Math 1512 **I'm seeing stars**

Star Polygons!  Wow...this is quite the procedure to figure out, but it is so neat to see the end result.
*Utilizing a circle, equally spaced points on the circle are connected in an order specific to each problem and completed the star.

For example: n=the # of equally spaced points on the circle
                      d=the dth point to which the segments are drawn

Points ABCDE are spread equally on a circle. For the five points, every two points are connected by a line.  This is denoted {n} ={5 }.   
                                    d       2

                        

   * I found this example on Hyper Flight-Geometric Construction, and thought it would be a great way to put clock templates to use in the classroom for a completely different purpose than telling time!

A five pointed star just for kids. If you can tell time you can sketch this and other stars by hand. Oh, use the template at first.

The illustration above is not copyrighted.

Draw a star, any perfect star. Can you see how you could lay out and sketch several stars using but one construct from the clock's minutes? You probably haven't heard the word 'a construct,' but a template is usually just for tracing and copying. Can you join the points by skipping some? Odd and even number of points makes a big difference. 

After mastering the skill of equally spacing the points on the circle and connecting the segments, the lesson goes into greater detail on calculating the dent angles and point angles.

*the point angles would be best described as the star point angles

*the dent angles would be best described as the angle formed by the bent line between two points that form the point angles

As best described by our text book, (O'Daffer,2008,p694) star shaped polygons have n congruent point angles with measure a, and n congruent dent angles B such that B= (360) + a 

                                                                                                              n

A six pointed, start shaped polygon with point angle 30° is denoted by 630°.  For this measurement the dent angle can be calculated by: (360) + 30°=90°  

                                              6

Constructing the star shaped polygon can be done as follows:

     a. Plot 6 equally spaced points on the circle

     b. Connect two of the points A and B, and construct 45° angles at those two points, which then   produces a 90° dent angle.

     c. Using a compass the other dent angle points can be drawn

I had several circles drawn on many pieces of paper at first when I was starting my drawings and then realized that I could utilize the same circle several times by borrowing my kids marker set to simply draw each star in a different color.