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for="vector-user-links-dropdown-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-ellipsis mw-ui-icon-wikimedia-ellipsis"></span> <span class="vector-dropdown-label-text">כלים אישיים</span> </label> <div class="vector-dropdown-content"> <div id="p-personal" class="vector-menu mw-portlet mw-portlet-personal user-links-collapsible-item" title="תפריט משתמש" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-sitesupport" class="user-links-collapsible-item mw-list-item"><a href="//donate.wikimedia.org/wiki/Special:FundraiserRedirector?utm_source=donate&utm_medium=sidebar&utm_campaign=C13_he.wikipedia.org&uselang=he"><span>תרומה לוויקיפדיה</span></a></li><li id="pt-createaccount" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=%D7%9E%D7%99%D7%95%D7%97%D7%93:%D7%94%D7%A8%D7%A9%D7%9E%D7%94_%D7%9C%D7%97%D7%A9%D7%91%D7%95%D7%9F&returnto=%D7%97%D7%91%D7%95%D7%A8%D7%AA+%D7%94%D7%A1%D7%99%D7%91%D7%95%D7%91+%283%29SO&returntoquery=veaction%3Dedit%26redirect%3Dno" title="מומלץ ליצור חשבון ולהיכנס אליו, אך אין חובה לעשות זאת"><span class="vector-icon mw-ui-icon-userAdd mw-ui-icon-wikimedia-userAdd"></span> <span>יצירת חשבון</span></a></li><li id="pt-login" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=%D7%9E%D7%99%D7%95%D7%97%D7%93:%D7%9B%D7%A0%D7%99%D7%A1%D7%94_%D7%9C%D7%97%D7%A9%D7%91%D7%95%D7%9F&returnto=%D7%97%D7%91%D7%95%D7%A8%D7%AA+%D7%94%D7%A1%D7%99%D7%91%D7%95%D7%91+%283%29SO&returntoquery=veaction%3Dedit%26redirect%3Dno" title="מומלץ להיכנס לחשבון, אך אין חובה לעשות זאת [o]" accesskey="o"><span class="vector-icon mw-ui-icon-logIn mw-ui-icon-wikimedia-logIn"></span> <span>כניסה לחשבון</span></a></li> </ul> </div> </div> <div id="p-user-menu-anon-editor" class="vector-menu mw-portlet mw-portlet-user-menu-anon-editor" > <div class="vector-menu-heading"> דפים לעורכים שלא נכנסו לחשבון <a href="/wiki/%D7%A2%D7%96%D7%A8%D7%94:%D7%91%D7%A8%D7%95%D7%9B%D7%99%D7%9D_%D7%94%D7%91%D7%90%D7%99%D7%9D" aria-label="מידע נוסף על עריכה"><span>מידע נוסף</span></a> </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-anoncontribs" class="mw-list-item"><a href="/wiki/%D7%9E%D7%99%D7%95%D7%97%D7%93:%D7%94%D7%AA%D7%A8%D7%95%D7%9E%D7%95%D7%AA_%D7%A9%D7%9C%D7%99" title="רשימת העריכות שנעשו מכתובת IP זו [y]" accesskey="y"><span>תרומות</span></a></li><li id="pt-anontalk" class="mw-list-item"><a href="/wiki/%D7%9E%D7%99%D7%95%D7%97%D7%93:%D7%94%D7%A9%D7%99%D7%97%D7%94_%D7%A9%D7%9C%D7%99" title="דיון על העריכות שנעשו מכתובת IP זו [n]" accesskey="n"><span>שיחה</span></a></li> </ul> </div> </div> </div> </div> </nav> </div> </header> </div> <div class="mw-page-container"> <div class="mw-page-container-inner"> <div 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class="mw-body-header vector-page-titlebar"> <h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">חבורת הסיבוב (3)SO</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 mw-interlanguage-selector" aria-label="מעבר לערך בשפה אחרת. זמין ב־13 שפות" > <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-13" 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">13 שפות</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/3D_rotation_group" title="3D rotation group – אנגלית" lang="en" hreflang="en" data-title="3D rotation group" data-language-autonym="English" data-language-local-name="אנגלית" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Grup_de_rotaci%C3%B3_3D" title="Grup de rotació 3D – קטלאנית" lang="ca" hreflang="ca" data-title="Grup de rotació 3D" data-language-autonym="Català" data-language-local-name="קטלאנית" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Grupa_rotac%C3%AD_v_trojrozm%C4%9Brn%C3%A9m_prostoru" title="Grupa rotací v trojrozměrném prostoru – צ׳כית" lang="cs" hreflang="cs" data-title="Grupa rotací v trojrozměrném prostoru" data-language-autonym="Čeština" data-language-local-name="צ׳כית" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Drehgruppe" title="Drehgruppe – גרמנית" lang="de" hreflang="de" data-title="Drehgruppe" data-language-autonym="Deutsch" data-language-local-name="גרמנית" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/3-dimensia_turnada_grupo" title="3-dimensia turnada grupo – אספרנטו" lang="eo" hreflang="eo" data-title="3-dimensia turnada grupo" data-language-autonym="Esperanto" data-language-local-name="אספרנטו" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Grupo_de_rotaci%C3%B3n_SO(3)" title="Grupo de rotación SO(3) – ספרדית" lang="es" hreflang="es" data-title="Grupo de rotación SO(3)" data-language-autonym="Español" data-language-local-name="ספרדית" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/3%EC%B0%A8%EC%9B%90_%EC%A7%81%EA%B5%90%EA%B5%B0" title="3차원 직교군 – קוריאנית" lang="ko" hreflang="ko" data-title="3차원 직교군" data-language-autonym="한국어" data-language-local-name="קוריאנית" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Rotatiegroep" title="Rotatiegroep – הולנדית" lang="nl" hreflang="nl" data-title="Rotatiegroep" data-language-autonym="Nederlands" data-language-local-name="הולנדית" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Grupa_obrot%C3%B3w" title="Grupa obrotów – פולנית" lang="pl" hreflang="pl" data-title="Grupa obrotów" data-language-autonym="Polski" data-language-local-name="פולנית" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Grupo_de_rota%C3%A7%C3%A3o" title="Grupo de rotação – פורטוגזית" lang="pt" hreflang="pt" data-title="Grupo de rotação" data-language-autonym="Português" data-language-local-name="פורטוגזית" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%93%D1%80%D1%83%D0%BF%D0%BF%D0%B0_%D0%B2%D1%80%D0%B0%D1%89%D0%B5%D0%BD%D0%B8%D0%B9" title="Группа вращений – רוסית" lang="ru" hreflang="ru" data-title="Группа вращений" data-language-autonym="Русский" data-language-local-name="רוסית" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/SO(3)" title="SO(3) – אוקראינית" lang="uk" hreflang="uk" data-title="SO(3)" data-language-autonym="Українська" data-language-local-name="אוקראינית" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E6%97%8B%E8%BD%89%E7%BE%A4" title="旋轉群 – סינית" lang="zh" hreflang="zh" data-title="旋轉群" data-language-autonym="中文" data-language-local-name="סינית" 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/Q1256500#sitelinks-wikipedia" title="עריכת קישורים בין־לשוניים" class="wbc-editpage">עריכת הקישורים</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="מרחבי שם"> <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/%D7%97%D7%91%D7%95%D7%A8%D7%AA_%D7%94%D7%A1%D7%99%D7%91%D7%95%D7%91_(3)SO" title="צפייה בדף התוכן [c]" accesskey="c"><span>ערך</span></a></li><li id="ca-talk" class="new vector-tab-noicon mw-list-item"><a href="/w/index.php?title=%D7%A9%D7%99%D7%97%D7%94:%D7%97%D7%91%D7%95%D7%A8%D7%AA_%D7%94%D7%A1%D7%99%D7%91%D7%95%D7%91_(3)SO&action=edit&redlink=1" rel="discussion" class="new" title="שיחה על דף התוכן (הדף אינו קיים) [t]" accesskey="t"><span>שיחה</span></a></li> </ul> </div> </div> <div id="vector-variants-dropdown" class="vector-dropdown emptyPortlet" > <input type="checkbox" id="vector-variants-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-variants-dropdown" class="vector-dropdown-checkbox " aria-label="שינוי הגוון השפה" > <label id="vector-variants-dropdown-label" for="vector-variants-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet" aria-hidden="true" ><span class="vector-dropdown-label-text">עברית</span> </label> <div class="vector-dropdown-content"> <div id="p-variants" class="vector-menu mw-portlet mw-portlet-variants emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> </div> </div> </nav> </div> <div id="right-navigation" class="vector-collapsible"> <nav aria-label="צפיות"> <div id="p-views" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-views" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-view" class="selected vector-tab-noicon mw-list-item"><a href="/wiki/%D7%97%D7%91%D7%95%D7%A8%D7%AA_%D7%94%D7%A1%D7%99%D7%91%D7%95%D7%91_(3)SO"><span>קריאה</span></a></li><li id="ca-edit" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=%D7%97%D7%91%D7%95%D7%A8%D7%AA_%D7%94%D7%A1%D7%99%D7%91%D7%95%D7%91_(3)SO&action=edit" title="עריכת קוד המקור של הדף הזה [e]" accesskey="e"><span>עריכת קוד מקור</span></a></li><li id="ca-ve-edit" class="collapsible vector-tab-noicon mw-list-item"><a href="/w/index.php?title=%D7%97%D7%91%D7%95%D7%A8%D7%AA_%D7%94%D7%A1%D7%99%D7%91%D7%95%D7%91_(3)SO&veaction=edit" title="עריכת הדף הזה [v]" accesskey="v"><span>עריכה</span></a></li><li id="ca-history" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=%D7%97%D7%91%D7%95%D7%A8%D7%AA_%D7%94%D7%A1%D7%99%D7%91%D7%95%D7%91_(3)SO&action=history" title="גרסאות קודמות של דף זה [h]" accesskey="h"><span>גרסאות קודמות</span></a></li> </ul> </div> </div> </nav> <nav class="vector-page-tools-landmark" aria-label="כלי דף"> <div 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class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=%D7%97%D7%91%D7%95%D7%A8%D7%AA_%D7%94%D7%A1%D7%99%D7%91%D7%95%D7%91_(3)SO&action=edit" title="עריכת קוד המקור של הדף הזה [e]" accesskey="e"><span>עריכת קוד מקור</span></a></li><li id="ca-more-ve-edit" class="collapsible vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=%D7%97%D7%91%D7%95%D7%A8%D7%AA_%D7%94%D7%A1%D7%99%D7%91%D7%95%D7%91_(3)SO&veaction=edit" title="עריכת הדף הזה [v]" accesskey="v"><span>עריכה</span></a></li><li id="ca-more-history" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=%D7%97%D7%91%D7%95%D7%A8%D7%AA_%D7%94%D7%A1%D7%99%D7%91%D7%95%D7%91_(3)SO&action=history"><span>גרסאות קודמות</span></a></li> </ul> </div> </div> <div id="p-tb" class="vector-menu mw-portlet mw-portlet-tb" > <div class="vector-menu-heading"> כללי </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="t-whatlinkshere" class="mw-list-item"><a href="/wiki/%D7%9E%D7%99%D7%95%D7%97%D7%93:%D7%93%D7%A4%D7%99%D7%9D_%D7%94%D7%9E%D7%A7%D7%95%D7%A9%D7%A8%D7%99%D7%9D_%D7%9C%D7%9B%D7%90%D7%9F/%D7%97%D7%91%D7%95%D7%A8%D7%AA_%D7%94%D7%A1%D7%99%D7%91%D7%95%D7%91_(3)SO" title="רשימה של כל דפי הוויקי שמקשרים לדף הזה [j]" accesskey="j"><span>דפים המקושרים לכאן</span></a></li><li id="t-recentchangeslinked" class="mw-list-item"><a href="/wiki/%D7%9E%D7%99%D7%95%D7%97%D7%93:%D7%A9%D7%99%D7%A0%D7%95%D7%99%D7%99%D7%9D_%D7%91%D7%93%D7%A4%D7%99%D7%9D_%D7%94%D7%9E%D7%A7%D7%95%D7%A9%D7%A8%D7%99%D7%9D/%D7%97%D7%91%D7%95%D7%A8%D7%AA_%D7%94%D7%A1%D7%99%D7%91%D7%95%D7%91_(3)SO" rel="nofollow" title="השינויים האחרונים בדפים המקושרים מהדף הזה [k]" accesskey="k"><span>שינויים בדפים המקושרים</span></a></li><li id="t-specialpages" class="mw-list-item"><a href="/wiki/%D7%9E%D7%99%D7%95%D7%97%D7%93:%D7%93%D7%A4%D7%99%D7%9D_%D7%9E%D7%99%D7%95%D7%97%D7%93%D7%99%D7%9D" title="רשימה של כל הדפים המיוחדים [q]" accesskey="q"><span>דפים 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href="/w/index.php?title=%D7%9E%D7%99%D7%95%D7%97%D7%93:%D7%9E%D7%A7%D7%A6%D7%A8_%D7%9B%D7%AA%D7%95%D7%91%D7%95%D7%AA&url=https%3A%2F%2Fhe.wikipedia.org%2Fw%2Findex.php%3Ftitle%3D%25D7%2597%25D7%2591%25D7%2595%25D7%25A8%25D7%25AA_%25D7%2594%25D7%25A1%25D7%2599%25D7%2591%25D7%2595%25D7%2591_%283%29SO%26veaction%3Dedit"><span>קבלת כתובת מקוצרת</span></a></li><li id="t-urlshortener-qrcode" class="mw-list-item"><a href="/w/index.php?title=%D7%9E%D7%99%D7%95%D7%97%D7%93:QrCode&url=https%3A%2F%2Fhe.wikipedia.org%2Fw%2Findex.php%3Ftitle%3D%25D7%2597%25D7%2591%25D7%2595%25D7%25A8%25D7%25AA_%25D7%2594%25D7%25A1%25D7%2599%25D7%2591%25D7%2595%25D7%2591_%283%29SO%26veaction%3Dedit"><span>הורדת קוד 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"> הדפסה/יצוא </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="coll-create_a_book" class="mw-list-item"><a href="/w/index.php?title=%D7%9E%D7%99%D7%95%D7%97%D7%93:%D7%A1%D7%A4%D7%A8&bookcmd=book_creator&referer=%D7%97%D7%91%D7%95%D7%A8%D7%AA+%D7%94%D7%A1%D7%99%D7%91%D7%95%D7%91+%283%29SO"><span>יצירת ספר</span></a></li><li id="coll-download-as-rl" class="mw-list-item"><a href="/w/index.php?title=%D7%9E%D7%99%D7%95%D7%97%D7%93:DownloadAsPdf&page=%D7%97%D7%91%D7%95%D7%A8%D7%AA_%D7%94%D7%A1%D7%99%D7%91%D7%95%D7%91_%283%29SO&action=show-download-screen"><span>הורדה כ־PDF</span></a></li><li id="t-print" class="mw-list-item"><a href="/w/index.php?title=%D7%97%D7%91%D7%95%D7%A8%D7%AA_%D7%94%D7%A1%D7%99%D7%91%D7%95%D7%91_(3)SO&printable=yes" title="גרסה להדפסה של הדף הזה [p]" accesskey="p"><span>גרסה להדפסה</span></a></li> </ul> </div> </div> <div id="p-wikibase-otherprojects" class="vector-menu mw-portlet mw-portlet-wikibase-otherprojects" > <div class="vector-menu-heading"> במיזמים אחרים </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="t-wikibase" class="wb-otherproject-link wb-otherproject-wikibase-dataitem mw-list-item"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q1256500" title="קישור לפריט המשויך במאגר הנתונים [g]" accesskey="g"><span>פריט ויקינתונים</span></a></li> </ul> </div> </div> </div> </div> </div> </div> </nav> </div> </div> </div> <div class="vector-column-end"> <div class="vector-sticky-pinned-container"> <nav class="vector-page-tools-landmark" aria-label="כלי דף"> <div id="vector-page-tools-pinned-container" class="vector-pinned-container"> </div> </nav> <nav class="vector-appearance-landmark" aria-label="מראה"> <div id="vector-appearance-pinned-container" class="vector-pinned-container"> <div id="vector-appearance" class="vector-appearance vector-pinnable-element"> <div class="vector-pinnable-header vector-appearance-pinnable-header vector-pinnable-header-pinned" data-feature-name="appearance-pinned" data-pinnable-element-id="vector-appearance" data-pinned-container-id="vector-appearance-pinned-container" data-unpinned-container-id="vector-appearance-unpinned-container" > <div class="vector-pinnable-header-label">מראה</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-appearance.pin">העברה לסרגל הצד</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-appearance.unpin">הסתרה</button> </div> </div> </div> </nav> </div> </div> <div id="bodyContent" class="vector-body" aria-labelledby="firstHeading" data-mw-ve-target-container> <div class="vector-body-before-content"> <div class="mw-indicators"> </div> <div id="siteSub" class="noprint">מתוך ויקיפדיה, האנציקלופדיה החופשית</div> </div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-rtl mw-parser-output" lang="he" dir="rtl"><p><b>חבורת הסיבוב בשלושה ממדים</b>, המכונה <b>(SO(3</b> היא <a href="/wiki/%D7%97%D7%91%D7%95%D7%A8%D7%94_(%D7%9E%D7%91%D7%A0%D7%94_%D7%90%D7%9C%D7%92%D7%91%D7%A8%D7%99)" title="חבורה (מבנה אלגברי)">חבורת</a> כל הסיבובים סביב <a href="/wiki/%D7%A8%D7%90%D7%A9%D7%99%D7%AA_%D7%94%D7%A6%D7%99%D7%A8%D7%99%D7%9D" class="mw-redirect" title="ראשית הצירים">ראשית צירים</a> במרחב <a href="/wiki/%D7%9E%D7%A8%D7%97%D7%91_%D7%AA%D7%9C%D7%AA-%D7%9E%D7%9E%D7%93%D7%99" title="מרחב תלת-ממדי"><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} ^{3}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">R</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ \mathbb {R} ^{3}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/78f5d3ab4274ff721a459b33cbf297676d01d542" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.313ex; height:2.676ex;" alt="{\displaystyle \ \mathbb {R} ^{3}}"></span></a>, תחת <a href="/wiki/%D7%94%D7%A8%D7%9B%D7%91%D7%AA_%D7%A4%D7%95%D7%A0%D7%A7%D7%A6%D7%99%D7%95%D7%AA" title="הרכבת פונקציות">הרכבה</a>. <b>(SO(3</b> היא <a href="/wiki/%D7%97%D7%91%D7%95%D7%A8%D7%AA_%D7%9C%D7%99" title="חבורת לי">חבורת לי</a> <a href="/w/index.php?title=%D7%97%D7%91%D7%95%D7%A8%D7%94_%D7%A7%D7%95%D7%9E%D7%A4%D7%A7%D7%98%D7%99%D7%AA&action=edit&redlink=1" class="new" title="חבורה קומפקטית (הדף אינו קיים)">קומפקטית</a> מ<a href="/w/index.php?title=%D7%9E%D7%9E%D7%93_%D7%A9%D7%9C_%D7%97%D7%91%D7%95%D7%A8%D7%AA_%D7%9C%D7%99&action=edit&redlink=1" class="new" title="ממד של חבורת לי (הדף אינו קיים)">ממד</a> 3. מנקודת מבט כללית יותר, <b>(SO(3</b> היא <a href="/w/index.php?title=%D7%94%D7%97%D7%91%D7%95%D7%A8%D7%94_%D7%94%D7%90%D7%95%D7%A8%D7%AA%D7%95%D7%92%D7%95%D7%A0%D7%9C%D7%99%D7%AA&action=edit&redlink=1" class="new" title="החבורה האורתוגונלית (הדף אינו קיים)">החבורה האורתוגנלית המיוחדת</a> של ה<a href="/wiki/%D7%AA%D7%91%D7%A0%D7%99%D7%AA_%D7%A8%D7%99%D7%91%D7%95%D7%A2%D7%99%D7%AA" title="תבנית ריבועית">תבנית הריבועית</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 \ x_{1}^{2}+x_{2}^{2}+x_{3}^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <msubsup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> <mo>+</mo> <msubsup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> <mo>+</mo> <msubsup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ x_{1}^{2}+x_{2}^{2}+x_{3}^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b353c56b928ac1a106214d917dbcc9663fb9fc66" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:13.413ex; height:3.176ex;" alt="{\displaystyle \ x_{1}^{2}+x_{2}^{2}+x_{3}^{2}}"></span>. </p><p>החבורה (SO(3 משמשת לתיאור כל סימטריות הסיבוב של גוף, כמו גם כל האוריינטציות האפשריות שלו במרחב. היא נמצאת בשימוש נרחב בחישובים פיזיקליים ובמיוחד ב<a href="/wiki/%D7%A4%D7%99%D7%96%D7%99%D7%A7%D7%94_%D7%92%D7%A8%D7%A2%D7%99%D7%A0%D7%99%D7%AA" title="פיזיקה גרעינית">פיזיקה גרעינית</a> כאשר מתארים <a href="/wiki/%D7%97%D7%9C%D7%A7%D7%99%D7%A7%D7%99%D7%9D_%D7%90%D7%9C%D7%9E%D7%A0%D7%98%D7%A8%D7%99%D7%99%D7%9D" class="mw-redirect" title="חלקיקים אלמנטריים">חלקיקים אלמנטריים</a> עם <a href="/wiki/%D7%A1%D7%A4%D7%99%D7%9F_(%D7%A4%D7%99%D7%96%D7%99%D7%A7%D7%94)" title="ספין (פיזיקה)">ספין</a> שלם, וכן בתחומי התעופה, הטילאות ובכלל בכל מקום שנדרשת הדמיה של גופים נעים ומסתובבים במרחב. </p><p>על פי הגדרה, סיבוב סביב ראשית הצירים הוא טרנספורמציה המשמרת את ראשית הצירים, את המרחק האוקלידי (ולכן היא <a href="/wiki/%D7%90%D7%99%D7%96%D7%95%D7%9E%D7%98%D7%A8%D7%99%D7%94" title="איזומטריה">איזומטריה</a>), ואת ה<a href="/wiki/%D7%90%D7%95%D7%A8%D7%99%D7%99%D7%A0%D7%98%D7%A6%D7%99%D7%94_(%D7%90%D7%9C%D7%92%D7%91%D7%A8%D7%94_%D7%9C%D7%99%D7%A0%D7%99%D7%90%D7%A8%D7%99%D7%AA)" title="אוריינטציה (אלגברה ליניארית)">אוריינטציה</a>. כל סיבוב לא-טריוויאלי מוגדר על ידי ציר הסיבוב (קו העובר דרך ראשית הצירים) וזווית הסיבוב. <a href="/wiki/%D7%A4%D7%95%D7%A0%D7%A7%D7%A6%D7%99%D7%99%D7%AA_%D7%94%D7%96%D7%94%D7%95%D7%AA" title="פונקציית הזהות">פונקציית הזהות</a> מקיימת את תנאי הסיבוב ולכן מהווה סיבוב בעצמה. לכל סיבוב ישנו ערך <a href="/wiki/%D7%A4%D7%95%D7%A0%D7%A7%D7%A6%D7%99%D7%94_%D7%94%D7%A4%D7%99%D7%9B%D7%94" title="פונקציה הפיכה">הופכי</a> יחיד. לפי <a href="/wiki/%D7%9E%D7%A9%D7%A4%D7%98_%D7%94%D7%A1%D7%99%D7%91%D7%95%D7%91%D7%99%D7%9D_%D7%A9%D7%9C_%D7%90%D7%95%D7%99%D7%9C%D7%A8" title="משפט הסיבובים של אוילר">משפט הסיבובים של אוילר</a>, הרכבה של שני סיבובים מוגדרת על ידי סיבוב שקול. </p><p>סיבובים הם <a href="/wiki/%D7%98%D7%A8%D7%A0%D7%A1%D7%A4%D7%95%D7%A8%D7%9E%D7%A6%D7%99%D7%94_%D7%9C%D7%99%D7%A0%D7%99%D7%90%D7%A8%D7%99%D7%AA" class="mw-redirect" title="טרנספורמציה ליניארית">טרנספורמציות ליניאריות</a> במרחב <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} ^{3}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">R</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ \mathbb {R} ^{3}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/78f5d3ab4274ff721a459b33cbf297676d01d542" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.313ex; height:2.676ex;" alt="{\displaystyle \ \mathbb {R} ^{3}}"></span> וניתנות לייצוג על ידי מטריצה לאחר שנבחר <a href="/wiki/%D7%91%D7%A1%D7%99%D7%A1_(%D7%90%D7%9C%D7%92%D7%91%D7%A8%D7%94_%D7%9C%D7%99%D7%A0%D7%99%D7%90%D7%A8%D7%99%D7%AA)" class="mw-redirect" title="בסיס (אלגברה ליניארית)">בסיס</a> של <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} ^{3}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">R</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ \mathbb {R} ^{3}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/78f5d3ab4274ff721a459b33cbf297676d01d542" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.313ex; height:2.676ex;" alt="{\displaystyle \ \mathbb {R} ^{3}}"></span>. בפרט, אם נקבע <a href="/wiki/%D7%91%D7%A1%D7%99%D7%A1_%D7%90%D7%95%D7%A8%D7%AA%D7%95%D7%A0%D7%95%D7%A8%D7%9E%D7%9C%D7%99" class="mw-redirect" title="בסיס אורתונורמלי">בסיס אורתונורמלי</a> של <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} ^{3}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">R</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ \mathbb {R} ^{3}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/78f5d3ab4274ff721a459b33cbf297676d01d542" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.313ex; height:2.676ex;" alt="{\displaystyle \ \mathbb {R} ^{3}}"></span>, כל סיבוב יהיה <a href="/wiki/%D7%9E%D7%98%D7%A8%D7%99%D7%A6%D7%94_%D7%9E%D7%99%D7%99%D7%A6%D7%92%D7%AA" class="mw-redirect" title="מטריצה מייצגת">מיוצג</a> על ידי <a href="/wiki/%D7%9E%D7%98%D7%A8%D7%99%D7%A6%D7%94_%D7%90%D7%95%D7%A8%D7%AA%D7%95%D7%92%D7%95%D7%A0%D7%9C%D7%99%D7%AA" title="מטריצה אורתוגונלית">מטריצה אורתוגונלית</a> 3X3. </p><p>החבורה (SO(3 יכולה איפה להיות מוגדרת על ידי חבורת המטריצות המתוארות לעיל תחת פעולת כפל מטריצות. מטריצות אלו מכונות "מטריצות אורתוגונליות מיוחדות" (<b>S</b>pecial <b>O</b>rthogonal Matrices), ולכן הסימון <b>SO</b>. </p>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">אוחזר מתוך "<a dir="ltr" href="https://he.wikipedia.org/w/index.php?title=חבורת_הסיבוב_(3)SO&oldid=36159085">https://he.wikipedia.org/w/index.php?title=חבורת_הסיבוב_(3)SO&oldid=36159085</a>"</div></div> <div id="catlinks" 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