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This talk looks beyond origami as a childhood pastime and an art form and instead, explores origami as a source of many interesting mathematical problems, including one called the fold-and-cut problem. The fold and cut theorem states that it is possible, given a piece of paper and any polygonal shape, to find a series of folds of that paper such that the given shape can be generated with a single cut. This talk explores two proofs of the theorem and and a Ruby implementation of a solver that determines the correct series of folds given any input polygon. There will be a live demo of the program and paper cutting! Help us caption & translate this video! http://amara.org/v/IPww/
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In the talk titled **"Fold, Paper, Scissors..."** by **Amy Wibowo** at the **Ruby on Ales 2016** event, the speaker explores the connection between origami and mathematics, particularly focusing on the **Fold-and-Cut Theorem**. This theorem states that any polygonal shape can be generated from a single cut in a folded piece of paper. Amy begins by discussing her background in computer science and her long-standing interest in origami, which led her to take a unique course on paper folding algorithms. Key Points Discussed: - **Fold-and-Cut Theorem**: This theorem asserts that with appropriate folds, any polygonal shape can be obtained with a single cut from a piece of paper. This notion was historically referenced in a Japanese puzzle book from 1721. - **Demonstration**: Amy demonstrates the theorem using a swan shape created from folded paper. - **Conceptual Understanding**: To achieve the one-cut capability, the speaker explains methods to align the polygon’s edges through various fold configurations, including aligning angles with bisectors. - **Straight Skeleton**: Introducing the concept of a straight skeleton, which is derived by shrinking the polygon while maintaining a fixed distance from its edges, thus assisting in determining how to align edges for cutting purposes. - **Edge Cases in Calculation**: Amy discusses potential complications when essential edges merge or when shapes separate during the folding process. - **Ruby Solver Implementation**: She created a Ruby implementation to visually demonstrate the folding process and share insights on solving for simpler input polygons using graphical tools. - **Limitations of the Straight Skeleton**: It is revealed that although the straight skeleton outlines necessary folds, additional folds are required to ensure that the final shape can be flat-folded. - **Flat-Foldability Theory**: A critical discussion on what it means for shapes to be flat-foldable and the importance of perpendicular lines, also referred to as helper lines, in facilitating this flat-folding. - **Future Work**: Amy expresses her excitement about enhancing her Ruby app further by including additional computational folding theories, and also highlights how these algorithms can apply in fields like space exploration for mechanisms like compacting solar panels. Conclusion: Amy invites the audience to discuss origami, coding, and computer science education further. She encourages those interested in the intersections of these fields to connect during the break. The talk ultimately demonstrates the fascinating interplay of mathematics, art, and technology through origami and practical applications with programming.
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