Problem of the Week 807

Connect the Dots

This beautiful problem, which has an intuitive appeal that can lead even professional geometers astray, is due to noted mathematician and expositor Victor Klee of the University of Washington.

For a set E in 3-space, let L(E) consist of all points on all lines determined by any two points of E. Thus if V consists of the four vertices of a regular tetrahedron, then L(V) consists of the six edges of the tetrahedron, extended infinitely in both directions.

True or False: Every point of 3-space is in L(L(V))?

I used this problem over four years ago, but because my book containing Macalester PoWs from 1968-1995 will be out soon, this semester is my last chance to reuse some of the best ones that will be included in that collection.

© Copyright 1996 Stan Wagon. Reproduced with permission.

The Math Forum

2 October 1998