Demonstration of the construction of a regular polygon by reducing vertical lines from a point, to a pencil of lines which intersect at one point, and connecting the intersection points that are created.
The polygon shown was prepared by means of the GeoGebra software, in accordance with the required stages of construction. The pencil of lines has 9 lines, but this number may be changed by dragging the point located on the straight line under the inscription “n = 9”. The number of lines in the pencil can be varied in the range 3 ≤ n ≤ 14. For each value of n, the magnitude of the angle between the lines in the pencil appears on the figure.