Suggestion: First guess the answer before doing any calculation. PUZZLE: Let S and T be unit segments in 3-space with S parallel to the z-axis, with midpoint at (-x,0,0) and T parallel to the y-axis, with midpoint at ( x,0,0). Connect each endpoint of S to one endpoint of T so as to get disjoint segments U and V. Set m(x) := the (least) distance between U and V. QUESTION: What is the limit of m(x) as x -> oo ? --Dan _____________________________________________________________________ "It don't mean a thing if it ain't got that certain je ne sais quoi." --Peter Schickele
On 12/27/08, Dan Asimov <dasimov@earthlink.net> wrote:
Suggestion: First guess the answer before doing any calculation.
PUZZLE: Let S and T be unit segments in 3-space with S parallel to the z-axis, with midpoint at (-x,0,0) and T parallel to the y-axis, with midpoint at ( x,0,0).
Connect each endpoint of S to one endpoint of T so as to get disjoint segments U and V.
Set m(x) := the (least) distance between U and V.
QUESTION: What is the limit of m(x) as x -> oo ?
--Dan
_____________________________________________________________________ "It don't mean a thing if it ain't got that certain je ne sais quoi." --Peter Schickele
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Project orthographically onoy the yz-plane, and use symmetry about it. The distance 1/sqrt2 is constant, independent of x. WFL
participants (2)
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Dan Asimov -
Fred lunnon