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Interactive geometry programs such as GeoGebra and CaRMetal are powerful tools for learning about geometry. You can use them to explore the basic principles of paper-folding (Origami). I learned about the mathematics of folding paper circles from: "Circle Origami Axioms", on Maria Droujkova's Math 2.0 Interest Group. I wondered if a rule for folding paper circles would apply to other shapes, and chose to explore triangles. An interesting configuration of folds is discovered when the triangle is equilateral. Using simple tricks, such as hidden line removal, the geometry diagram simulates a folded piece of paper. You can download my paper "Generalisation of a Paper-Folding Axiom and its Exploration using I..." and the data files for Geogebra, Dr Geo and CaRMetal from i2geo.net. You can also download the PDF file from Scribd.com. The paper is condensed into a slideshow on SlideShare.net.
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