Regular Polygons (with Limits)

Author:
A B Cron

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.

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.