Constructing Polygons:
Outlines of mechanical parts are often polygons. For example, in diagram (a), present a plate with a cut in the shape of an irregular octagon 1-8. Via measuring the lengths of an octagon's sides we can transfer or reconstruct it.
Some octagon may be divided into a series of triangles, into that the original octagon is divided. During do this example; triangles can be obtained via drawing diagonals 3-7, 3-8 and 2-8 in diagram (a). They are reconstructed in the given succession.
Sketch a vertical line and transfer to it the measured length 51-61 of the base 5-6 as displays in diagram (b).
Sketch two horizontal lines with points 51 and 61 and transfer the lengths 5-4 and 6-7, respectively.
From points 71 and 41, thus obtained as the centers and along with radius equivalent to the diagonal 7-3 and the side 3-4, respectively, describe two arcs to intersect at point 31 that will be one of the vertices of the essential octagon.
Proceeding in the similar way we determine the vertex 81, then 21 and finally 11, taking like the base lengths 31-71, 31-81, and 21-81, respectively.
In constructing a polygon, the way of orthogonal coordinates may be employed also. In this case, not the lengths of the polygon's sides however the coordinates of its vertices are measured. From the vertices of the octagon or points 1 to 8 in diagram (a), sketch perpendicular to the horizontal line AB. Sketch a horizontal line of convenient length in diagram (c) and mark off on it the distances among the perpendiculars to this line and transfer to them the corresponding distances among the line AB and the vertices or points 1 to 8 of the original octagon displays in diagram (a).
Special Methods of Drawing Some Regular Polygons, Given the Length of any Number of Sides