I recall from a discussion thread some week ago we talked about different ways to pedagogically explain differentiability.
So I came up with this idea that if there for each point there exists a circular "wheel" of some radius $0 < \epsilon_R < \infty$ ( that there exists such an $\epsilon_R$ ), so that circle's center is "above" the function, the wheel lays tangent to the curve and "rolls" along the curve without crossing it (while possibly having to change radius once in a while).
Would this be possible for all differentiable functions?
Own work:
A step discontinous function (which obviously is not differentiable) does not qualify as no matter how small we make $\epsilon_R$, we won't reach every point on each side of the step discontinuity ( and also the circle would need "jumping" which is not allowed ).
