>My method using a guess takes 9 steps (changing step 2 to a full >circle). A second iteration of my construction, adds only three more >steps (12 total), but increases the accuracy way beyond the 12 step >construction in the article.
On further review of the mentioned article I realize that reseting the compass and drawing the arc count as two steps. This increases the step count in my construction to 11 and 14. Also, to get to this count the order of construction needs to change to minimize resets of the compass. I appologize for any inconvenience and did not mean to missrepresent.