This can be foound in N. L. White - Matroid Applications page 2.
Unidimensional case
Author considers a set of points $P = \{ p_i | i \in \mathbb{N} \}$. In this case points are to be considered on the real line, so it is really simple, no components, just scalars.
Author considers that two points, arbitrarily chosen in the set, say $p_i,p_j \in P$. Then he wants to evaluate their distance $|| p_i - p_j ||$. No problems till now. All the calculations are done in order to find a good relation and see that, if those points are connected using a rigid bar and they move with a certain speed then their distance as they move must not change. This is possible using derivates.
He also says that the distance and its square must not change. Makes sense of course.
Than he writes the following.
\frac{d}{dt}[p_i(t)-p_j(t)]^2 = [p_i(t)-p_j(t)][p'_i(t)-p'_j(t)] = 0
What's this, can you explain?