From Elementary Differential Geometry by Pressley
I don't understand the last paragraph. Why does it show $\gamma$ lies on the sphere $\mathcal S$ with center $\mathbf a$ and radius $1/\kappa$?
2026-03-30 14:11:18.1774879878
A curve of constant curvature and zero torsion must be a circle
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$$ \|\gamma - \mathbf{a}\| = {1\over\kappa}$$ says that the distance from $\gamma$ to $\mathbf{a}$ is the constant value $1\over \kappa$.
Now, what is the definition of a sphere $S$ of radius $1\over\kappa$ about $\mathbf a$?