Michael Reid wrote: << . . . by the way, this is reminiscent of a problem posed a while back by dan, concerning a sequence of unit spheres such that each was tangent to the previous three. dan, did you ever send solution(s) to the list? i remember working on it and sending my solution off-list as requested
I *thought* I posted an answer -- I recall composing one -- but maybe I never sent it to math-fun. Repeat of (equivalent) question, in case anyone else wants to claim an answer: ------------------------- Given mutually tangent unit balls B_k, 1 <= k <= 4, in 3-space that are mutually tangent, inductively define B_(n+4), n >= 1, (uniquely) by the condition that it is tangent to B_(n+k), 1 <= k <= 3, and that it is not B_n. QUESTION: Do there exist distinct positive j, k, such that the interiors of B_j and B_k intersect ? --------------------------------------------- --Dan _____________________________________________________________________ "It don't mean a thing if it ain't got that certain je ne sais quoi." --Peter Schickele