Pentagon

In geometry, a pentagon is a five-sided polygon. Just like the pentagram it hides the golden mean in a multitude of ways.

The process of drawing a pentagon was described by Euclid in Elements c:a 500 B.C.

• Draw a horizontal line with a circle the size of your desired pentagon that has its center on this line.
• Put your compasses' needle where the circles' circumference crosses the horizontal line, and draw a half-circle through the center of your first circle, crossing the circumference of the first circle in two places. Draw a vertical line through the points where the half-circle crosses the first circle. This line will pass through a point we call (a).
• Open your compasses so that you can, when placing the needle in the two intersections between the horizontal line and the first circle, draw a small cross above and below the horizontal line, outside the first circle, with one line of the cross from each point. If you join these crosses you will obtain a line perpendicular to the horizontal line, also passing through the center of the first circle. The point where this line crosses the circumference of the first circle on the top, we call (b). This is the first corner of the pentagon.
• Put the compasses' needle in (a) and drawing a circle segment passing through (b) and down through the horizontal line, obtaining a point on this line we call (c).
• Put the needle in (b) and pass a circle segment through (c) and the first circle. These points on the first circle are the second and third corners of the pentagon.
• Without extending the compasses, put its needle in the second and third corners, and draw circle segments passing through the first circle to find the two remaining corners.
• Join the corners and you have a pentagon. By joining the corners by two more lines you obtain a pentagram.