The Mathematics of Hair Braiding.

I live in a village in Alaska where so many kids wear their hair braided in intricate pattern or can braid hair beautifully. There have been days when I fixed my hair in a side braid and one of my students told me, I'd done it wrong so she redid it.

Other times, a girl asked to braid my hair and fixed it so it formed a french braid into a braided bun.  Some moms go crazy with their creative braiding.

In general, hair braiding is made up of repeated geometric patterns.  In mathematics, a braid is any collection of strands that cross each other. Braids also have a beginning and end which as static but the strands themselves can be moved around by pushing or pulling so one braid changes into another braid.

African American culture is known for it cornrows which have been studied.  Cornrows use translation, rotation, reflection, and dilation to create styles from simple linear rows to complex curves and spirals. In addition, the process involves fractals because if you've ever watched anyone braiding hair, you'll notice the same shape is repeated over and over but in the process it shifts and becomes smaller and smaller.

If you are interested in playing around with braids, you can check this program out.  In the lower left corner, you can click on the picture of a woman with braids.  Every time you click, you see a new picture with a different braid pattern done in the hair.  some are quite simple, while others are quite complex.  In addition, you can play with the program to see how changing numbers change the final product.

In mathematics, standard braids are made up of three strands but they can be made of two, four, five, or more strands but think back to the hair braids you've seen.  Most are made of three strands either up and over or under and up to create the pattern but sometimes you see two strands twisted together to create a pattern.  I've done something called a fishtail braid using four strands in an almost woven pattern and I know some professional hair braiding people have used five strands.

If you get a chance to look at pictures of braided hair, especially the kind that uses multiple rows, you might notice the rows run parallel to each other and sometimes, they might run into each other at perpendicular angles.  The next time you see someone with braided hair, remember you are observing math at work.

Let me know what you think, have a great day.