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In differential geometry, the principal radius of curvature $\rho$ is defined as the reciprocal of the principal curvature $\kappa$. But suppose one of my principal curvatures is 0. How can the principal radius of curvature be $1/0$?

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At such a point, we can say that the radius of curvature is infinite. It's not unusual to extend the real line with $+\infty$ and $-\infty$ to unify certain statements and computations. As long as one is careful enough to avoid indeterminate expressions like $0\cdot \infty$ or $\infty-\infty$, it works well.

Examples of usage: this answer and this one.

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