{"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\/tk\/exhibit\/poster-17\/","title":{"rendered":"poster 17"},"content":{"rendered":"
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Rytsary\u0148 sy\u00fdahaty<\/b><\/h2>

Taryhy \u00e7u\u0148luk:<\/b> \u015eahzadany\u0148 sy\u00fdahaty \u2014 \u015fahmat tahtasyndaky her bir kwadraty takyk bir gezek ziyarat ed\u00fd\u00e4n matematiki tertipdir. Ol hem strategiki synag, hem-de dyn\u00e7 aly\u015f matematikasyny\u0148 klassiki meselesidir.<\/span><\/p>

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Menzili:<\/b><\/p>

Bu mesele h\u00e4zirki zaman a\u00e7yly\u015fyndan gaty uzak. M\u00e4lim bolan i\u0148 gadymy \u00e7\u00f6zg\u00fctler 9-njy asyra degi\u015flidir we Bagdady\u0148 al-Adli hem-de as-Suli \u00fdaly ussatlary tarapyndan h\u00f6d\u00fcrlenendir. Mundan ba\u015fga-da, 9-njy asyry\u0148 hind edebi\u00fdatynda Ka\u015fmiri \u015fahyry Rudrata \"Kavyalankara\" atly eserinde bu matematiki estetika g\u00f6rkezdi; ol eserinde \u015f\u00f6val\u00fdeni\u0148 sy\u00fdahat tertibine la\u00fdyk gel\u00fd\u00e4n bir go\u015fgy d\u00f6retdi.<\/p>

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G\u00fcnbatar edebi\u00fdaty:<\/b><\/p>

13-nji asyrda Kastili\u00fdany\u0148 paty\u015fasy Alfonso X me\u015fhur Libro de los Juegos (O\u00fdunlar Kitaby) eserinde \u015f\u00f6val\u00fdeni\u0148 hereketine esaslanan \u00e7yl\u015fyrymly manewrleri g\u00f6rkezdi. Emma mesel\u00e4ni\u0148 h\u00e4zirki zaman matematiki bin\u00fdady 1759-njy \u00fdylda Leonhard Euler tarapyndan d\u00f6\u015f\u00fcldi; onu\u0148 analizi h\u00e4zir graf teorisini\u0148 bin\u00fdat da\u015flaryny\u0148 biri h\u00f6km\u00fcnde ykrar edil\u00fd\u00e4r.<\/p>

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A\u00fdratynlyklary:<\/b><\/p>

\u00ddapyk (ga\u00fdtadan gir\u00fd\u00e4n) gezelen\u00e7:<\/b> Eger at ba\u015flangy\u00e7 kadrdan takyk bir at \u00e4dimi uzaklykdaky kadrda dursa, ol derrew gezisini ga\u00fdtadan ba\u015flap biler.<\/p>

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A\u00e7yk gezelen\u00e7:<\/b><\/p>

Eger \u015f\u00f6val\u00fde her bir kar\u00f6\u00fde bar\u00fdan bolsa-da, ahyrynda ba\u015flan nokada bir hereket bilen \u00fdetip bilme\u00fd\u00e4n kar\u00f6\u00fdde gutar\u00fdan bolsa.<\/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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8 Paty\u015fa Meselesi: Dijkstra we Strukturala\u015fdyrylan Programmirle\u00fd\u015fi\u0148 D\u00fc\u015fmegi<\/b><\/h2>

1848-nji \u00fdylda Maks Bezzel tarapyndan \u00f6\u0148e s\u00fcr\u00fclen we Karl Fridrix Ga\u00fdus \u00fdaly dahileri\u0148 \u00fcns\u00fcni \u00f6z\u00fcne \u00e7eken bu mesele, 1970-nji \u00fdyllarda h\u00e4zirki zaman komp\u00fduter ylymlaryny\u0148 atalaryny\u0148 biri Edsger W. Dijkstra tarapyndan \u201cprogrammirleme manifesti\u201dne \u00f6w\u00fcrildi.<\/p>

Dijkstra bilen DFS arasyndaky baglany\u015fyk<\/b><\/h3>

\u00d6z\u00fcni\u0148 esasy eserinde, <\/span>Strukturala\u015fdyrylan programmirleme bo\u00fdun\u00e7a bellikler<\/span><\/i> (1972) Dijkstra sekiz paty\u015fa meselesini ulanyp, algoritmi\u0148 \u201c\u00e4dimme-\u00e4dim k\u00e4mille\u015fdiri\u015f\u201d di\u00fdip atlandyr\u00fdan prosesi arkaly n\u00e4dip sistematik ta\u00fddan d\u00fcz\u00fcli\u015fini g\u00f6rkezdi.\u201d<\/span><\/p>

  • DFS we yzga ga\u00fddyp g\u00f6zlemek: Dijkstra bir satrda paty\u015fany \u00fderle\u015fdirmek we indiki satra ge\u00e7mek (Depth-First Search \u2013 DFS) hem-de \u00f6l\u00fc nokata \u00fdetende \u00f6\u0148ki \u00e4dime ga\u00fddyp, ba\u015fga bir m\u00fcmkin\u00e7iligi synap g\u00f6rmek (Backtracking) usulyny gurlu\u015fly programmirle\u00fd\u015fini\u0148 i\u0148 arassa mysaly h\u00f6km\u00fcnde kesgitledi.<\/li><\/ul>

    Yzla\u015fdyrmagy\u0148 g\u00fc\u00fdji:<\/b><\/p>

    Dijkstra-ny\u0148 pikiri\u00e7e, bu \u00e7emele\u015fme \u201csynag-we-\u00fdal\u0148y\u015f\u201d prosesini kem-kemden kemsiz logiki tertibe \u00f6w\u00fcrmekde ilkinji uly \u00e4dim bolup dur\u00fdar, bir 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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    Bugda\u00fd we \u015eahmat Tahtasy Meselesi: Eksponensial \u00f6s\u00fc\u015f<\/b><\/h3>

    Rivayat we gelip \u00e7yky\u015fy:<\/b><\/p>

    Rivayata g\u00f6r\u00e4, \u015fahmaty\u0148 ixtira\u00e7ysy Sissa bin Dahir o\u00fdny Hindistany\u0148 paty\u015fasyna h\u00f6d\u00fcrl\u00e4pdir. Paty\u015fa ondan ha\u00fdsy sylagy isle\u00fd\u00e4ndigini sorapdyr. Sissa \u00fd\u00f6neke\u00fd\u00e7e bir ha\u00fdy\u015f etdi: \u201c\u015eahmat tahtasyny\u0148 ilkinji g\u00f6z\u00fcne bir bugda\u00fd d\u00e4ne, ikinji g\u00f6z\u00fcne iki, \u00fc\u00e7\u00fcnji g\u00f6z\u00fcne d\u00f6rt, so\u0148raky her g\u00f6z\u00fcne \u00f6\u0148k\u00fcsini\u0148 iki esse k\u00f6p berilmegi isle\u00fd\u00e4rin.\u201d Paty\u015fa ilki bu ha\u00fdy\u015fy \u201cbir el \u00fdeterlik bugda\u00fd\u201d di\u00fdip pikir edip ret etdi; emma hasaplama ba\u015flanda, hem hazyna, hem-de d\u00fcn\u00fd\u00e4ni\u0148 \u00e4hli bugda\u00fd gorlaryny\u0148 bu talaby kanagatlandyrmaga \u00fdeterlik d\u00e4ldigi belli boldy.<\/p>

    Taryhy \u00fdazgy: Ibn Hallikan (1256)<\/b><\/p>

    Bu me\u015fhur heka\u00fdany\u0148 ilkinji belli \u00fdazma \u00fdadyg\u00e4rligi 1256-njy \u00fdylda me\u015fhur biyograf we taryh\u00e7y Ibn H\u00e4llikan tarapyndan dokumentirlenen. Ibn H\u00e4llikan bu wakany eserine di\u0148e bir heka\u00fda h\u00f6km\u00fcnde d\u00e4l, e\u00fdsem matematika\u0148 hy\u00fdaly\u0148 \u00e7\u00e4klerini n\u00e4hili gi\u0148eld\u00fd\u00e4ndigini\u0148 subutnamasy h\u00f6km\u00fcnde go\u015fdy.<\/p>

    Matematiki hakykat:<\/b><\/p>

    Bu \u015fahmat tahtasyndaky 64 kwadrat \u00fc\u00e7in berlen ha\u00fdy\u015f geometrik \u00f6s\u00fc\u015fi\u0148 (eksponent \u00f6s\u00fc\u015fi\u0148) i\u0148 arassa mysaly bolup dur\u00fdar. Her kwadratdaky mukdar formulany ulanyp hasaplan\u00fdar. 2n-1<\/sup><\/strong> . Bugda\u00fdy\u0148 jemi mukdaryny ber\u00fd\u00e4n de\u0148lem\u00e4 \u015ful g\u00f6rn\u00fc\u015fde:<\/span><\/p>

    \u00a0<\/p>

    S =<\/span>


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

    2i<\/i><\/sup> = 264<\/sup> \u2212 bir<\/span><\/p><\/div>

    Bu hasaplama netijesinde alnan uly san \u015fudur:<\/p>

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

    N\u00e4me \u00fc\u00e7in bu \u015fon\u00e7a m\u00f6h\u00fcmdir?<\/b><\/p>

    • \u00d6s\u00fc\u015fi\u0148 m\u00f6\u00e7beri:<\/b> Bu san d\u00fcn\u00fd\u00e4ni\u0148 h\u00e4zirki jemi \u00fdyllyk bugda\u00fd \u00f6n\u00fcm\u00e7iligini\u0148 takmynan 2000 esse de\u0148dir.\u00a0<\/span><\/li><\/ul>

      Stratejik sapak:<\/b> Bu mesele liderlere we strategi\u00fda\u00e7ylara ki\u00e7i \u00fc\u00fdtge\u015fmeleri\u0148 (\u201ciki esse k\u00f6peltmek\u201d) wagty\u0148 ge\u00e7megi bilen dolandyryp bolmajak g\u00fc\u00fd\u00e7lere \u00f6wr\u00fclip biljekdigini \u00f6wred\u00fd\u00e4n gadymy akyl dersidir.<\/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\/tk\/wp-json\/wp\/v2\/pages\/963","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/shatranj.art\/tk\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/shatranj.art\/tk\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/shatranj.art\/tk\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/shatranj.art\/tk\/wp-json\/wp\/v2\/comments?post=963"}],"version-history":[{"count":22,"href":"https:\/\/shatranj.art\/tk\/wp-json\/wp\/v2\/pages\/963\/revisions"}],"predecessor-version":[{"id":1443,"href":"https:\/\/shatranj.art\/tk\/wp-json\/wp\/v2\/pages\/963\/revisions\/1443"}],"up":[{"embeddable":true,"href":"https:\/\/shatranj.art\/tk\/wp-json\/wp\/v2\/pages\/743"}],"wp:attachment":[{"href":"https:\/\/shatranj.art\/tk\/wp-json\/wp\/v2\/media?parent=963"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}