Iteratively Reflecting a Point in the Sides of a Triangle

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Let , , denote the reflections of a point in the extended sides of a triangle. Reflect a point to get the points , , (iteration 1). Reflect , , to get the six points , , , , , (iteration 2), but for efficiency, skip . Continue, so that at iteration 8, for example, a typical point would be , with the only restriction on the composition of reflections being that no reflection appears twice in a row. At iteration , there are new points, though some may overlap due to a special triangle or special position of .

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You can drag the point and the vertices of the triangle.

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Contributed by: George Beck (January 2016)
Open content licensed under CC BY-NC-SA


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