A tale of touching tubes
Mathematicians find way to put seven cylinders in contact without using their ends
NO IFS, ASHES OR BUTTS Seven cylinders can each touch each other using only their sides, not their ends, mathematicians have discovered.
D. Mackenzie
ATLANTA — Over 50 years ago, the popular mathematics writer Martin Gardner and readers of Scientific American pondered a challenge: Can you place seven cigarettes so that each cigarette touches every one of the others?
Gardner had a solution, but it was unsatisfying because some of the cigarettes’ ends touched others’ sides. If that end of a cigarette were lit, it would no longer touch its neighbor. Mathematicians wondered whether an arrangement could be found with only side-to-side contacts using infinitely long cylinders.
On March 20 at Gathering 4 Gardner, a conference to celebrate Gardner, mathematician Sándor Bozóki of the Hungarian Academy of Sciences in Budapest presented a solution of this more challenging problem, which was also posted online last summer at arXiv.org. Bozóki and colleagues used three months of computer time to solve 20
