{"id":963,"date":"2026-02-22T15:16:26","date_gmt":"2026-02-22T15:16:26","guid":{"rendered":"https:\/\/shatranj.art\/?page_id=963"},"modified":"2026-02-23T11:10:10","modified_gmt":"2026-02-23T11:10:10","slug":"poster-17","status":"publish","type":"page","link":"https:\/\/shatranj.art\/cs\/exhibit\/poster-17\/","title":{"rendered":"plak\u00e1t 17"},"content":{"rendered":"
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\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\"\"\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
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Ryt\u00ed\u0159sk\u00e1 prohl\u00eddka<\/b><\/h2>

Historick\u00e1 hloubka:<\/b> Jezdcova cesta je matematick\u00e1 posloupnost, p\u0159i n\u00ed\u017e jezdec nav\u0161t\u00edv\u00ed ka\u017ed\u00e9 pol\u00ed\u010dko na \u0161achovnici p\u0159esn\u011b jednou. Jedn\u00e1 se o strategickou v\u00fdzvu a z\u00e1rove\u0148 o klasick\u00fd probl\u00e9m rekrea\u010dn\u00ed matematiky.<\/span><\/p>

\u00a0<\/p>

P\u016fvod:<\/b><\/p>

Tento probl\u00e9m nen\u00ed zdaleka novodob\u00fdm objevem. Nejstar\u0161\u00ed zn\u00e1m\u00e1 \u0159e\u0161en\u00ed poch\u00e1zej\u00ed z 9. stolet\u00ed a p\u0159edlo\u017eili je bagd\u00e1d\u0161t\u00ed mist\u0159i jako Al-Adli a As-Suli. V indick\u00e9 literatu\u0159e 9. stolet\u00ed nav\u00edc ka\u0161m\u00edrsk\u00fd b\u00e1sn\u00edk Rudrata demonstroval tuto matematickou estetiku ve sv\u00e9m d\u00edle Kavyalankara, kde slo\u017eil b\u00e1se\u0148, kter\u00e1 sledovala posloupnost ryt\u00ed\u0159sk\u00e9ho turn\u00e9.<\/p>

\u00a0<\/p>

Z\u00e1padn\u00ed literatura:<\/b><\/p>

Ve 13. stolet\u00ed p\u0159edstavil kastilsk\u00fd kr\u00e1l Alfons X. ve sv\u00e9 slavn\u00e9 knize Libro de los Juegos (Kniha her) slo\u017eit\u00e9 man\u00e9vry zalo\u017een\u00e9 na pohybu ryt\u00ed\u0159e. Modern\u00ed matematick\u00e9 z\u00e1klady tohoto probl\u00e9mu v\u0161ak polo\u017eil v roce 1759 Leonhard Euler, jeho\u017e anal\u00fdza je dnes uzn\u00e1v\u00e1na jako jeden ze z\u00e1kladn\u00edch kamen\u016f teorie graf\u016f.<\/p>

\u00a0<\/p>

Charakteristika:<\/b><\/p>

Uzav\u0159en\u00e1 (opakovan\u00e1) prohl\u00eddka:<\/b> Pokud jezdec skon\u010d\u00ed na poli, kter\u00e9 je p\u0159esn\u011b o jeden tah vzd\u00e1leno od v\u00fdchoz\u00edho pole, m\u016f\u017ee okam\u017eit\u011b za\u010d\u00edt obch\u016fzku znovu.<\/p>

\u00a0<\/p>

Otev\u0159en\u00e1 prohl\u00eddka:<\/b><\/p>

Pokud jezdec nav\u0161t\u00edv\u00ed v\u0161echna pole, ale skon\u010d\u00ed na poli, ze kter\u00e9ho se nem\u016f\u017ee dostat do v\u00fdchoz\u00edho bodu jedn\u00edm tahem.<\/span><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t

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Probl\u00e9m 8 kr\u00e1loven: Dijkstra a zrod strukturovan\u00e9ho programov\u00e1n\u00ed<\/b><\/h2>

Tento probl\u00e9m, kter\u00fd v roce 1848 polo\u017eil Max Bezzel a p\u0159it\u00e1hl pozornost g\u00e9ni\u016f, jako byl Carl Friedrich Gauss, byl v 70. letech 20. stolet\u00ed jedn\u00edm z otc\u016f modern\u00ed informatiky Edsgerem W. Dijkstrou p\u0159etvo\u0159en v \u201cprogram\u00e1torsk\u00fd manifest\u201d.<\/p>

Spojitost mezi Dijkstrou a DFS<\/b><\/h3>

Ve sv\u00e9m z\u00e1sadn\u00edm d\u00edle, <\/span>Pozn\u00e1mky ke strukturovan\u00e9mu programov\u00e1n\u00ed<\/span><\/i> (1972) Dijkstra pou\u017eil probl\u00e9m 8 kr\u00e1loven, aby uk\u00e1zal, jak lze systematicky vytv\u00e1\u0159et algoritmus pomoc\u00ed procesu, kter\u00fd nazval \u201cpostupn\u00e9 zp\u0159es\u0148ov\u00e1n\u00ed\u201d.\u201d<\/span><\/p>

  • DFS a zp\u011btn\u00e9 sledov\u00e1n\u00ed: Dijkstra definoval metodu kladen\u00ed kr\u00e1lovny do \u0159ady a sestupov\u00e1n\u00ed k dal\u0161\u00ed (Depth-First Search - DFS) a n\u00e1vrat k p\u0159edchoz\u00edmu kroku, aby se pokusil o jinou mo\u017enost, kdy\u017e naraz\u00ed na slepou uli\u010dku (Backtracking), jako nej\u010dist\u0161\u00ed p\u0159\u00edklad strukturovan\u00e9ho programov\u00e1n\u00ed.<\/li><\/ul>

    S\u00edla zp\u011btn\u00e9ho sledov\u00e1n\u00ed:<\/b><\/p>

    Podle Dijkstry tento p\u0159\u00edstup p\u0159edstavuje prvn\u00ed v\u00fdznamn\u00fd miln\u00edk ve zdokonalov\u00e1n\u00ed procesu \u201cpokus-omyl\u201d do bezchybn\u00e9 logick\u00e9 posloupnosti, kterou m\u016f\u017ee spoluautor<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t

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    Probl\u00e9m p\u0161enice a \u0161achovnice: exponenci\u00e1ln\u00ed r\u016fst<\/b><\/h3>

    Legenda a p\u016fvod:<\/b><\/p>

    Podle p\u0159\u00edb\u011bhu, kdy\u017e vyn\u00e1lezce \u0161ach\u016f Sissa bin Dahir p\u0159edstavil hru indick\u00e9mu kr\u00e1li, zeptal se ho kr\u00e1l, jakou odm\u011bnu by cht\u011bl. Sissa vyslovil zd\u00e1nliv\u011b skromnou prosbu: \u201cChci jedno zrnko p\u0161enice za prvn\u00ed pol\u00ed\u010dko \u0161achovnice, dv\u011b za druh\u00e9, \u010dty\u0159i za t\u0159et\u00ed a za ka\u017ed\u00e9 dal\u0161\u00ed pol\u00ed\u010dko dvojn\u00e1sobek toho p\u0159edchoz\u00edho.\u201d Sissi si p\u0159\u00e1l, aby se mu dostalo odm\u011bny. Kr\u00e1l tento po\u017eadavek zpo\u010d\u00e1tku odm\u00edtl v domn\u011bn\u00ed, \u017ee jde jen o \u201chrst p\u0161enice\u201d; kdy\u017e v\u0161ak za\u010dal po\u010d\u00edtat, uk\u00e1zalo se, \u017ee na spln\u011bn\u00ed tohoto po\u017eadavku by nesta\u010dila ani st\u00e1tn\u00ed pokladna, ani ve\u0161ker\u00e9 sv\u011btov\u00e9 z\u00e1soby p\u0161enice.<\/p>

    Historick\u00fd z\u00e1znam: Ibn Challik\u00e1n (1256)<\/b><\/p>

    Prvn\u00ed zn\u00e1m\u00fd p\u00edsemn\u00fd z\u00e1znam tohoto slavn\u00e9ho p\u0159\u00edb\u011bhu poch\u00e1z\u00ed z roku 1256 od zn\u00e1m\u00e9ho \u017eivotopisce a historika Ibn Challik\u00e1na. Ibn Challik\u00e1n tuto ud\u00e1lost zahrnul do sv\u00e9ho d\u00edla nejen jako p\u0159\u00edb\u011bh, ale jako d\u016fkaz toho, jak matematika posouv\u00e1 hranice p\u0159edstavivosti.<\/p>

    Matematick\u00e1 realita:<\/b><\/p>

    Tento po\u017eadavek na 64 pol\u00ed na \u0161achovnici je nej\u010dist\u0161\u00edm p\u0159\u00edkladem geometrick\u00e9 progrese (exponenci\u00e1ln\u00edho r\u016fstu). \u010c\u00e1stka na ka\u017ed\u00e9m pol\u00ed\u010dku se vypo\u010d\u00edt\u00e1 podle vzorce 2n-1<\/sup><\/strong> . Rovnice pro stanoven\u00ed celkov\u00e9ho mno\u017estv\u00ed p\u0161enice je n\u00e1sleduj\u00edc\u00ed:<\/span><\/p>

    \u00a0<\/p>

    S =<\/span>


    63<\/span>
    \u2211<\/span>
    i<\/i>=0<\/span>
    <\/span><\/p>

    2i<\/i><\/sup> = 264<\/sup> - 1<\/span><\/p><\/div>

    Obrovsk\u00e9 \u010d\u00edslo, kter\u00e9 z tohoto v\u00fdpo\u010dtu vypl\u00fdv\u00e1, je:<\/p>

    18,446,744,073,709,551,615<\/b><\/p>

    Pro\u010d je to tak d\u016fle\u017eit\u00e9?<\/b><\/p>

    • Rozsah r\u016fstu:<\/b> Toto \u010d\u00edslo odpov\u00edd\u00e1 p\u0159ibli\u017en\u011b 2 000n\u00e1sobku sou\u010dasn\u00e9 celkov\u00e9 ro\u010dn\u00ed produkce p\u0161enice na sv\u011bt\u011b.\u00a0<\/span><\/li><\/ul>

      Strategick\u00e1 lekce:<\/b> Tento probl\u00e9m je prastarou lekc\u00ed moudrosti, kter\u00e1 u\u010d\u00ed v\u016fdce a strat\u00e9gy, jak se mal\u00e9 zm\u011bny (\u201czdvojen\u00ed\u201d) mohou \u010dasem prom\u011bnit v nekontrolovateln\u00e9 s\u00edly.<\/span><\/p><\/div><\/div>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>","protected":false},"excerpt":{"rendered":"

      The Knight’s Tour Historical Depth: The Knight’s Tour is a mathematical sequence in which a knight visits every single square on a chessboard exactly once. It is both a strategic challenge and a classic problem in recreational mathematics. \u00a0 Origins: This problem is far from a modern discovery. The earliest known solutions date back to […]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":743,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-963","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/shatranj.art\/cs\/wp-json\/wp\/v2\/pages\/963","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/shatranj.art\/cs\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/shatranj.art\/cs\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/shatranj.art\/cs\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/shatranj.art\/cs\/wp-json\/wp\/v2\/comments?post=963"}],"version-history":[{"count":22,"href":"https:\/\/shatranj.art\/cs\/wp-json\/wp\/v2\/pages\/963\/revisions"}],"predecessor-version":[{"id":1443,"href":"https:\/\/shatranj.art\/cs\/wp-json\/wp\/v2\/pages\/963\/revisions\/1443"}],"up":[{"embeddable":true,"href":"https:\/\/shatranj.art\/cs\/wp-json\/wp\/v2\/pages\/743"}],"wp:attachment":[{"href":"https:\/\/shatranj.art\/cs\/wp-json\/wp\/v2\/media?parent=963"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}