Origami and Geometric Constructions.

(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 …

…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.