Introduction

It may not occur to contemporary students that architects, surveyors, and drafters once did their work by hand, without the aid of computers. The nineteenth-century drawing instruments used to prepare engineering drawings may seem unusual in their form and materials to a twenty-first century audience. Meanwhile, although they likely used protractors to measure and draw angles in middle school and learned a general proof for bisecting the angle in high school, even mathematics majors may never realize that someone had to divide the circle precisely in order to manufacture instruments that measure angles. The rectangular protractor was a fixture of the engineering toolbox in the nineteenth century (Figure 1). Replicating this device is a convenient way of introducing abstract processes for drawing angles of a certain number of degrees to students in preservice teaching courses and perhaps also at the secondary level. This chapter provides the historical context for rectangular protractors and instructions for making them.

Description and history

A rectangular protractor is simply a device for laying off and measuring angles in which the angle marks are displayed around the three sides of a rectangle instead of along a semicircular arc. English mathematical practitioners invented the protractor at the end of the sixteenth century to aid navigators and surveyors who needed to plot sea courses or to make technical drawings of land and buildings. [1] Although the first protractors were circular in shape, instrument makers throughout Europe began to provide other formats over the next several decades.