of orientation, useful in geometry and engineering.

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Properties of Hexaflexagons

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They can be folded and flipped to reveal different faces, demonstrating geometric flexibility.

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Applications of Möbius Strips

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Used in various fields such as mathematics, art, and engineering to illustrate concepts of non-orientability.

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Real-world examples of Reuleaux Triangles

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Used in drill bits and other tools where a constant width is required.

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Characteristics of Twisted Cylinders

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They challenge traditional notions of inside and outside in geometry.

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Importance of Fixed-width shapes in design

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They optimize space and material usage in engineering and architecture.