Regular m/n-Polygons


How to make regular m/n-polygon

The following figures show the example of drawing a regular m/n-polygon when m=7 and n=3.

1. Draw a circle.Mark m points on the circle so that the circle is devided into equal arcs. Number the points 1,2,3, ...., m counterclockwise.

2. Draw a line segment between the first point and the n+1 th point.

3. Draw a line segment between n+1 th point and 2n+1 th point.

4. Repeat the same process.

Applet

Activity

  1. Find m and n that constructs the same polygon as m=5 and n=2.
  2. Find the sum of the marked angles when m=5 and n=1.
  3. Find the sum of the marked angles when m=5 and n=2.
  4. Find the sum of the marked angles when m=7 and n=3.
  5. Find the sum of the marked angles when m=7 and n=2.
  6. Find the general formula for the sum of the marked angles.