a combinatorial geometry problem, related (in a surprising way) to the graham's g.c.d. conjecture, is as follows. let $n\ge 1$ be an integer. given a vector $(a_1 , ... , a_n)\in r^n$, write $$ a^+ := ( \max(a_1,0) , ... , \max(a_n,0) ) $$ (the "projection of $a$ onto the positive orthant"), and for a set $a\subset r^n$ put $$ a^+ := \{ a^+ : a\in a \}. $$ how small $|(a-a)^+|$ can be for a set $a\subset r^n$ of given cardinality $|a|$? we discuss previously known results and report on recent developments due to ron holzman, rom pinchasi, and the presenter.