[{"@context":"http:\/\/schema.org\/","@type":"BlogPosting","@id":"https:\/\/wiki.edu.vn\/all2jp\/wiki11\/archives\/12324#BlogPosting","mainEntityOfPage":"https:\/\/wiki.edu.vn\/all2jp\/wiki11\/archives\/12324","headline":"Pappus Centroid\u5b9a\u7406","name":"Pappus Centroid\u5b9a\u7406","description":"before-content-x4 \u5b9a\u7406\u306f\u3001\u958b\u3044\u305f\u30b7\u30ea\u30f3\u30c0\u30fc\u3001\u30b3\u30fc\u30f3\u3001\u7403\u4f53\u306b\u9069\u7528\u3055\u308c\u3001\u305d\u306e\u8868\u9762\u3092\u53d6\u5f97\u3057\u307e\u3057\u305f\u3002\u91cd\u5fc3\u306f\u9060\u304f\u306b\u3042\u308a\u307e\u3059 a \u56de\u8ee2\u8ef8\u306e\uff08\u8d64\uff09\u3002 Pappus Centroid\u5b9a\u7406 \u3001AS\u3082\u77e5\u3063\u3066\u3044\u307e\u3059 \u30ac\u30eb\u30c7\u30a3\u30f3\u5b9a\u7406 \u3001 Theorem de Pappus-Guldin o \u30d1\u30d7\u30b9\u306e\u5b9a\u7406 \u3001\u8868\u9762\u3068\u9769\u65b0\u7684\u306a\u56fa\u4f53\u3092\u305d\u308c\u305e\u308c\u306e\u91cd\u5fc3\u3092\u95a2\u9023\u4ed8\u3051\u308b2\u3064\u306e\u5b9a\u7406\u306e\u540d\u524d\u3067\u3059\u3002 after-content-x4 \u5b9a\u7406\u306f\u3001\u30a2\u30ec\u30af\u30b5\u30f3\u30c9\u30ea\u30a2\u3068\u30dd\u30fc\u30eb\u30fb\u30b0\u30eb\u30c7\u30a3\u30f3\u306e\u30d1\u30c3\u30d1\u30b9\u306b\u8d77\u56e0\u3057\u3066\u3044\u307e\u3059\u3002 Table of Contents","datePublished":"2022-02-07","dateModified":"2022-02-07","author":{"@type":"Person","@id":"https:\/\/wiki.edu.vn\/all2jp\/wiki11\/archives\/author\/lordneo#Person","name":"lordneo","url":"https:\/\/wiki.edu.vn\/all2jp\/wiki11\/archives\/author\/lordneo","image":{"@type":"ImageObject","@id":"https:\/\/secure.gravatar.com\/avatar\/44a4cee54c4c053e967fe3e7d054edd4?s=96&d=mm&r=g","url":"https:\/\/secure.gravatar.com\/avatar\/44a4cee54c4c053e967fe3e7d054edd4?s=96&d=mm&r=g","height":96,"width":96}},"publisher":{"@type":"Organization","name":"Enzyklop\u00e4die","logo":{"@type":"ImageObject","@id":"https:\/\/wiki.edu.vn\/wiki4\/wp-content\/uploads\/2023\/08\/download.jpg","url":"https:\/\/wiki.edu.vn\/wiki4\/wp-content\/uploads\/2023\/08\/download.jpg","width":600,"height":60}},"image":{"@type":"ImageObject","@id":"https:\/\/upload.wikimedia.org\/wikipedia\/commons\/thumb\/f\/fd\/Pappus_centroid_theorem_areas.gif\/400px-Pappus_centroid_theorem_areas.gif","url":"https:\/\/upload.wikimedia.org\/wikipedia\/commons\/thumb\/f\/fd\/Pappus_centroid_theorem_areas.gif\/400px-Pappus_centroid_theorem_areas.gif","height":"240","width":"400"},"url":"https:\/\/wiki.edu.vn\/all2jp\/wiki11\/archives\/12324","wordCount":5171,"articleBody":"     (adsbygoogle = window.adsbygoogle || []).push({});before-content-x4 \u5b9a\u7406\u306f\u3001\u958b\u3044\u305f\u30b7\u30ea\u30f3\u30c0\u30fc\u3001\u30b3\u30fc\u30f3\u3001\u7403\u4f53\u306b\u9069\u7528\u3055\u308c\u3001\u305d\u306e\u8868\u9762\u3092\u53d6\u5f97\u3057\u307e\u3057\u305f\u3002\u91cd\u5fc3\u306f\u9060\u304f\u306b\u3042\u308a\u307e\u3059 a \u56de\u8ee2\u8ef8\u306e\uff08\u8d64\uff09\u3002 Pappus Centroid\u5b9a\u7406 \u3001AS\u3082\u77e5\u3063\u3066\u3044\u307e\u3059 \u30ac\u30eb\u30c7\u30a3\u30f3\u5b9a\u7406 \u3001 Theorem de Pappus-Guldin o \u30d1\u30d7\u30b9\u306e\u5b9a\u7406 \u3001\u8868\u9762\u3068\u9769\u65b0\u7684\u306a\u56fa\u4f53\u3092\u305d\u308c\u305e\u308c\u306e\u91cd\u5fc3\u3092\u95a2\u9023\u4ed8\u3051\u308b2\u3064\u306e\u5b9a\u7406\u306e\u540d\u524d\u3067\u3059\u3002        (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4\u5b9a\u7406\u306f\u3001\u30a2\u30ec\u30af\u30b5\u30f3\u30c9\u30ea\u30a2\u3068\u30dd\u30fc\u30eb\u30fb\u30b0\u30eb\u30c7\u30a3\u30f3\u306e\u30d1\u30c3\u30d1\u30b9\u306b\u8d77\u56e0\u3057\u3066\u3044\u307e\u3059\u3002 Table of Contents       (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4\u6700\u521d\u306e\u5b9a\u7406 [ \u7de8\u96c6\u3057\u307e\u3059 ] \u5b9a\u7406\u306b\u3088\u308b\u3068 [ \u7de8\u96c6\u3057\u307e\u3059 ] \u30c7\u30e2\u30f3\u30b9\u30c8\u30ec\u30fc\u30b7\u30e7\u30f3 [ \u7de8\u96c6\u3057\u307e\u3059 ] \u6700\u521d\u306e\u5b9a\u7406 [ \u7de8\u96c6\u3057\u307e\u3059 ] \u5b9a\u7406\u306b\u3088\u308b\u3068 [ \u7de8\u96c6\u3057\u307e\u3059 ] \u5916\u90e8\u30ea\u30f3\u30af [ \u7de8\u96c6\u3057\u307e\u3059 ] \u6700\u521d\u306e\u5b9a\u7406 [ \u7de8\u96c6\u3057\u307e\u3059 ] \u305f\u3068\u3048\u3070\u3001\u30de\u30a4\u30ca\u30fc\u30e9\u30b8\u30aa\u30d6\u30eb\u306e\u8868\u9762\u306e\u9818\u57df r {displaystyle r} \u30e9\u30b8\u30aa\u5e02\u9577 r {displaystyle r} \u306f\uff1a        (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4a = \uff08 2 pi r \uff09\uff09 \uff08 2 pi r \uff09\uff09 = 4 pi 2r r \u3002 {displaystyle a =\uff082pi r\uff09\uff082pi r\uff09= 4pi ^{2} rr\u3002\u3001} \u3053\u3053\u3067\u3001\u3088\u308a\u5c0f\u3055\u306a\u534a\u5f84\u306f\u6a2a\u5186\u5f62\u8868\u9762\u306b\u5bfe\u5fdc\u3057\u307e\u3059\u3002\u4e3b\u306a\u534a\u5f84\u306f\u3001\u4e3b\u8981\u306a\u30b8\u30a7\u30cd\u30e9\u30c8\u30ea\u30c3\u30af\u30b9\u5468\u56f2\u306e\u534a\u5f84\u3067\u3059\u3002 \u5b9a\u7406\u306b\u3088\u308b\u3068 [ \u7de8\u96c6\u3057\u307e\u3059 ] \u305f\u3068\u3048\u3070\u3001\u30de\u30a4\u30ca\u30fc\u30e9\u30b8\u30aa\u30d6\u30eb\u306e\u30dc\u30ea\u30e5\u30fc\u30e0\u3082 r {displaystyle r} \u30e9\u30b8\u30aa\u5e02\u9577 r {displaystyle r} \u306f \u306e = \uff08 pi r 2 \uff09\uff09 \uff08 2 pi r \uff09\uff09 = 2 pi 2 r r 2 \u3002 {displaystyle v =\uff08pi r^{2}\uff09\uff082pi r\uff09= 2pi^{2} rr^{2}\u3002\u3001}  \u3069\u3053 r {displaystyle r} \u305d\u308c\u306f\u30de\u30a4\u30ca\u30fc\u30af\u30ed\u30b9\u30bb\u30af\u30b7\u30e7\u30f3\u306e\u534a\u5f84\u3067\u3042\u308a\u3001 r {displaystyle r} \u305d\u308c\u306f\u3001\u30e1\u30b8\u30e3\u30fc\u307e\u305f\u306f\u30b8\u30a7\u30cd\u30e9\u30c8\u30ea\u30c3\u30af\u30b9\u306e\u5468\u56f2\u306e\u534a\u5f84\u3067\u3059\u3002 \u30c7\u30e2\u30f3\u30b9\u30c8\u30ec\u30fc\u30b7\u30e7\u30f3 [ \u7de8\u96c6\u3057\u307e\u3059 ] \u6700\u521d\u306e\u5b9a\u7406 [ \u7de8\u96c6\u3057\u307e\u3059 ] \u95a2\u6570\u306b\u3088\u3063\u3066\u5b9a\u7fa9\u3055\u308c\u305f\u30d5\u30e9\u30c3\u30c8\u66f2\u7dda\u306b\u306a\u308a\u307e\u3059 \u3068 = f \uff08 \u30d0\u30c4 \uff09\uff09 {displaystyle y = f\uff08x\uff09} \u3001\u9589\u3058\u305f\u9593\u9694\u3067 [ a \u3001 b ] {displaystyle [a\u3001b]} \u9023\u7d9a\u3057\u3066\u3044\u307e\u3059\u3002\u6b21\u306b\u3001\u66f2\u7dda\u304c\u306e\u8ef8\u3092\u56de\u308b\u3068\u304d\u306b\u751f\u6210\u3055\u308c\u308b\u9769\u547d\u56fa\u4f53\u306e\u9818\u57df \u30d0\u30c4 {displaystyle x} \u306f\uff1a \uff08 \u521d\u3081 \uff09\uff09 a = 2 pi \u222b abf \uff08 \u30d0\u30c4 \uff09\uff09 1+(dydx)2d \u30d0\u30c4 {displaystyle a = 2pi int _ {a}^{b} f\uff08x\uff09{sqrt {1+left\uff08{frac {dy} {dx}}\u53f3\uff09^{2}}\u3001dx}}}}}}  \uff08 2.1 \uff09\uff09 y\u00af=\u222babf(x)1+(dydx)2dx\u222bab1+(dydx)2dx=\u222babf(x)1+(dydx)2dxL{displayStyle {begin {array} {rcl} {overline {y}}\uff06=\uff06{frac {displaystyle int _ {a}^{b} f\uff08x\uff09{sqrt {1+left\uff08{frac {dy} {dy} {dx}} {disply\uff09^{dx}} {2}}}} {2}}}} }^{b} {sqrt {1+left\uff08{frac {dy} {dx}}\u53f3\uff09^{2}}}\u3001dx}} \\\uff06=\uff06{frac {displaystyle int _ {a}^{b} f\uff08x {2}}}\u3001dx} {displaystyle l}} end {array}}}}}  \u4e00\u65b9\u3001\u5ea7\u6a19 \u3068 \u00af {displaystyle {overline {y}}} \u3053\u306e\u66f2\u7dda\u306e\u91cd\u5fc3\u304b\u3089\u6b21\u306e\u3088\u3046\u306b\u8a08\u7b97\u3055\u308c\u307e\u3059\u3002 \u3068\u3059\u308c\u3070 l {displaystyle l} \u305d\u308c\u306f\u5206\u6bcd\u306b\u793a\u3055\u308c\u3066\u3044\u308b\u30d5\u30e9\u30c3\u30c8\u66f2\u7dda\u306e\u9577\u3055\u3067\u3059\u3002 \u65b9\u7a0b\u5f0f\u3092\u63a8\u6e2c\u3059\u308b\u306e\u306f\u7c21\u5358\u3067\u3059\uff08 2 \uff09\u305d\u308c\u306f\u6b21\u306e\u3088\u3046\u306b\u5909\u63db\u3057\u307e\u3059\uff1a \uff08 3 \uff09\uff09 a = 2 pi y\u00afl {displaystyle a = 2pi {overline {y}} l}  \u30c7\u30e2\u30f3\u30b9\u30c8\u30ec\u30fc\u30b7\u30e7\u30f3\u3092\u5b8c\u4e86\u3057\u307e\u3059\u3002 \u5b9a\u7406\u306b\u3088\u308b\u3068 [ \u7de8\u96c6\u3057\u307e\u3059 ] 2\u3064\u306e\u95a2\u6570\u306b\u306a\u308a\u307e\u3059 f \uff08 \u30d0\u30c4 \uff09\uff09 {displaystyle f\uff08x\uff09} \u3068 g \uff08 \u30d0\u30c4 \uff09\uff09 {displaystyle g\uff08x\uff09} \u9593\u9694\u3067\u9023\u7d9a\u3057\u3066\u5b9a\u7fa9\u3055\u308c\u3066\u3044\u307e\u3059 [ a \u3001 b ] {displaystyle [a\u3001b]} \u3001 \u305d\u306e\u3088\u3046\u306a f \uff08 \u30d0\u30c4 \uff09\uff09 \u2265 g \uff08 \u30d0\u30c4 \uff09\uff09 {displaystyle f\uff08x\uff09geq g\uff08x\uff09} \u305d\u3057\u3066\u3001\u305d\u308c\u306f\u5730\u57df\u306e\u5e73\u3089\u306a\u9818\u57df\u3092\u533a\u5207\u308a\u307e\u3059 a {displaystyle a} \u3002\u30dc\u30ea\u30e5\u30fc\u30e0 \u306e {displaystyle v} X\u8ef8\u306e\u5468\u308a\u306b\u3053\u306e\u9818\u57df\u3092\u56de\u3059\u3068\u304d\u306b\u751f\u6210\u3055\u308c\u308b\u9769\u547d\u306e\u56fa\u4f53\u306e\u3046\u3061\u3001\u30ea\u30f3\u30b0\u6cd5\u306b\u3088\u3063\u3066\u8a08\u7b97\u3055\u308c\u307e\u3059\u3002\u7d50\u679c\u306f\u6b21\u306e\u3068\u304a\u308a\u3067\u3059\u3002 \uff08 4 \uff09\uff09 \u306e = pi \u222b ab[ f(x)2\u2212g(x)2] d \u30d0\u30c4 {displaystyle v = pi int _ {a}^{b}\u5de6[f\uff08x\uff09^{2} -g\uff08x\uff09^{2}\u53f3]\u3001dx}  \u4e00\u65b9\u3001\u5ea7\u6a19\u3092\u8a08\u7b97\u3057\u307e\u3059 \u3068 \u00af {displaystyle {overline {y}}} \u66f2\u7dda\u306b\u3088\u3063\u3066\u533a\u5207\u3089\u308c\u305f\u5e73\u3089\u306a\u9818\u57df\u306e\u91cd\u5fc3 f \uff08 \u30d0\u30c4 \uff09\uff09 {displaystyle f\uff08x\uff09} \u3068 g \uff08 \u30d0\u30c4 \uff09\uff09 {displaystyle g\uff08x\uff09} \u3053\u306e\u65b9\u7a0b\u5f0f\u304c\u4f7f\u7528\u3055\u308c\u307e\u3059\uff1a \uff08 5 \uff09\uff09 y\u00af=\u222bab(f(x)+g(x))\u2217(f(x)\u2212g(x))dx2\u222bab[f(x)\u2212g(x)]dx=\u222bab[f(x)2\u2212g(x)2]dx2\u222bab[f(x)\u2212g(x)]dx=\u222bab[f(x)2\u2212g(x)2]dx2A{displaystyle {begin {array} {rcl} {overline {y}}\uff06=\uff06{frac {displaystyle int _ {a}^{b}\uff08f\uff08x\uff09+g\uff08x\uff09\uff09 x}} \\\\\uff06=\uff06{frac {displaystyle int _ {a}^{b} left [f\uff08x\uff09^{2} -g\uff08x\uff09^{2}\u53f3]\u3001dx} {displaystyle 2int _ {a}^{b}\u5de6[F\uff08x\uff09-g\uff08x\uff09-g\uff08x\uff09\u3001dx\uff09\u3001dx\uff09\u3001dx\uff09\u3001dx} _ {a}^{b}\u5de6[f\uff08x\uff09^{2} -g\uff08x\uff09^{2}\u53f3]\u3001dx} {displaystyle 2a}} end {array}}}}}}  \u3068\u3059\u308c\u3070 a {displaystyle a} 2\u3064\u306e\u66f2\u7dda\u3067\u69cb\u6210\u3055\u308c\u308b\u30a8\u30ea\u30a2\u3067\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u30dc\u30ea\u30e5\u30fc\u30e0\u65b9\u7a0b\u5f0f\u306f\u6b21\u306e\u3088\u3046\u306b\u518d\u5ea6\u8a18\u8ff0\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002 \uff08 6 \uff09\uff09 \u306e = 2 pi a y\u00af{displaystyle v = 2pi a {overline {y}}}  \u30c7\u30e2\u30f3\u30b9\u30c8\u30ec\u30fc\u30b7\u30e7\u30f3\u3092\u5b8c\u4e86\u3057\u307e\u3059\u3002\u8a08\u7b97\u304c\u5ea7\u6a19\u3092\u6307\u3059\u5834\u5408 \u30d0\u30c4 \u00af {displaystyle {overline {x}}} \u8a08\u7b97\u306f\u985e\u4f3c\u3057\u3066\u304a\u308a\u3001\u3053\u306e\u5834\u5408\u306f\u6b21\u306e\u5834\u5408\u306b\u4f8b\u5916\u3092\u4f5c\u6210\u3057\u307e\u3059\u3002 \uff08 7 \uff09\uff09 \u306e = 2 pi \u222b ab\u30d0\u30c4 \u2217 [ f \uff08 \u30d0\u30c4 \uff09\uff09  –  g \uff08 \u30d0\u30c4 \uff09\uff09 ] d \u30d0\u30c4 {displaystyle v = 2pi int _ {a}^{b} x*[f\uff08x\uff09-g\uff08x\uff09]\u3001dx}  \u305f\u3060\u3057\u3001\u9818\u57df\u306f\u6700\u521d\u306b\u793a\u3055\u308c\u3066\u3044\u308b\u3088\u3046\u306b\u8a08\u7b97\u3055\u308c\u3066\u3044\u307e\u3059\u3002 \u9818\u57df\u3068\u306e\u4ea4\u5dee\u70b9\u306e\u306a\u3044\u7dda\u306e\u5468\u308a\u306e\u9769\u547d\u306e\u91cf\u3092\u56fa\u4f53\u306b\u8a08\u7b97\u3057\u305f\u3044\u5834\u5408\u3001\u30d5\u30a9\u30fc\u30e0 \u3068 = a \u30d0\u30c4 + b {displaystyle y = ax+b} \u3053\u306e\u5b9a\u7406\u306f\u3001\u91cd\u5fc3\u3068\u524d\u8a18\u7dda\u306e\u9593\u306e\u8ddd\u96e2\u304c\u8a08\u7b97\u3055\u308c\u308b\u3053\u3068\u3092\u6761\u4ef6\u306b\u4f7f\u7528\u3067\u304d\u307e\u3059\u3002 \u5916\u90e8\u30ea\u30f3\u30af [ \u7de8\u96c6\u3057\u307e\u3059 ]          (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4"},{"@context":"http:\/\/schema.org\/","@type":"BreadcrumbList","itemListElement":[{"@type":"ListItem","position":1,"item":{"@id":"https:\/\/wiki.edu.vn\/all2jp\/wiki11\/#breadcrumbitem","name":"Enzyklop\u00e4die"}},{"@type":"ListItem","position":2,"item":{"@id":"https:\/\/wiki.edu.vn\/all2jp\/wiki11\/archives\/12324#breadcrumbitem","name":"Pappus Centroid\u5b9a\u7406"}}]}]