>It turns out that the accuracy of Mark's construction sort >of falls between the two methods described in the Monthly >article mentioned by Steve.
I also checked out the article mentioned (good article, thanks Steve). The difference between the two methods shown in the article is the number of steps; 9 for the less accurate and 12 for the more accurate. 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.
Of course these are just theoretical accuracies not practical. Mr. Lindberg's construction from the article does have much longer distances between points defining the lines and is therefore more practical in the real world.