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.
Tags: complete graphs, heptagon, nonagon, Wegmans
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January 19, 2008 at 7:56 pm |
[…] Heptagons in Harry Potter! A few nights ago my four-year old pulled out a Harry Potter game in which Hagrid and Harry collect tokens and buy up school supplies in Diagon alley, all the while trying to avoid bumping into Malfoy. We opened it up, and lo and behold I noticed for the first time that several of the tokens are regular heptagons! So much for my theory that heptagons are hard to find. […]
April 16, 2008 at 8:26 pm |
[…] I’ve been looking for regular heptagons lately, ever since I discovered them in cookie-cake lids and pill-boxes, Harry Potter tokens, coins, and architecture. It turns out that there are a whole host of regular […]
June 9, 2008 at 6:32 am |
i wish i could find a regular heptagon somewhere other than at school!!!
i need to find pictures and examples of all 2D and 3D shapes for a project that is due by the 2nd of june!!! please help Super.M
June 9, 2008 at 7:11 am |
If you look under the Polygons category or do a search for heptagon you’ll see what we’ve found. Does that help? There’s more on 2D here than 3D, though.
If there’s another specific shape you’re looking for, let me know and I’ll see what I can come up with.
June 28, 2008 at 12:05 am |
[…] not be too surprising. Wegmans is, after all, the store that thought to put heptagons and nonagons on the design of their cookie cakes (from back in the day when I thought heptagons were unusual, instead of all over the […]