A regular Septagon (also called a Heptagon) is a polygon with seven congruent sides and seven congruent angles.

## The approximate construction of a regular Septagon.

The regular septagon can not be constructed by ruler and compass constructions. However, a good approximation can be given with the following procedure.

Show that

BCcan not be the side of the regular septagon.Determine an estimate of how much error there is in using

BCfor the side of a regular septagon inscribed in a circle of radiusr.

Some buildings that have a base of a regular septagon.

Catholic Church in Cherokee, North Carolina

The Calatrava Chicago Spire building

The pictures are artists renderings of the building for which construction started in 2007. The building was to have 124 stories with apartments and business sites. The downturn in the economy caused work to stop in 2008 and in 2010 it was decided that the building would not be finished.

Cherokee Indian Council House

Another Cherokee House

Reproductions. Original structures have not survived.