The post two days ago (Junk Food Geometry) focused on edible polygons, but perhaps my favorite examples of grocery store polygons are inedible: the cookie cake tops at Wegmans. The aspect that stood out initially to me is that they are non-standard polygons. The medium sized one, shown to the left, is a heptagon! This cookie top and a pillbox we once found are the only two real-life examples I’ve seen of regular heptagons. Edited to add : of course, within days I found heptagons in a Harry Potter game and in coins.
The large cookie cake tops are regular nonagons, and are unique as far as I know.
But wait, there’s more! If you look at the lines in between, there are a lot of math problems that can be done. For example, you can talk about complete graphs. This can come up in a course on graph theory, but also when discussing the problem of how many handshakes there are in a collection of 7 or 9 people (if every pair shakes hands): each person would be represented by a vertex, and the total number of lines would be the total number of handshakes.
Coloring part of the graph can emphasize other points. This example to the left is one way of leading to the formula for the sum of the interior angles of a polygon. Here you can see the heptagon divided into 5 triangles, each of which has angles summing to 180°, so the sum of the interior angles of a heptagon must be 5·180°=900°.
Finally, given all of the symmetry and interesting shapes apparent, I think a creative problem would be to calculate each of the angles in this figure. Or to calculate the total number of triangles (including overlaps) that appear in the Wegman’s Cookie Cake Tops. Or the total number of quadrilaterals (including overlaps).
Thanks Wegmans! Cool lids!
Photos by Heather Ames Lewis.