In the New Scientist article "It's a wrap" (New Scientist, December 20-27, 2008, pp66-67), it is asserted that mathematicians have proven that in two dimensions, given six or less circular objects and an elastic wrapper, a "sausage" of the circles arranged in a straight line encloses the minimum possible area within the wrapper.
They may have "proven" it mathematically, but the assertion can be disproven by construction in a matter of minutes, without even having to do any calculations.