DAUGHTERS, BRAIDS, AND PONYTAILS. I found this explanation of the Ponytail Shape Equation by Edward Willett helpful. It also appealed to me because he comments on his experiences fashioning a ponytail in the mornings from his daughters long hair. It brought back memories of my one experience with my daughter’s long hair. Annalisa was 6 or 7 and had very long. very thick, very wavy hair. We were staying at a hotel while visiting Mary Jane’s family, and I was going to take the kids swimming while Mary Jane made a particularly stressful family visit. What I had forgotten was that Annalisa was going to need to wear a swimming cap, and I had no idea of how to braid her hair. I wound up, as Annalisa has confirmed, forming her hair into two handfuls and making a double knot—something like a granny knot. Annalisa also recalls Mary Jane spending about three hours with a bottle of conditioner on her hair that evening. But finally, she recalls that we had a good time swimming.

When Edward Willett says: “The research provides new understanding of how a bundle of hair swells, due to the outward pressure arising from collisions among the component hairs”, I understand the phenomenon even though I wouldn’t have a chance at the mathematics.

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