Below it should have been made explicit that we consider only a single parallel pair of summand diameters in each direction separately. Strictly speaking, both should furthermore be translated to meet the origin, in order for their sum / mean to become a formally 1-space affair. More generally, for convex summands, in any given direction only their extremal points are relevant to their sum / mean. Comments on the Low Rollers screed are invited. While it suffers from an absence of diagrams, that on page 2 of Roberts report is a partial substitute. And in that connection I have already spotted one misprint: Stage (A): for "d = 0" read "d = c" WFL On 1/13/13, Fred lunnon <fred.lunnon@gmail.com> wrote:
On 1/12/13, Warren Smith <warren.wds@gmail.com> wrote:
1. The Minkowski sum of two constant-width convex objects, is another. Scaling and/or rotating one, yields another.
What appeared fiendishly involved in the special case M_V (+) M_F is immediately seen to be a one-liner when abstracted.
Minkowski sum commutes with (ie. is invariant under) translation, so the diameter lines in both summands can be brought into coincidence; then the (1-space) mean width in that direction is the mean of the widths.
QED & DUH! WFL