المربع السحري: حاصل جمع كل الصفوف والأعمدة والأقطار

Keep going

26 مارس 2013

(0)

في الرياضيات المسلية، المربع السحري هي مصفوفة مربعة ذات حيز $(n)$ ، مكونة من

$n^2$ أعداد صحيحة، بحيث أن حاصل جمع $(n)$ رقم في كلّ من الصفوف والأعمدة

والأقطار الرئيسية يؤدي لنفس الحاصل. توجد مربعات سحرية مهما كان الحيز $n\ge1$

بإقصاء $n=2$ (أربع أعداد)، مع كون الحالة $n=1$ تعتبر أمرا بديهيا.

يبين الشكل التالي مثالا لمربع سحري من $n=3$

لاحظ أن مجموع كل سطر وعمود وقطر رئيسي يساوي دائما 15. يسمى هذا المجموع

ثابتا سحريا $(M)$ وقيمته بصفة عامة:

$M(n) = \frac{n(n^2+1)}{2}$

Reactions

أخر المواضيع من قسم : الرياضيات المسلية

تعليقات

window['__wavt'] = 'AOuZoY5BW7s2RoJRb1m1hDgRiPXEsUeeBQ:1735322204923';_WidgetManager._Init('//www.blogger.com/rearrange?blogID\x3d2985102397141835048','//a7la3alaam.blogspot.com/2013/03/blog-post_4899.html','2985102397141835048'); _WidgetManager._SetDataContext([{'name': 'blog', 'data': {'blogId': '2985102397141835048', 'title': '\u0623\u062d\u0640\u0644\u0649 \u0639\u0640\u0640\u0640\u0627\u0644\u0645', 'url': 'https://a7la3alaam.blogspot.com/2013/03/blog-post_4899.html', 'canonicalUrl': 'https://a7la3alaam.blogspot.com/2013/03/blog-post_4899.html', 'homepageUrl': 'https://a7la3alaam.blogspot.com/', 'searchUrl': 'https://a7la3alaam.blogspot.com/search', 'canonicalHomepageUrl': 'https://a7la3alaam.blogspot.com/', 'blogspotFaviconUrl': 'https://a7la3alaam.blogspot.com/favicon.ico', 'bloggerUrl': 'https://www.blogger.com', 'hasCustomDomain': false, 'httpsEnabled': true, 'enabledCommentProfileImages': true, 'gPlusViewType': 'FILTERED_POSTMOD', 'adultContent': false, 'analyticsAccountNumber': '', 'encoding': 'UTF-8', 'locale': 'ar', 'localeUnderscoreDelimited': 'ar', 'languageDirection': 'rtl', 'isPrivate': false, 'isMobile': false, 'isMobileRequest': false, 'mobileClass': '', 'isPrivateBlog': false, 'isDynamicViewsAvailable': true, 'feedLinks': '\x3clink rel\x3d\x22alternate\x22 type\x3d\x22application/atom+xml\x22 title\x3d\x22\u0623\u062d\u0640\u0644\u0649 \u0639\u0640\u0640\u0640\u0627\u0644\u0645 - Atom\x22 href\x3d\x22https://a7la3alaam.blogspot.com/feeds/posts/default\x22 /\x3e\n\x3clink rel\x3d\x22alternate\x22 type\x3d\x22application/rss+xml\x22 title\x3d\x22\u0623\u062d\u0640\u0644\u0649 \u0639\u0640\u0640\u0640\u0627\u0644\u0645 - RSS\x22 href\x3d\x22https://a7la3alaam.blogspot.com/feeds/posts/default?alt\x3drss\x22 /\x3e\n\x3clink rel\x3d\x22service.post\x22 type\x3d\x22application/atom+xml\x22 title\x3d\x22\u0623\u062d\u0640\u0644\u0649 \u0639\u0640\u0640\u0640\u0627\u0644\u0645 - Atom\x22 href\x3d\x22https://www.blogger.com/feeds/2985102397141835048/posts/default\x22 /\x3e\n\n\x3clink rel\x3d\x22alternate\x22 type\x3d\x22application/atom+xml\x22 title\x3d\x22\u0623\u062d\u0640\u0644\u0649 \u0639\u0640\u0640\u0640\u0627\u0644\u0645 - Atom\x22 href\x3d\x22https://a7la3alaam.blogspot.com/feeds/1755931971283322828/comments/default\x22 /\x3e\n', 'meTag': '', 'adsenseClientId': 'ca-pub-2425327435332491', 'adsenseHostId': 'ca-host-pub-1556223355139109', 'adsenseHasAds': true, 'adsenseAutoAds': false, 'boqCommentIframeForm': true, 'loginRedirectParam': '', 'view': '', 'dynamicViewsCommentsSrc': '//www.blogblog.com/dynamicviews/4224c15c4e7c9321/js/comments.js', 'dynamicViewsScriptSrc': '//www.blogblog.com/dynamicviews/361ce9cf7a112c52', 'plusOneApiSrc': 'https://apis.google.com/js/platform.js', 'disableGComments': true, 'interstitialAccepted': false, 'sharing': {'platforms': [{'name': '\u0627\u0644\u062d\u0635\u0648\u0644 \u0639\u0644\u0649 \u0627\u0644\u0631\u0627\u0628\u0637', 'key': 'link', 'shareMessage': '\u0627\u0644\u062d\u0635\u0648\u0644 \u0639\u0644\u0649 \u0627\u0644\u0631\u0627\u0628\u0637', 'target': ''}, {'name': 'Facebook', 'key': 'facebook', 'shareMessage': '\u0645\u0634\u0627\u0631\u0643\u0629 \u0625\u0644\u0649 Facebook', 'target': 'facebook'}, {'name': '\u0643\u062a\u0627\u0628\u0629 \u0645\u062f\u0648\u0646\u0629 \u062d\u0648\u0644 \u0647\u0630\u0647 \u0627\u0644\u0645\u0634\u0627\u0631\u0643\u0629', 'key': 'blogThis', 'shareMessage': '\u0643\u062a\u0627\u0628\u0629 \u0645\u062f\u0648\u0646\u0629 \u062d\u0648\u0644 \u0647\u0630\u0647 \u0627\u0644\u0645\u0634\u0627\u0631\u0643\u0629', 'target': 'blog'}, {'name': 'X', 'key': 'twitter', 'shareMessage': '\u0645\u0634\u0627\u0631\u0643\u0629 \u0625\u0644\u0649 X', 'target': 'twitter'}, {'name': 'Pinterest', 'key': 'pinterest', 'shareMessage': '\u0645\u0634\u0627\u0631\u0643\u0629 \u0625\u0644\u0649 Pinterest', 'target': 'pinterest'}, {'name': '\u0628\u0631\u064a\u062f \u0625\u0644\u0643\u062a\u0631\u0648\u0646\u064a', 'key': 'email', 'shareMessage': '\u0628\u0631\u064a\u062f \u0625\u0644\u0643\u062a\u0631\u0648\u0646\u064a', 'target': 'email'}], 'disableGooglePlus': true, 'googlePlusShareButtonWidth': 0, 'googlePlusBootstrap': '\x3cscript type\x3d\x22text/javascript\x22\x3ewindow.___gcfg \x3d {\x27lang\x27: \x27ar\x27};\x3c/script\x3e'}, 'hasCustomJumpLinkMessage': false, 'jumpLinkMessage': '\u0642\u0631\u0627\u0621\u0629 \u0627\u0644\u0645\u0632\u064a\u062f', 'pageType': 'item', 'postId': '1755931971283322828', 'postImageUrl': 'http://upload.wikimedia.org/wikipedia/commons/thumb/e/e4/Magicsquareexample.svg/180px-Magicsquareexample.svg.png', 'pageName': '\u0627\u0644\u0645\u0631\u0628\u0639 \u0627\u0644\u0633\u062d\u0631\u064a: \u062d\u0627\u0635\u0644 \u062c\u0645\u0639 \u0643\u0644 \u0627\u0644\u0635\u0641\u0648\u0641 \u0648\u0627\u0644\u0623\u0639\u0645\u062f\u0629 \u0648\u0627\u0644\u0623\u0642\u0637\u0627\u0631 ', 'pageTitle': '\u0623\u062d\u0640\u0644\u0649 \u0639\u0640\u0640\u0640\u0627\u0644\u0645: \u0627\u0644\u0645\u0631\u0628\u0639 \u0627\u0644\u0633\u062d\u0631\u064a: \u062d\u0627\u0635\u0644 \u062c\u0645\u0639 \u0643\u0644 \u0627\u0644\u0635\u0641\u0648\u0641 \u0648\u0627\u0644\u0623\u0639\u0645\u062f\u0629 \u0648\u0627\u0644\u0623\u0642\u0637\u0627\u0631 ', 'metaDescription': ''}}, {'name': 'features', 'data': {}}, {'name': 'messages', 'data': {'edit': '\u062a\u0639\u062f\u064a\u0644', 'linkCopiedToClipboard': '\u062a\u0645 \u0646\u0633\u062e \u0627\u0644\u0631\u0627\u0628\u0637 \u0625\u0644\u0649 \u0627\u0644\u062d\u0627\u0641\u0638\u0629', 'ok': '\u062d\u0633\u0646\u064b\u0627', 'postLink': '\u0631\u0627\u0628\u0637 \u0627\u0644\u0645\u0634\u0627\u0631\u0643\u0629'}}, {'name': 'template', 'data': {'name': 'custom', 'localizedName': '\u0645\u062e\u0635\u0635', 'isResponsive': true, 'isAlternateRendering': false, 'isCustom': true}}, {'name': 'view', 'data': {'classic': {'name': 'classic', 'url': '?view\x3dclassic'}, 'flipcard': {'name': 'flipcard', 'url': '?view\x3dflipcard'}, 'magazine': {'name': 'magazine', 'url': '?view\x3dmagazine'}, 'mosaic': {'name': 'mosaic', 'url': '?view\x3dmosaic'}, 'sidebar': {'name': 'sidebar', 'url': '?view\x3dsidebar'}, 'snapshot': {'name': 'snapshot', 'url': '?view\x3dsnapshot'}, 'timeslide': {'name': 'timeslide', 'url': '?view\x3dtimeslide'}, 'isMobile': false, 'title': '\u0627\u0644\u0645\u0631\u0628\u0639 \u0627\u0644\u0633\u062d\u0631\u064a: \u062d\u0627\u0635\u0644 \u062c\u0645\u0639 \u0643\u0644 \u0627\u0644\u0635\u0641\u0648\u0641 \u0648\u0627\u0644\u0623\u0639\u0645\u062f\u0629 \u0648\u0627\u0644\u0623\u0642\u0637\u0627\u0631 ', 'description': '', 'featuredImage': 'https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_vsV3WCvNHn1QuSUSucknQ8REkZW0gThYu2yjcuJMw6QEewgcMCuXjVCZbiTpTLPyFIADLSTIysht9d_rtI_skohujJ7dx4TIcSjVmsw3CNpgWS4dQovloYG9l0INQR9MwImRCpGukb3JadRMKlfQlVvuoipx3WS2CoKoyFDWUJGb8x37fY8bR2k4MmhluIWeYaeJQ', 'url': 'https://a7la3alaam.blogspot.com/2013/03/blog-post_4899.html', 'type': 'item', 'isSingleItem': true, 'isMultipleItems': false, 'isError': false, 'isPage': false, 'isPost': true, 'isHomepage': false, 'isArchive': false, 'isLabelSearch': false, 'postId': 1755931971283322828}}, {'name': 'widgets', 'data': [{'title': '\u0627\u0644\u0635\u0641\u062d\u0627\u062a', 'type': 'PageList', 'sectionId': 'pages', 'id': 'PageList1'}, {'title': '\u0623\u062d\u0640\u0644\u0649 \u0639\u0640\u0640\u0640\u0627\u0644\u0645 (\u0631\u0623\u0633 \u0627\u0644\u0635\u0641\u062d\u0629)', 'type': 'Header', 'sectionId': 'logo', 'id': 'Header1'}, {'title': '\u0627\u0644\u0642\u0627\u0626\u0645\u0629 \u0627\u0644\u0631\u0626\u064a\u0633\u064a\u0629', 'type': 'LinkList', 'sectionId': 'menu', 'id': 'LinkList22'}, {'title': '', 'type': 'HTML', 'sectionId': 'TopPost-sc', 'id': 'HTML3'}, {'title': '\u0623\u062d\u062f\u062b \u0627\u0644\u0645\u0648\u0627\u0636\u064a\u0639 [slide]', 'type': 'Label', 'sectionId': 'TopPost-sc', 'id': 'Label2'}, {'title': '', 'type': 'HTML', 'sectionId': 'Postcs1', 'id': 'HTML4'}, {'title': '\u0631\u0633\u0627\u0626\u0644 \u0627\u0644\u0645\u062f\u0648\u0646\u0629 \u0627\u0644\u0625\u0644\u0643\u062a\u0631\u0648\u0646\u064a\u0629', 'type': 'Blog', 'sectionId': 'Tempnec', 'id': 'Blog1', 'posts': [{'id': '1755931971283322828', 'title': '\u0627\u0644\u0645\u0631\u0628\u0639 \u0627\u0644\u0633\u062d\u0631\u064a: \u062d\u0627\u0635\u0644 \u062c\u0645\u0639 \u0643\u0644 \u0627\u0644\u0635\u0641\u0648\u0641 \u0648\u0627\u0644\u0623\u0639\u0645\u062f\u0629 \u0648\u0627\u0644\u0623\u0642\u0637\u0627\u0631 ', 'featuredImage': 'https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_vsV3WCvNHn1QuSUSucknQ8REkZW0gThYu2yjcuJMw6QEewgcMCuXjVCZbiTpTLPyFIADLSTIysht9d_rtI_skohujJ7dx4TIcSjVmsw3CNpgWS4dQovloYG9l0INQR9MwImRCpGukb3JadRMKlfQlVvuoipx3WS2CoKoyFDWUJGb8x37fY8bR2k4MmhluIWeYaeJQ', 'showInlineAds': true}], 'footerBylines': [{'regionName': 'footer1', 'items': [{'name': 'author', 'label': '\u0643\u062a\u0628:'}, {'name': 'timestamp', 'label': '\u0622\u062e\u0631 \u062a\u062d\u062f\u064a\u062b:'}, {'name': 'comments', 'label': 'comments'}, {'name': 'share', 'label': ''}, {'name': 'backlinks', 'label': 'Related Posts'}]}, {'regionName': 'footer2', 'items': [{'name': 'labels', 'label': '\u0627\u0644\u0642\u0633\u0645:'}]}, {'regionName': 'footer3', 'items': [{'name': 'reactions', 'label': 'Reactions'}]}], 'allBylineItems': [{'name': 'author', 'label': '\u0643\u062a\u0628:'}, {'name': 'timestamp', 'label': '\u0622\u062e\u0631 \u062a\u062d\u062f\u064a\u062b:'}, {'name': 'comments', 'label': 'comments'}, {'name': 'share', 'label': ''}, {'name': 'backlinks', 'label': 'Related Posts'}, {'name': 'labels', 'label': '\u0627\u0644\u0642\u0633\u0645:'}, {'name': 'reactions', 'label': 'Reactions'}]}, {'title': '\u0623\u0639\u0644\u0627\u0646 \u0645\u0646\u062a\u0635\u0641 \u0627\u0644\u0645\u0648\u0636\u0648\u0639', 'type': 'HTML', 'sectionId': 'PostAds', 'id': 'HTML202'}, {'title': '\u0623\u0639\u0644\u0627\u0646 \u0623\u062e\u0631 \u0627\u0644\u0645\u0648\u0636\u0648\u0639', 'type': 'HTML', 'sectionId': 'PostAds', 'id': 'HTML203'}, {'title': '\u0627\u0639\u0644\u0627\u0646 \u0628\u0639\u062f \u0627\u0648\u0644 \u0641\u0642\u0631\u0629', 'type': 'HTML', 'sectionId': 'PostAds', 'id': 'HTML205'}, {'title': '\u0627\u0639\u0644\u0627\u0646 \u0628\u0639\u062f \u062b\u0627\u0646\u064a \u0641\u0642\u0631\u0629', 'type': 'HTML', 'sectionId': 'PostAds', 'id': 'HTML206'}, {'title': '\u0627\u0639\u0644\u0627\u0646 \u0628\u0639\u062f \u062b\u0627\u0644\u062b \u0641\u0642\u0631\u0629', 'type': 'HTML', 'sectionId': 'PostAds', 'id': 'HTML207'}, {'title': '\u0645\u064a\u0632\u0629 \u062c\u062f\u0648\u0644 \u0627\u0644\u062a\u0646\u0642\u0644', 'type': 'HTML', 'sectionId': 'AddOns', 'id': 'HTML1'}, {'title': '\u0645\u064a\u0632\u0629 \u0642\u062f \u064a\u0639\u062c\u0628\u0643 \u0627\u064a\u0636\u0627', 'type': 'HTML', 'sectionId': 'AddOns', 'id': 'HTML2'}, {'title': '', 'type': 'HTML', 'sectionId': 'Postcs5', 'id': 'HTML5'}, {'title': '\u0627\u0644\u0628\u062d\u062b', 'type': 'HTML', 'sectionId': 'sidepar', 'id': 'HTML6'}, {'title': '\u0627\u0644\u0645\u0648\u0627\u0636\u064a\u0639 \u0627\u0644\u0631\u0627\u0626\u062c\u0629', 'type': 'PopularPosts', 'sectionId': 'sidepar', 'id': 'PopularPosts1', 'posts': [{'title': '\u062a\u0641\u0633\u064a\u0631 \u062d\u0644\u0645 \u0627\u0644\u0633\u0642\u0648\u0637 \u0645\u0646 \u0645\u0643\u0627\u0646 \u0645\u0631\u062a\u0641\u0639', 'id': 5178671211022708312}, {'title': '\u062d\u064a\u0648\u0627\u0646\u0627\u062a \u064a\u0628\u062f\u0623 \u0627\u0633\u0645\u0647\u0627 \u0628\u062d\u0631\u0641 \u0627\u0644\u0631\u0627\u0621', 'id': 6325814802432765}, {'title': '\u0647\u0644 \u062e\u0644\u0637 \u0627\u0644\u0632\u0646\u062c\u0628\u064a\u0644 \u0645\u0639 \u0627\u0644\u0642\u0631\u0641\u0647 \u064a\u0646\u062a\u062c \u0645\u0627\u062f\u0629 \u0627\u0644\u063a\u0644\u0648\u0643\u064a\u0632\u0631\u064a\u0646\u064a\u0646 \u0627\u0644\u0633\u0627\u0645\u0629\u061f', 'id': 6101509042704204001}, {'title': '\u062a\u0641\u0633\u064a\u0631 \u0627\u0644\u062d\u0644\u0645 \u0628\u0627\u0644\u062d\u0630\u0627\u0621', 'id': 7658131937466580623}]}, {'title': '\u0645\u0648\u0636\u0648\u0639 \u0645\u0645\u064a\u0632', 'type': 'FeaturedPost', 'sectionId': 'sidepar', 'id': 'FeaturedPost1', 'postId': '751760552567109735'}, {'title': '\u0645\u0648\u0627\u0642\u0639 \u0627\u0644\u062a\u0648\u0627\u0635\u0644 \u0627\u0644\u0625\u062c\u062a\u0645\u0627\u0639\u064a', 'type': 'LinkList', 'sectionId': 'footer-social', 'id': 'LinkList2'}]}]); _WidgetManager._RegisterWidget('_PageListView', new _WidgetInfo('PageList1', 'pages', document.getElementById('PageList1'), {'title': '\u0627\u0644\u0635\u0641\u062d\u0627\u062a', 'links': [{'isCurrentPage': false, 'href': '/', 'title': '\u0627\u0644\u0635\u0641\u062d\u0629 \u0627\u0644\u0631\u0626\u064a\u0633\u064a\u0629'}, {'isCurrentPage': false, 'href': 'https://a7la3alaam.blogspot.com/p/index.html', 'id': '634945491986330562', 'title': '\u0627\u0644\u0627\u0631\u0634\u064a\u0641'}, {'isCurrentPage': false, 'href': 'https://a7la3alaam.blogspot.com/p/privacy-policy.html', 'id': '2836252865733540951', 'title': '\u0633\u064a\u0627\u0633\u0629 \u0627\u0644\u062e\u0635\u0648\u0635\u064a\u0629'}, {'isCurrentPage': false, 'href': 'https://a7la3alaam.blogspot.com/p/terms-of-use_20.html', 'id': '1666290592615694812', 'title': '\u0627\u062a\u0641\u0627\u0642\u064a\u0629 \u0627\u0644\u0627\u0633\u062a\u062e\u062f\u0627\u0645'}, {'isCurrentPage': false, 'href': 'https://a7la3alaam.blogspot.com/p/contact.html', 'id': '4855634809751399273', 'title': '\u0627\u062a\u0635\u0644 \u0628\u0646\u0627'}], 'mobile': false, 'showPlaceholder': true, 'hasCurrentPage': false}, 'displayModeFull')); _WidgetManager._RegisterWidget('_HeaderView', new _WidgetInfo('Header1', 'logo', document.getElementById('Header1'), {}, 'displayModeFull')); _WidgetManager._RegisterWidget('_LinkListView', new _WidgetInfo('LinkList22', 'menu', document.getElementById('LinkList22'), {}, 'displayModeFull')); _WidgetManager._RegisterWidget('_HTMLView', new _WidgetInfo('HTML3', 'TopPost-sc', document.getElementById('HTML3'), {}, 'displayModeFull')); _WidgetManager._RegisterWidget('_LabelView', new _WidgetInfo('Label2', 'TopPost-sc', document.getElementById('Label2'), {}, 'displayModeFull')); _WidgetManager._RegisterWidget('_HTMLView', new _WidgetInfo('HTML4', 'Postcs1', document.getElementById('HTML4'), {}, 'displayModeFull')); _WidgetManager._RegisterWidget('_BlogView', new _WidgetInfo('Blog1', 'Tempnec', document.getElementById('Blog1'), {'cmtInteractionsEnabled': false, 'lightboxEnabled': true, 'lightboxModuleUrl': 'https://www.blogger.com/static/v1/jsbin/4234554620-lbx__ar.js', 'lightboxCssUrl': 'https://www.blogger.com/static/v1/v-css/1964470060-lightbox_bundle_rtl.css'}, 'displayModeFull')); _WidgetManager._RegisterWidget('_HTMLView', new _WidgetInfo('HTML202', 'PostAds', document.getElementById('HTML202'), {}, 'displayModeFull')); _WidgetManager._RegisterWidget('_HTMLView', new _WidgetInfo('HTML203', 'PostAds', document.getElementById('HTML203'), {}, 'displayModeFull')); _WidgetManager._RegisterWidget('_HTMLView', new _WidgetInfo('HTML205', 'PostAds', document.getElementById('HTML205'), {}, 'displayModeFull')); _WidgetManager._RegisterWidget('_HTMLView', new _WidgetInfo('HTML206', 'PostAds', document.getElementById('HTML206'), {}, 'displayModeFull')); _WidgetManager._RegisterWidget('_HTMLView', new _WidgetInfo('HTML207', 'PostAds', document.getElementById('HTML207'), {}, 'displayModeFull')); _WidgetManager._RegisterWidget('_HTMLView', new _WidgetInfo('HTML1', 'AddOns', document.getElementById('HTML1'), {}, 'displayModeFull')); _WidgetManager._RegisterWidget('_HTMLView', new _WidgetInfo('HTML2', 'AddOns', document.getElementById('HTML2'), {}, 'displayModeFull')); _WidgetManager._RegisterWidget('_HTMLView', new _WidgetInfo('HTML5', 'Postcs5', document.getElementById('HTML5'), {}, 'displayModeFull')); _WidgetManager._RegisterWidget('_HTMLView', new _WidgetInfo('HTML6', 'sidepar', document.getElementById('HTML6'), {}, 'displayModeFull')); _WidgetManager._RegisterWidget('_PopularPostsView', new _WidgetInfo('PopularPosts1', 'sidepar', document.getElementById('PopularPosts1'), {}, 'displayModeFull')); _WidgetManager._RegisterWidget('_FeaturedPostView', new _WidgetInfo('FeaturedPost1', 'sidepar', document.getElementById('FeaturedPost1'), {}, 'displayModeFull')); _WidgetManager._RegisterWidget('_LinkListView', new _WidgetInfo('LinkList2', 'footer-social', document.getElementById('LinkList2'), {}, 'displayModeFull'));

أحـلى عـــالم

القائمة الرئيسية

الصفحات

المربع السحري: حاصل جمع كل الصفوف والأعمدة والأقطار

أخر المواضيع من قسم : الرياضيات المسلية

تعليقات

إرسال تعليق