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The Mercedes knot problem
Jurišić, Aleksandar
Problem je geometrijske narave in spada med topologijo in teorijo vozlov. Na sredi sobe si predstavljamo žogo, ki je povezana s tremi elastikami ▫$b$▫, ▫$m$▫ in ▫$w$▫ na steno. Elastike lahko ...poljubno premikamo, ne moremo pa jih pretrgati, konci so fiksirani. Vpašamo se, če jih lahko premaknemo tako, da se elastika ▫$m$▫ večkrat ovije okrog elastike ▫$w$▫. Problem je dobil ime Mercedes zaradi žoge in treh vpetih elastik. Najprej "prevedemo" nalogo v matematični jezik in podamo delno rešitev. Pokažemo, kako enostavno navijemo elastiko ▫$m$▫ dvakrat oziroma sodokrat okoli elastike ▫$w$▫, nato pa poskušamo razumeti bistvo problema z vidika teorije vozlov, končno pa predstavimo tudi popolno rešitev (neeksistenčni del originalnega problema smo rešili z uporabo zvojnega števila. Omenimo tudi več povezav s tem problemom in omenimo nekatere primere uporabe (spini in kvantna fizika, efekti encimov na DNA, model kvaternionske grupe, periskop za podmornice).
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