I only realized from this question and the answers to it that quadratic Bézier curves are the envelopes of the lines used to compute them iteratively. That is, if a quadratic Bézier curve for points $P_0$, $P_1$, $P_2$ is constructed by linearly interpolating between $P_0$ and $P_1$ and between $P_1$ and $P_2$ and then again linearly interpolating along the line between the two resulting points, then the Bézier curve is the envelope of those lines.
I'm wondering whether this generalizes to higher Bézier curves. An $n$-th order Bézier curve can be analogously constructed by $n$ iterations of linear interpolation. Is it the envelope of any of the lines used in that construction? Or of the higher-order curves that are generated in the intermediate stages of the construction? Or both? If so, how can we see this most easily?
An answer for cubic Bézier curves would already be interesting, even if it doesn't generalize to higher orders.
(I tried searching for “Bézier” and “envelope” but didn't find anything useful, partly because the top hits are all about an Inkscape extension called Bezier Envelope.)