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id="toc-mw-content-text" class="vector-toc-list-item vector-toc-level-1"> <a href="#" class="vector-toc-link"> <div class="vector-toc-text">Início</div> </a> </li> <li id="toc-Referências" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Referências"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Referências</span> </div> </a> <ul id="toc-Referências-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Conteúdo" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="Alternar o índice" > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-listBullet mw-ui-icon-wikimedia-listBullet"></span> <span class="vector-dropdown-label-text">Alternar o índice</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-titlebar-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">Rede diagonal</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox 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Disponível em 20 línguas" > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-20" aria-hidden="true" ><span class="vector-icon mw-ui-icon-language-progressive mw-ui-icon-wikimedia-language-progressive"></span> <span class="vector-dropdown-label-text">20 línguas</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%B4%D8%A8%D9%83%D8%A9_(%D9%86%D8%B8%D8%B1%D9%8A%D8%A9_%D8%A7%D9%84%D8%B2%D9%85%D8%B1)" title="شبكة (نظرية الزمر) — árabe" lang="ar" hreflang="ar" data-title="شبكة (نظرية الزمر)" data-language-autonym="العربية" data-language-local-name="árabe" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Bodov%C3%A1_m%C5%99%C3%AD%C5%BE" title="Bodová mříž — checo" lang="cs" hreflang="cs" data-title="Bodová mříž" data-language-autonym="Čeština" data-language-local-name="checo" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-cv mw-list-item"><a href="https://cv.wikipedia.org/wiki/%D0%A0%D0%B5%D1%88%D0%B5%D1%82%D0%BA%D0%B5_(%D0%B3%D0%B5%D0%BE%D0%BC%D0%B5%D1%82%D1%80%D0%B8)" title="Решетке (геометри) — chuvash" lang="cv" hreflang="cv" data-title="Решетке (геометри)" data-language-autonym="Чӑвашла" data-language-local-name="chuvash" class="interlanguage-link-target"><span>Чӑвашла</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Gitter_(Mathematik)" title="Gitter (Mathematik) — alemão" lang="de" hreflang="de" data-title="Gitter (Mathematik)" data-language-autonym="Deutsch" data-language-local-name="alemão" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Lattice_(group)" title="Lattice (group) — inglês" lang="en" hreflang="en" data-title="Lattice (group)" data-language-autonym="English" data-language-local-name="inglês" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Red_(grupo)" title="Red (grupo) — espanhol" lang="es" hreflang="es" data-title="Red (grupo)" data-language-autonym="Español" data-language-local-name="espanhol" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D9%85%D8%B4%D8%A8%DA%A9%D9%87_(%DA%AF%D8%B1%D9%88%D9%87)" title="مشبکه (گروه) — persa" lang="fa" hreflang="fa" data-title="مشبکه (گروه)" data-language-autonym="فارسی" data-language-local-name="persa" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/R%C3%A9seau_(g%C3%A9om%C3%A9trie)" title="Réseau (géométrie) — francês" lang="fr" hreflang="fr" data-title="Réseau (géométrie)" data-language-autonym="Français" data-language-local-name="francês" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%A1%D7%A8%D7%99%D7%92_(%D7%92%D7%90%D7%95%D7%9E%D7%98%D7%A8%D7%99%D7%94)" title="סריג (גאומטריה) — hebraico" lang="he" hreflang="he" data-title="סריג (גאומטריה)" data-language-autonym="עברית" data-language-local-name="hebraico" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Reticolo_(gruppo)" title="Reticolo (gruppo) — italiano" lang="it" hreflang="it" data-title="Reticolo (gruppo)" data-language-autonym="Italiano" data-language-local-name="italiano" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E6%A0%BC%E5%AD%90_(%E6%95%B0%E5%AD%A6)" title="格子 (数学) — japonês" lang="ja" hreflang="ja" data-title="格子 (数学)" data-language-autonym="日本語" data-language-local-name="japonês" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Rooster_(wiskunde)" title="Rooster (wiskunde) — neerlandês" lang="nl" hreflang="nl" data-title="Rooster (wiskunde)" data-language-autonym="Nederlands" data-language-local-name="neerlandês" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Gitter_i_matematikk" title="Gitter i matematikk — norueguês nynorsk" lang="nn" hreflang="nn" data-title="Gitter i matematikk" data-language-autonym="Norsk nynorsk" data-language-local-name="norueguês nynorsk" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Punkt_kratowy" title="Punkt kratowy — polaco" lang="pl" hreflang="pl" data-title="Punkt kratowy" data-language-autonym="Polski" data-language-local-name="polaco" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Re%C8%9Bea_(geometrie)" title="Rețea (geometrie) — romeno" lang="ro" hreflang="ro" data-title="Rețea (geometrie)" data-language-autonym="Română" data-language-local-name="romeno" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%A0%D0%B5%D1%88%D1%91%D1%82%D0%BA%D0%B0_(%D0%B3%D0%B5%D0%BE%D0%BC%D0%B5%D1%82%D1%80%D0%B8%D1%8F)" title="Решётка (геометрия) — russo" lang="ru" hreflang="ru" data-title="Решётка (геометрия)" data-language-autonym="Русский" data-language-local-name="russo" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Gitter_(grupp)" title="Gitter (grupp) — sueco" lang="sv" hreflang="sv" data-title="Gitter (grupp)" data-language-autonym="Svenska" data-language-local-name="sueco" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D2%90%D1%80%D0%B0%D1%82%D0%BA%D0%B0_(%D0%B3%D0%B5%D0%BE%D0%BC%D0%B5%D1%82%D1%80%D1%96%D1%8F)" title="Ґратка (геометрія) — ucraniano" lang="uk" hreflang="uk" data-title="Ґратка (геометрія)" data-language-autonym="Українська" data-language-local-name="ucraniano" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/L%C6%B0%E1%BB%9Bi_(nh%C3%B3m)" title="Lưới (nhóm) — vietnamita" lang="vi" hreflang="vi" data-title="Lưới (nhóm)" data-language-autonym="Tiếng Việt" data-language-local-name="vietnamita" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E6%A0%BC%E5%AD%90" title="格子 — chinês" lang="zh" hreflang="zh" data-title="格子" data-language-autonym="中文" data-language-local-name="chinês" class="interlanguage-link-target"><span>中文</span></a></li> </ul> <div class="after-portlet after-portlet-lang"><span class="wb-langlinks-edit wb-langlinks-link"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q1096885#sitelinks-wikipedia" title="Editar hiperligações interlínguas" class="wbc-editpage">Editar hiperligações</a></span></div> </div> </div> </div> </header> <div class="vector-page-toolbar"> <div class="vector-page-toolbar-container"> <div id="left-navigation"> <nav aria-label="Espaços nominais"> <div id="p-associated-pages" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-associated-pages" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-nstab-main" class="selected vector-tab-noicon mw-list-item"><a href="/wiki/Rede_diagonal" title="Ver a página de conteúdo [c]" accesskey="c"><span>Artigo</span></a></li><li id="ca-talk" class="new vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Discuss%C3%A3o:Rede_diagonal&action=edit&redlink=1" rel="discussion" class="new" title="Discussão sobre o conteúdo da página (página não existe) [t]" accesskey="t"><span>Discussão</span></a></li> </ul> </div> </div> <div id="vector-variants-dropdown" class="vector-dropdown emptyPortlet" > <input 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href="/wiki/Especial:P%C3%A1ginas_afluentes/Rede_diagonal" title="Lista de todas as páginas que contêm hiperligações para esta [j]" accesskey="j"><span>Páginas afluentes</span></a></li><li id="t-recentchangeslinked" class="mw-list-item"><a href="/wiki/Especial:Altera%C3%A7%C3%B5es_relacionadas/Rede_diagonal" rel="nofollow" title="Mudanças recentes nas páginas para as quais esta contém hiperligações [k]" accesskey="k"><span>Alterações relacionadas</span></a></li><li id="t-upload" class="mw-list-item"><a href="/wiki/Wikipedia:Carregar_ficheiro" title="Carregar ficheiros [u]" accesskey="u"><span>Carregar ficheiro</span></a></li><li id="t-specialpages" class="mw-list-item"><a href="/wiki/Especial:P%C3%A1ginas_especiais" title="Lista de páginas especiais [q]" accesskey="q"><span>Páginas especiais</span></a></li><li id="t-permalink" class="mw-list-item"><a href="/w/index.php?title=Rede_diagonal&oldid=61846985" title="Hiperligação permanente para esta revisão desta página"><span>Hiperligação permanente</span></a></li><li id="t-info" class="mw-list-item"><a href="/w/index.php?title=Rede_diagonal&action=info" title="Mais informações sobre esta página"><span>Informações da página</span></a></li><li id="t-cite" class="mw-list-item"><a href="/w/index.php?title=Especial:Citar&page=Rede_diagonal&id=61846985&wpFormIdentifier=titleform" title="Informação sobre como citar esta página"><span>Citar esta página</span></a></li><li id="t-urlshortener" class="mw-list-item"><a href="/w/index.php?title=Especial:UrlShortener&url=https%3A%2F%2Fpt.wikipedia.org%2Fwiki%2FRede_diagonal"><span>Obter URL encurtado</span></a></li><li id="t-urlshortener-qrcode" class="mw-list-item"><a href="/w/index.php?title=Especial:QrCode&url=https%3A%2F%2Fpt.wikipedia.org%2Fwiki%2FRede_diagonal"><span>Descarregar código QR</span></a></li> </ul> </div> </div> <div id="p-coll-print_export" class="vector-menu mw-portlet mw-portlet-coll-print_export" > <div class="vector-menu-heading"> Imprimir/exportar </div> <div 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id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="pt" dir="ltr"><div class="hatnote"><span typeof="mw:File"><span><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Disambig_grey.svg/20px-Disambig_grey.svg.png" decoding="async" width="20" height="15" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Disambig_grey.svg/30px-Disambig_grey.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Disambig_grey.svg/40px-Disambig_grey.svg.png 2x" data-file-width="260" data-file-height="200" /></span></span> <b>Nota:</b> Se procura outros sentidos do termo, veja <a href="/wiki/Reticulado" title="Reticulado">reticulado</a>.</div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/Ficheiro:Equilateral_Triangle_Lattice.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/9/97/Equilateral_Triangle_Lattice.svg/220px-Equilateral_Triangle_Lattice.svg.png" decoding="async" width="220" height="220" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/97/Equilateral_Triangle_Lattice.svg/330px-Equilateral_Triangle_Lattice.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/97/Equilateral_Triangle_Lattice.svg/440px-Equilateral_Triangle_Lattice.svg.png 2x" data-file-width="220" data-file-height="220" /></a><figcaption>Rede diagonal em um <a href="/wiki/Espa%C3%A7o_bidimensional" title="Espaço bidimensional">espaço bidimensional</a>.</figcaption></figure> <p>Em <a href="/wiki/Geometria" title="Geometria">geometria</a> e <a href="/wiki/Teoria_dos_grupos" title="Teoria dos grupos">teoria dos grupos</a>, uma <b>rede diagonal</b> em <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbb {R} ^{n}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">R</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbb {R} ^{n}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c510b63578322050121fe966f2e5770bea43308d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.897ex; height:2.343ex;" alt="{\displaystyle \mathbb {R} ^{n}}"></span> é um <a href="/wiki/Subgrupo" title="Subgrupo">subgrupo</a> de <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbb {R} ^{n}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">R</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbb {R} ^{n}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c510b63578322050121fe966f2e5770bea43308d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.897ex; height:2.343ex;" alt="{\displaystyle \mathbb {R} ^{n}}"></span> que é isomorfo a <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbb {Z} ^{n}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">Z</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbb {Z} ^{n}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a9b5de7ced4588982b574fe19894aec6a3ca4c49" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.769ex; height:2.343ex;" alt="{\displaystyle \mathbb {Z} ^{n}}"></span> e que <a href="/wiki/Espa%C3%A7o_vectorial_gerado" title="Espaço vectorial gerado">gera</a> o <a href="/wiki/Espa%C3%A7o_vetorial" title="Espaço vetorial">espaço vetorial</a> <a href="/wiki/N%C3%BAmero_real" title="Número real">real</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbb {R} ^{n}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">R</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msup> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbb {R} ^{n}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/76ef548febfc9981762740107858be9e3a5576c3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.543ex; height:2.343ex;" alt="{\displaystyle \mathbb {R} ^{n}.}"></span> Em outras palavras, para qualquer <a href="/wiki/Base_(%C3%A1lgebra_linear)" title="Base (álgebra linear)">base</a> de <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbb {R} ^{n}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">R</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbb {R} ^{n}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c510b63578322050121fe966f2e5770bea43308d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.897ex; height:2.343ex;" alt="{\displaystyle \mathbb {R} ^{n}}"></span> o subgrupo de todas as <a href="/wiki/Combina%C3%A7%C3%A3o_linear" title="Combinação linear">combinações lineares</a> com coeficientes inteiros dos vetores de base forma uma rede diagonal. Uma rede diagonal pode ser visto como um <a href="/wiki/Malha_plana_por_pol%C3%ADgonos_regulares" title="Malha plana por polígonos regulares">malha plana regular</a> de um espaço por uma <a href="/wiki/C%C3%A9lula_unit%C3%A1ria" title="Célula unitária">célula unitária</a>.<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span>[</span>1<span>]</span></a></sup> </p><p>As redes diagonais têm muitas aplicações significativas em <a href="/wiki/Matem%C3%A1tica_pura" title="Matemática pura">matemática pura</a>, particularmente em relação às <a href="/wiki/%C3%81lgebra_de_Lie" title="Álgebra de Lie">álgebras de Lie,</a> <a href="/wiki/Teoria_dos_n%C3%BAmeros" title="Teoria dos números">teoria dos números</a> e <a href="/wiki/Teoria_dos_grupos" title="Teoria dos grupos">teoria dos grupos</a>. Eles também surgem na <a href="/wiki/Matem%C3%A1tica_aplicada" title="Matemática aplicada">matemática aplicada</a> em conexão com a teoria da codificação, na criptografia por causa da dureza computacional conjecturada de vários problemas de rede e são usados de várias maneiras nas ciências físicas. </p> <h2 id="Referências" style="cursor: help;" title="Esta seção foi configurada para não ser editável diretamente. Edite a página toda ou a seção anterior em vez disso."><span id="Refer.C3.AAncias"></span>Referências</h2> <div class="reflist" style="list-style-type: decimal;"><div class="mw-references-wrap"><ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><a href="#cite_ref-1">↑</a></span> <span class="reference-text"> <ul><li><cite id="CITEREFConwaySloane1999" class="citation"><a href="/wiki/John_Horton_Conway" class="mw-redirect" title="John Horton Conway">Conway, John Horton</a>; <a href="/wiki/Neil_Sloane" title="Neil Sloane">Sloane, Neil J. A.</a> (1999), <i>Sphere Packings, Lattices and Groups</i>, <a href="/wiki/International_Standard_Book_Number" title="International Standard Book Number">ISBN</a> <a href="/wiki/Especial:Fontes_de_livros/978-0-387-98585-5" title="Especial:Fontes de livros/978-0-387-98585-5">978-0-387-98585-5</a>, Grundlehren der Mathematischen Wissenschaften, <b>290</b> 3rd ed. , Berlin, New York: <a href="/wiki/Springer-Verlag" class="mw-redirect" title="Springer-Verlag">Springer-Verlag</a>, <a href="/wiki/Mathematical_Reviews" title="Mathematical Reviews">MR</a> <a rel="nofollow" class="external text" href="//www.ams.org/mathscinet-getitem?mr=0920369">0920369</a></cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fpt.wikipedia.org%3ARede+diagonal&rft.au=Sloane%2C+Neil+J.+A.&rft.aufirst=John+Horton&rft.aulast=Conway&rft.btitle=Sphere+Packings%2C+Lattices+and+Groups&rft.date=1999&rft.edition=3rd&rft.genre=book&rft.isbn=978-0-387-98585-5&rft.place=Berlin%2C+New+York&rft.pub=Springer-Verlag&rft.series=Grundlehren+der+Mathematischen+Wissenschaften&rft_id=%2F%2Fwww.ams.org%2Fmathscinet-getitem%3Fmr%3D0920369&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook" class="Z3988"><span style="display:none;"> </span></span></li></ul> </span></li> </ol></div></div> <ul class="noprint navigation-box" style="border-top: solid silver 1px; border-right: solid silver 1px; border-bottom:1px solid silver; border-left: solid silver 1px; padding:3px; background-color: #F9F9F9; text-align: center; margin-top:10px; margin-left: 0; clear: both;"><li style="display: inline;"><span style="white-space: nowrap; margin: auto 1.5em"><span style="margin-right: 0.5em"><span typeof="mw:File"><a href="/wiki/Ficheiro:Nuvola_apps_edu_mathematics-p.svg" title="Portal da matemática"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/c/c2/Nuvola_apps_edu_mathematics-p.svg/25px-Nuvola_apps_edu_mathematics-p.svg.png" decoding="async" width="25" height="25" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/c2/Nuvola_apps_edu_mathematics-p.svg/38px-Nuvola_apps_edu_mathematics-p.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/c2/Nuvola_apps_edu_mathematics-p.svg/50px-Nuvola_apps_edu_mathematics-p.svg.png 2x" data-file-width="128" data-file-height="128" /></a></span></span> <span style="font-weight:bold"><a href="/wiki/Portal:Matem%C3%A1tica" title="Portal:Matemática">Portal da matemática</a></span></span></li> </ul> <table class="noprint" style="border-top:none; border-bottom:none; background:transparent; color: inherit"><tbody><tr> <td style="text-align: center;"><span typeof="mw:File"><a href="/wiki/Ficheiro:E-to-the-i-pi.svg" class="mw-file-description"><img alt="Ícone de esboço" src="//upload.wikimedia.org/wikipedia/commons/thumb/3/35/E-to-the-i-pi.svg/34px-E-to-the-i-pi.svg.png" decoding="async" width="34" height="30" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/35/E-to-the-i-pi.svg/51px-E-to-the-i-pi.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/35/E-to-the-i-pi.svg/68px-E-to-the-i-pi.svg.png 2x" data-file-width="512" data-file-height="453" /></a></span></td> <td><i>Este artigo sobre <a href="/wiki/Matem%C3%A1tica" title="Matemática">matemática</a> é um <a href="/wiki/Wikip%C3%A9dia:Esbo%C3%A7o" title="Wikipédia:Esboço">esboço</a>. 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