Giving Geometry Students An Added Edge In Constructions

Abstract

Several recent articles in this journal and in other NCTM publications indicate a continuing interest in alternatives to the straightedge-and-compass constructions of traditional high school geometry (see Bibliography). A description of various construction tools and techniques may be found in the literature (Eves 1963; Yates 1949), and the history of the topic from the time of the Greeks to the present is a fascinating one. Of the simple construction instruments, one of the least well known is the ruler with two parallel straightedges (a parallel ruler). In 1890, Adler (1906) showed that all the ruler-and-compass constructions can be done using only a ruler with two edges at a fixed angle; the parallel ruler is the special case with angle zero. There does not seem to be a treatment of constructions with the parallel ruler that is at once reasonably complete and accessible to high school geometry students. Most discussions make use of terminology and theorems beyond that usually covered at the high school level, and, further, much of even this material, such as Yates’s Geometrical Tools, is now out of print—surely an undeserved fate for so delightful a book.