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Math Magic Archive

Problem of the Month (August 2015)

This month we consider packing polylines, collections of infinitesimally thin line segments of length 1 connected at right angles. Some of these present no problem at all, we can pack infinitely many of them in a finite region without crossing by "nesting" them. Others require more space. For example, below are the best known packings of the polyline we call T3:

n=2

L = √2
n=6

L = 2
n=8

L = 1 + √2
n=10

L = 2 + √2/2
n=14

L = 2√2
n=16

L = 3

What are the best packings of T3 for other values of n? What about other small polylines?


You can see all the best known results here.

Submit your answers here.

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