Additional Math Pages & Resources

Wednesday, September 1, 2010

Wearing many hats, Part III

Let's look at all the types of hats we have again, and this time we'll use more math to classify them.


You might call this head gear by different names (perhaps GOOFY comes to mind for some?) because we have hats with ear flaps and hats with brims, hats with rolled edges and caps with bills. Driving caps and riding helmets, rain hats, snow beanies and fishing caps.

How can math help us understand and classify this head gear?

Yesterday we classified the colors and types of head gear. Today we could look at the method of retaining the hat on the head:
  • Hats can rely on gravity - see the driving cap in the middle row
  • Hats may have straps or strings that tie - see the first hat in the first and third rows. The helmet has straps too but they don't show in this photo
  • Hats like the snow beanie on the bottom row, and the red hat in the top row, rely on elasticity in the fabric (stretch) to stay on
  • Hat may be precisely fitted, like the top row middle, and rely on a bit of friction on the brow
  • Hats may use an elastic strap that can be tightened, like the last one - the fishing hat
  • Most caps have a strap across the back of the head that's adjustable
What are the purposes of hats? Can we classify some of those?
  • Style
  • Indicate that you belong to a certain people group (tribe, fan club, etc.)
  • Protection from weather or the elements (rain, cold, sun, heat, etc.)
  • Protection from accidents (helmets)
  • Advertising
Here's a challenge for you. Yesterday we created a grid to display the colors and types of hats. Now we are adding retention methods and purpose. Can we display all these characteristics in some sort of 4-dimensional chart???

Yes, we can. Here's a blank diagram - go for it!



If this amazes, astounds or frightens you, here's a really great discussion of Venn diagrams and how to use them.