In this post, I demonstrate how a pleating system can be controlled to form a semicircle. The first step I took was illustrating the elevation of the semicircle pattern so that I could measure the interior angles accurately. The thick red stroke represents a side view of the paper and its path. The 2 shades of grey represent the bounding semicircles that the pleat system cannot exceed. Throughout the entire arc, I only found 2 different angles, labeled below as Angle_A and Angle_B. I then took those angles and divided each of them by 2 to find the angle needed in the pattern. This simple formula enabled me to accurately plot the correct angles in my pattern. The last diagram is the final pattern. Red indicates a valley fold, blue indicates a mountain fold, and black indicates a cut line. The red and blue can be reversed, as long as it follows the same basic pattern. Notice how the blue-vertical-diagonal lines are much sharper than the red-vertical-diagonal lines. This allows the overall form of the system to curve around itself.
_extended semicircle pleating system_