Origami Equilateral TriangleDate: 04/26/2001 at 00:06:02 From: Oliver Subject: Folding Construction: Equilateral Triangle Hi, I have spent quite a long time trying to figure out how to create an equilateral triangle by folding; not using the sides of a piece of paper and using nothing but your hands and, of course, your brain. I have tried to make a hexagon from a piece of paper by folding, because that would give you six equilateral triangles, but I have had no luck in creating a hexagon from only folding. I would appreciate your help and I am thankful you took the time to read this. Oliver Date: 04/26/2001 at 12:36:34 From: Doctor Peterson Subject: Re: Folding Construction: Equilateral Triangle Hi, Oliver. I'm not quite sure what you mean by "not using the sides"; does that mean the edge of the paper can't form one of the sides of the triangle, or that you can't assume the sides are parallel, or what? I think what I've done probably is allowed, regardless of the interpretation. Origami books teach a standard way to make a 60-degree angle by folding, which you can use to accomplish the task. If you have two parallel lines and a perpendicular to them, form a third parallel midway between the first two, and then fold the perpendicular AB at an angle so that point A lies on the midline (A'), while the fold passes through point B. Then the fold BC will be at the desired angle: B| ---*--------------------------- |\ \ | \ \ | \ \ | \ \ | \ \ ---+-----\-------------+--------- | \ / A' | \ / | \ / | \ / | \ / ---+-----------X--------------- A| C You should be able to prove easily that ABC is half of an equilateral triangle. I folded a triangle in the middle of a piece of paper using this method, with the parallel and perpendicular lines being previously formed folds. - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/ |
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