The Math of Nail Clipping?

To demonstrate how I’m such a nerd (or such a math teacher, or both):

I was just clipping my nails, and started thinking about the math involved. Often when I clip I’ll only do 1 or 2 clips per nail, and they can come out really jagged, pointy, and sharp. But this time I did about five clips, closely following the curve of the nail and it came out much smoother.

Which makes sense, because I’m basically approximating the shape of my nail (a curve) with the nail clipper (a tangent line), and so the more tangent lines I used, the closer the approximation is.

Now the question just is if I can turn that into a WCYDWT, or if it’s too gross for that….