Polygons and Stars

Polygon basics: Based on Erfle, Wensel, Erfle and Polinka “Connecting Geometric Patterns to Numeric Patterns using the Polygons and Stars Excel File,” Spreadsheets in Education, 2021.

The link above takes you to a paper and Excel file (click here for the 1.Polygons and Stars Excel file). This paper is targeted to K-2 and hence can be covered very quickly for those who are beyond these grades. There are two main sheets there, Polygons and Stars, together with supplementary sheets that are of interest mainly to teachers. The first sheet (Polygons) introduces users to n, the number of vertices (and sides) in a regular polygon and the second sheet (Stars) introduces the notion of vertex jumps J which produce continuously drawn stars.

E1. How to read the string art portion of this book: Just The Basics (Chapter 1) . Note: In PwP, the identifier E# identifies this material as being in Chapter # of ESA.

E2. These explainers (short documents) supplement the article above. Those denoted MA (for Mathematical Approach) dive more deeply into the material and may not be accessible to primary school audiences.

  1. On how polygons are drawn: 1.1. How Polygons Are Drawn
  2. Continuously drawn stars: 1.2a. Stars that Work and Stars that Don’t
  3. Sharpest stars: Take 1, 1.3a. Sharpest Stars
  4. About angles: Take 1, 1.4a. Angles of Polygons and Stars
  5. Stars as rotating polygons and stars: 1.5a. Stars as Rotating Polygons
    1. MA. 1.5b. Angle Analysis of Stars as Rotating Polygons
  6. Internal Stars: 1.6a. Stars inside a Star
    1. MA. 1.6b. Analyzing Stars inside a Star
    2.  1.6c. Calculating Triangle Angles using Vertices

Draw a Star is a link to a four slide PowerPoint file (presented as a pdf) that I have used in classes to see how people draw a star. I have used this for multiple classes and my classes include both international and domestic students from various parts of the country. Surprisingly, I have found strong uniformity regarding how most of us draw a star. More than 80% of students I have surveyed start at the same vertex and move around the vertices in the same direction (I won’t tell you which vertex and which direction, but if you try this in your class, my guess is that you will figure it out). See what happens in your class, it only takes a couple of minutes and even college students found it fun.