Welcome to Playing with Polygons, PwP, a website that I am using to organize materials for an interactive book I am writing based upon a series of interrelated Excel files. These files use the vertices of regular polygons (obtained by connecting successive points that are equally spaced around a circle) to frame each image and are controlled by Up/Down 🞁/🞃 Scroll Arrows and Click-Boxes ☑ so users need not be familiar with Excel to play with the files. By playing with the arrows and watching what happens, even very young users begin to see patterns … that is, they begin to make connections between numbers and images.
Such interactive play strengthens mathematical intuition and encourages learning even in the absence of formal discussion of a topic. To take the simplest example, if each regular polygon with n sides has a vertex at the top of the circle then the first few look like: 🜂 🝔 ⬠ ⬡ and we see that the bottom of the polygon will be flat if n is odd and pointed if n is even. Kindergartners can see this pattern … two years before even and odd is formally introduced into the curriculum according to Common Core State Standards, CCSS, 2.OA.3, or when that alternating pattern is more forcefully examined in grade four according to 4.OA.5, Generate and analyze patterns.
There are multiple audiences for PwP. One could consider PwP a book of recreational mathematics, not mathematical research or a mathematics textbook. It is certainly useful for those interested in mathematics education. But it would also be helpful in bridging the gap between mathematics and art. Although mathematics and art teachers in K-12 could certainly incorporate these materials into their classroom, they were initially developed for independent exploration outside the classroom. The idea was to create materials that were easy enough to use that students would want to explore each model and create their own patterns by manipulating the parameters of each model.
This link shows the general structure of PwP including main worksheets within each file. Current versions of the files as well as links to papers that have been created to supplement these files are located on separate pages. This link is to the book proposal itself; the first two pages lay out the overall structure and rationale, the remaining pages show images from each file to provide a glimpse of the range of images available using each file. K-12 teachers wishing to incorporate these materials into their classrooms will find ancillary materials such as short videos or lesson plans organized by grade. This link provides a table showing suggested topic coverage by day for different grades.