Domino effect and tractrix
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Consider a set of dominos standing along a straight line with equal distances between them.
Push the leftmost domino and assume they all fall except for the very last one. What curve do their tops trace?
To answer this question, imagine that the dominos are infinitely thin and thus replace each domino with a stick (of the same length). Then it is reasonable to assume that these sticks are tangent to the "ideal" curve that follows the tops of the dominos.
Thus, we need to find an equation of the cure that has the following property: segments of the tangent line, "trapped" between the curve and the x-axis, have constant length, call it a.