The problem of choice of a shoe lacing method among millions of possible variants has finally got a scientifically grounded solution. In particular, as it turned out, the popular cross method of lacing is also among the strongest methods from a scientific point of view.
Burkard Polster from Monash University situated in Melbourne (Australia) solved the problem with the help of the combinatorial mathematics methods. The discipline is employed for solution of a wide range of different problems: from search of optimal strategies for resource usage to definition of the most effective position of micro-systems on a circuit plate.
The Australian mathematician used the formulas describing the block and pulley mechanics and a mathematical model of an ideal shoe in order to calculate efforts required to lace a shoe. For instance, it was assumed that the surfaces were flat and holes on both sides of the shoe were exactly opposite each other; it was also assumed that there was no friction between the holes and the lace.
As it turned out, a shoe having seven pairs of lace holes can be laced in 400 millions of different methods. Results of the research revealed that the cross and the straight methods of lacing (the left and the middle on the picture correspondingly) were the strongest methods of lacing.
The cross method is especially convenient in those cases when the lace holes are too close to each other and the horizontal space between the laced parts is big enough. The straight method suits better for lacing of long strips with a small number of lace holes. However, this method is not actually very popular. It used to be very popular among military men, because this variant of lacing could be easily cut with only one stroke of a knife if soldiers were wounded in feet.
The most economic method of lacing is given to the right on the picture; it allows to lace shoes with shorter laces. But it is mostly used only with decorative purposes in the shoe shop windows.
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