# Helix of a curve

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Let $\gamma$ be a parametrized curve on a manifold $M$. The helix or spiral of $\gamma$ is a parametrized curve in $\R \times M$ that sends $t$ in the parameter domain to $(t,f(t))$. In other words, the helix of a curve is the Cartesian product of the curve with the identity-parametrized curve.
For a closed curve, viz a map $S^1 \to M$, we construct the helix using the map $\R \to M$ that composes the modulo map with the curve parametrization.