{"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\/ro\/exhibit\/poster-17\/","title":{"rendered":"poster 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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Turul cavalerului<\/b><\/h2>

Ad\u00e2ncime istoric\u0103:<\/b> Turul cavalerului este o secven\u021b\u0103 matematic\u0103 \u00een care un cavaler viziteaz\u0103 fiecare p\u0103trat de pe o tabl\u0103 de \u0219ah exact o dat\u0103. Este at\u00e2t o provocare strategic\u0103, c\u00e2t \u0219i o problem\u0103 clasic\u0103 \u00een matematica recreativ\u0103.<\/span><\/p>

\u00a0<\/p>

Origini:<\/b><\/p>

Aceast\u0103 problem\u0103 este departe de a fi o descoperire modern\u0103. Primele solu\u021bii cunoscute dateaz\u0103 din secolul al IX-lea, furnizate de mae\u0219tri din Bagdad precum Al-Adli \u0219i As-Suli. Mai mult, \u00een literatura indian\u0103 din secolul al IX-lea, poetul ca\u0219mirian Rudrata a demonstrat aceast\u0103 estetic\u0103 matematic\u0103 \u00een lucrarea sa Kavyalankara, unde a compus un poem care urm\u0103re\u0219te secven\u021ba turului unui cavaler.<\/p>

\u00a0<\/p>

Literatur\u0103 occidental\u0103:<\/b><\/p>

\u00cen secolul al XIII-lea, regele Alfonso al X-lea al Castiliei a prezentat manevre complexe bazate pe mi\u0219carea cavalerului \u00een celebrul s\u0103u Libro de los Juegos (Cartea Jocurilor). Cu toate acestea, fundamentul matematic modern al problemei a fost pus \u00een 1759 de Leonhard Euler, a c\u0103rui analiz\u0103 este acum recunoscut\u0103 ca fiind una dintre pietrele de temelie ale teoriei grafurilor.<\/p>

\u00a0<\/p>

Caracteristici:<\/b><\/p>

Tur \u00eenchis (reintrant):<\/b> Dac\u0103 cavalerul ajunge pe un p\u0103trat care se afl\u0103 la exact o mutare a cavalerului fa\u021b\u0103 de p\u0103tratul de plecare, \u00eei permite s\u0103 \u00eenceap\u0103 imediat turul din nou.<\/p>

\u00a0<\/p>

Tur deschis:<\/b><\/p>

Dac\u0103 cavalerul viziteaz\u0103 fiecare p\u0103trat, dar ajunge pe un p\u0103trat din care nu poate ajunge la punctul de plecare cu o singur\u0103 mi\u0219care.<\/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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Problema celor 8 regine: Dijkstra \u0219i na\u0219terea program\u0103rii structurate<\/b><\/h2>

Pus\u0103 de Max Bezzel \u00een 1848 \u0219i atr\u0103g\u00e2nd aten\u021bia unor genii precum Carl Friedrich Gauss, aceast\u0103 problem\u0103 a fost transformat\u0103 \u00eentr-un \u201cmanifest al program\u0103rii\u201d \u00een anii 1970 de c\u0103tre unul dintre p\u0103rin\u021bii informaticii moderne, Edsger W. Dijkstra.<\/p>

Leg\u0103tura dintre Dijkstra \u0219i DFS<\/b><\/h3>

\u00cen lucrarea sa fundamental\u0103, <\/span>Note privind programarea structurat\u0103<\/span><\/i> (1972), Dijkstra a utilizat problema celor 8 regine pentru a demonstra modul \u00een care un algoritm poate fi construit \u00een mod sistematic printr-un proces pe care l-a numit \u201crafinare treptat\u0103\u201d.\u201d<\/span><\/p>

  • DFS \u0219i Backtracking: Dijkstra a definit metoda de a plasa o regin\u0103 \u00eentr-un r\u00e2nd \u0219i de a cobor\u00ee la urm\u0103toarea (Depth-First Search - DFS) \u0219i de a reveni la pasul anterior pentru a \u00eencerca o alt\u0103 posibilitate \u00een cazul \u00een care se ajunge la un punct mort (Backtracking) ca fiind cel mai pur exemplu de programare structurat\u0103.<\/li><\/ul>

    Puterea de a da \u00eenapoi:<\/b><\/p>

    Potrivit lui Dijkstra, aceast\u0103 abordare reprezint\u0103 prima etap\u0103 major\u0103 \u00een rafinarea procesului \u201c\u00eencercare-eroare\u201d \u00eentr-o secven\u021b\u0103 logic\u0103 impecabil\u0103 pe care o co<\/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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    Problema gr\u00e2ului \u0219i a tablei de \u0219ah: cre\u0219terea exponen\u021bial\u0103<\/b><\/h3>

    Legend\u0103 \u0219i origine:<\/b><\/p>

    Conform pove\u0219tii, c\u00e2nd inventatorul \u0219ahului, Sissa bin Dahir, a prezentat jocul regelui Indiei, regele l-a \u00eentrebat ce recompens\u0103 ar dori. Sissa a f\u0103cut o cerere aparent modest\u0103: \u201cVreau un bob de gr\u00e2u pentru primul p\u0103trat al tablei de \u0219ah, doi pentru al doilea, patru pentru al treilea \u0219i, pentru fiecare p\u0103trat urm\u0103tor, de dou\u0103 ori mai mult dec\u00e2t cel precedent\u201d. Regele a respins ini\u021bial aceast\u0103 cerere, crez\u00e2nd c\u0103 este vorba doar de \u201cun pumn de gr\u00e2u\u201d; totu\u0219i, c\u00e2nd au \u00eenceput calculele, a devenit clar c\u0103 nici trezoreria \u0219i nici toate stocurile de gr\u00e2u ale lumii nu ar fi suficiente pentru a satisface aceast\u0103 cerere.<\/p>

    Record istoric: Ibn Khallikan (1256)<\/b><\/p>

    Prima \u00eenregistrare scris\u0103 cunoscut\u0103 a acestei pove\u0219ti celebre a fost consemnat\u0103 \u00een 1256 de c\u0103tre renumitul biograf \u0219i istoric Ibn Khallikan. Ibn Khallikan a inclus acest eveniment \u00een lucrarea sa nu doar ca o poveste, ci \u0219i ca o dovad\u0103 a modului \u00een care matematica \u00eempinge limitele imagina\u021biei.<\/p>

    Realitatea matematic\u0103:<\/b><\/p>

    Aceast\u0103 cerere f\u0103cut\u0103 pentru cele 64 de p\u0103trate de pe tabla de \u0219ah este cel mai pur exemplu de progresie geometric\u0103 (cre\u0219tere exponen\u021bial\u0103). Suma de pe fiecare p\u0103trat se calculeaz\u0103 folosind formula 2n-1<\/sup><\/strong> . Ecua\u021bia care furnizeaz\u0103 cantitatea total\u0103 de gr\u00e2u este urm\u0103toarea:<\/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>

    Cifra masiv\u0103 rezultat\u0103 din acest calcul este:<\/p>

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

    De ce este at\u00e2t de important?<\/b><\/p>

    • Scala de cre\u0219tere:<\/b> Acest num\u0103r este echivalent cu aproximativ de 2 000 de ori produc\u021bia anual\u0103 total\u0103 de gr\u00e2u din lume.\u00a0<\/span><\/li><\/ul>

      Lec\u021bie strategic\u0103:<\/b> Aceast\u0103 problem\u0103 este o veche lec\u021bie de \u00een\u021belepciune care \u00eei \u00eenva\u021b\u0103 pe lideri \u0219i strategi cum schimb\u0103rile mici (\u201cdublarea\u201d) se pot transforma \u00een timp \u00een for\u021be incontrolabile.<\/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\/ro\/wp-json\/wp\/v2\/pages\/963","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/shatranj.art\/ro\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/shatranj.art\/ro\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/shatranj.art\/ro\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/shatranj.art\/ro\/wp-json\/wp\/v2\/comments?post=963"}],"version-history":[{"count":22,"href":"https:\/\/shatranj.art\/ro\/wp-json\/wp\/v2\/pages\/963\/revisions"}],"predecessor-version":[{"id":1443,"href":"https:\/\/shatranj.art\/ro\/wp-json\/wp\/v2\/pages\/963\/revisions\/1443"}],"up":[{"embeddable":true,"href":"https:\/\/shatranj.art\/ro\/wp-json\/wp\/v2\/pages\/743"}],"wp:attachment":[{"href":"https:\/\/shatranj.art\/ro\/wp-json\/wp\/v2\/media?parent=963"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}