Additional Math Pages & Resources

Wednesday, February 2, 2011

Hair today, gone tomorrow Part I

Let's apply math to the hairs that plague us. We have hair on our heads, hair on various other parts of our bodies, and hair on our furniture from our pets.

I have read that the average person has about 5 million hairs on his or her body. Of those, perhaps 100,000 or so are on top of our heads. We are born with all the hair follicles (roots) that we will ever have. In fact, some babies are born hairy, with what are called lanugo hairs, but those quickly turn into vellus hairs or terminal hairs. Here's a very hairy baby related to one of our employees ...

Hair grows all the time, and falls out when it has done its duty. Although all of us (people) shed hair, it isn't that big a deal unless it ends up clogging the drain in the shower.

When we go bald we don't really stop growing hairs, the terminal hairs from those particular follicles just become ever so much finer and nearly invisible - they become vellus hairs. Most people have more-or-less visible terminal hair in various places, but invisible vellus hair elsewhere. Our skin is not completely hidden, thus we don't call our hairs fur, or a coat.

Why am I writing about hair and fur and coats? A convergence of hair-related activities, I guess. It's time for me to get my hair cut, AND I got a nifty advertising email from Dyson about a dog vacuuming attachment. This might turn into a best-selling item for them, as many dogs shed hair all over the place.  So today we will talk about pet hair/fur.

I only had one question for Dyson - Does it work on cats? Sadly, No. They say this new item is not good for cats. I can say from experience that vacuums and my cats don't get along. Although Tiger III looks cute here, that doesn't mean he won't bite me if I come near him with the vacuum!

Cats and dogs, along with many other mammals have what we call fur - dense hair all over their bodies. This fur may also be referred to as their coat. Cats have various types of hair, such as whiskers, guard hairs, down (undercoat), vellus (fine hairs), awn hairs, etc. You can see all those types of hair in the picture of Tiger's face.

The color of cat fur is determined by its genetic makeup. My cat's hair color is called red tabby. Did you notice how close his hair color is to the golden retriever in the Dyson ad? Here he is (above Tiger is on the left) with his friend Boomer from across the street (below Tiger is on the right). They look amazingly alike in size and coloration but came from different litters in different cities, so we are sure they are not related.

Here's one of our previous cats having a nap. We called him Tiger II. Yes he's enormous in this photo but he was 21 years old then, so his weight didn't seem to shorten his lifespan any.

I don't have pictures of Tiger I but he was also the same color. As for why we have had 3 cats of exactly the same coloration for a total (so far) of 32 years I can't say. We did have a completely black cat too, named Panther. Here she is giving me the "I can't be bothered with you" look.

Cat fur coloration is a complex topic and there's plenty of math in it! Sadly I have used up all my time showing you pictures of my pets, so you have to go elsewhere to learn more about the names for colors and to learn about the genetics behind coloration. And here's a site with an interactive tool so you can see what possible colors might come out of a litter (assuming you know the father and mother).

Tomorrow we'll cover more hair math.

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