Fig. 2808.
For finding the lengths of the sides of regular polygons, scales, such as shown in [Figs. 2808] and [2809], may be used, the construction being as follows:—
Fig. 2809.
Draw a horizontal line o p, [Fig. 2809], and at a right angle to it the line o b. Divide these two into inches and eighths of an inch, and draw lines meeting the corresponding divisions on o p, o b. From the point o draw the following lines: A line at 551⁄2 degrees from line o p, which is to serve for polygons having 9 sides; a line at 521⁄2 degrees to serve for polygons having 8 sides; a line at 49 degrees for polygons having 7 sides; a line at 45 degrees for 6 sides; a line at 40 degrees for polygons having 5 sides. It may be added, however, that additional lines may be drawn at the requisite angle for any other number of sides.
The application of the scale is as follows:—
The point o represents the centre of the polygon; hence from o to the requisite line of division on o b represents the radius of the work. From the line o b to the diagonal line (measured along the necessary horizontal line of division) is shown the length of a side of the polygon. From the point o, measured along the line having the requisite degrees of angle, to the horizontal line denoting the radius of the work, gives the diameter across corners of the polygon. The diameter across the flats of a square being given, its diameter across corners will be represented by the length of a line drawn from the necessary line of division on o b to the corresponding line of division on o p. A cylindrical body is to have six sides, its diameter being 2 inches, what will be the length of each side? Now, the radius of the 2-inch circle of the body is 1 inch; hence, find the figure 1 on line o b and measure along the corresponding horizontal line the distance from the 1 to the line of 45 degrees, as denoted by the thickened line.