Euclidean constructions : alternate tools to the traditional compass and straightedge

Includes bibliographical references (pages 110-112)This paper examines the question whether there are\ud alternate tools to the traditional compass and straightedge\ud capable of performing the same constructions. The\ud tools considered are: rusty compass and straightedge,\ud compass alone, straightedge alone (given one fixed circle\ud and its center), double-edged straightedge with parallel\ud sides, Mira, and paper folding. These tools are proved\ud to be adequate to perform all Euclidean constructions\ud (all constructions possible using a compass and straightedge).\ud The criteria for demonstrating this adequacy\ud are the "intersection criteria", i.e., determining the\ud points of intersection of any two lines, any line and\ud any circle, and any two circles.\ud The tools are then compared quantitatively to\ud determine the tool most easily used.\ud is used to make this comparison.\ud Geometrography\ud Finally the question of which tools are capable of\ud performing more constructions than are possible using\ud only a compass and straightedge is considered. The\ud ability of the Mira and paper folding to trisect any\ud angle, an impossible construction using compass and\ud straightedge, is demonstrated