# Regular Pentagons (with Limits)

- Author:
- A B Cron

## Regular Polygon Definitions with Limits (originally June 2014)

## General Instructions

Regular polygons are common in Geometry. This lesson begins with
demonstrating examples of some common regular polygons. All polygons have
a center which with regular polygons allow us to circumscribe or
inscribe a circles with the polygon. The radius of the circumscribed
circle is from this center to a vertex of the polygon. The distance from
the center of the polygon to the midpoint of a side is called the
apothem, or the radius of the inscribed circle.

## Additional Information

Excellent Resource: http://www.mathopenref.com/polygonregular.html
Names of Polygons: https://www.mathsisfun.com/geometry/polygons.html
This lesson can be extended to "Looking at LTF Polygons in a Circle",
this applet will assist in completing the exercise.
The circle on the screen is a unit circle; however, you can change the
radius to match any value you measure up to 8 units. The table will give
the results up to a 100-gon.
Table format from LTF activity on Limits of a Polygon in a Circle.
Triangle ABC is triangle formed by the point A and any side of the
polygon. The area of the polygon is the number of sides times the area
of Triangle ABC.
If you expand the radius of the circle and can no longer see the figure,
click mouse on point A and scroll the figure in and out...
Fred Gustavson suggest to refer to Archimedes on this subject. He circumscribed and inscribed
regular polygons sides 6 to 96 in doubling steps around a circle. By direct computation he showed that
3 10/71<π<3 1/7.