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Triangle Puzzle

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Author:Evelyn Sander, Geometry Forum Archives, The Geometry Center
Description: Pick an arbitrary point in the interior of an equilateral triangle. Now go halfway towards one of the three vertices (you get to pick which vertex). Now you are at a new point in the triangle. Again go halfway towards any vertex. Continue this process. What is the long-term behavior - what points can you reach after repeating this process an arbitrarily large number of times? ...they form a Sierpinski gasket.
Levels: High School (9-12), College
Languages: English
Resource Types: Problems/Puzzles
Math Topics: Triangles and Other Polygons

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