# Diagrams, week 2

We are classifying hexagons in the geometry course for future elementary and special ed teachers. There aren’t many established types of hexagons, so we made a few up.

Stacy is a hexagon with exactly three congruent acute angles. A Bob is a hexagon with exactly 5 right angles. We are pretty sure—but have not formalized the argument—that it is impossible for a Stacy to also be a Bob.

### 4 Responses to Diagrams, week 2

1. Will you share your classifications when they’re done? I have a basic math class (freshman) with low reading ability who will need some exposure to basic geometric shapes later this semester. It would be sweet to tell them that it was created by students who were willing to share online.

2. Christopher

Thanks for your interest Leslie. I will indeed. This is my second time through my hexagon classification ritual. It is interesting to see how different groups of students are ending up with different schemes.

Basically, I owe the world a full-blown blog post on this shenanigans, and I’ll get to it soon.

In the meantime, there’s this.

3. Michael Paul Goldenberg

If the class hasn’t formalized their argument about “no hexagon can be both a Bob and a Stacy, what, if anything, has made people informally sure that these are mutually exclusive classifications?

By the way, it remarkable how limited my own geometric imagination can be. I get so caught up with regular polygons that I feel like I need to set off a small explosive device to break my mental log-jam. Thanks for posting the student diagrams.

How soon, I wonder, before you have class members arguing like the ‘characters’ in Lakatos’ PROOFS AND REFUTATIONS and someone proposes a hexagon that another student wishes to declare a “monster”?