Though widely regarded as being impossible, constructing a regular heptagon can be done inexactly. You can make a regular heptagon to a tolerence of less than 1/2 of a degree. To construct a Heptagon, draw a circle and a radius AB. Pentasect the segments (divide it equally into 5 parts). Take the piece that is closest to the center of the circle (CA) and divide that segment into 3rds. Take two thirds of that segment and draw an arc through it with center B. Using that compass setting, work your way around the circle using where the arc and circle cross as the center of your next arc, etc. If you've worked carefully, the heptagon will be almost perfect, (in actuality, the compass setting doe not quite get you around the circle all of the way), but it is an excellent aproximation of a heptagon.

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