Origami and Geometric Constructions.

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(A comparison between straight edge and compass constructions and origami) In high school geometry students examine the types of geometrical operations that can be performed by using only a straight edge and a compass (SE&C). One learns how to draw a line connecting two points, how to draw circles, how to bisect angles, how to draw perpendicular lines, etc. In fact, you may remember that all SE&C constructions are a sequence …

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…Fusimi, "Let the angle you want to trisect originate from the lower left corner, ..., Unfold step 2 and extend crease L3 to the lower left corner (it should hit it!). The crease L3 will mark the angle (2/3)A." "Trisection of angle by H. Abe", Saiensu (the Japanese version of Scientific American), Oct. 1980 Peter Messer, "First fold a square into thirds, ..., then the ratio X/Y is the desired number, the cube root of two." "Crux Mathematicorum", 1986.