What is "n-curve"

We take the functional theoretic algebra C[0, 1] of curves. For each loop γ at 1, and each positive integer n, we define a curve γ called n-curve. The n-curves are interesting in two ways.

1. Their f-products, sums and differences give rise to many beautiful curves.
2. Using the n-curves, we can define a transformation of curves, called n-curving.