[{"@context":"http:\/\/schema.org\/","@type":"BlogPosting","@id":"https:\/\/wiki.edu.vn\/all2jp\/wiki10\/archives\/10988#BlogPosting","mainEntityOfPage":"https:\/\/wiki.edu.vn\/all2jp\/wiki10\/archives\/10988","headline":"\u30aa\u30ea\u30a8\u30f3\u30c6\u30c3\u30c9\u30a8\u30ea\u30a2 – \u30a6\u30a3\u30ad\u30da\u30c7\u30a3\u30a2","name":"\u30aa\u30ea\u30a8\u30f3\u30c6\u30c3\u30c9\u30a8\u30ea\u30a2 – \u30a6\u30a3\u30ad\u30da\u30c7\u30a3\u30a2","description":"\u4e00 \u5411\u304d\u306e\u3042\u308b\u30a8\u30ea\u30a2 \u521d\u7b49\u9818\u57df\u306e\u6570\u5b66\u7684\u30b5\u30d6\u30a8\u30ea\u30a2\u306e\u57fa\u672c\u5dee\u306e\u5e7e\u4f55\u5b66\u306e\u5225\u306e\u9818\u57df\u3067\u3059 \u30aa\u30ea\u30a8\u30f3\u30c6\u30eb\u30a8\u30ea\u30a2 \u3001\u305d\u306e\u53cc\u65b9\u306e\u3069\u308c\u304c\u5916\u5074\u307e\u305f\u306f\u5185\u5074\u306b\u3042\u308b\u304b\u3092\u6c7a\u5b9a\u3057\u307e\u3057\u305f\u3002 [\u521d\u3081] \u9762\u7a4d\u306e\u5411\u304d\u306f\u30012\u3064\u306e\u53ef\u80fd\u306a\u30b7\u30e3\u30de\u30eb\u578b\u30d9\u30af\u30c8\u30eb\u306e1\u3064\u3092\u9078\u629e\u3057\u3066\u6c7a\u5b9a\u3055\u308c\u307e\u3059\u3002 [2] \u8868\u9762\u306e\u5916\u5074\u306f\u3001\u9078\u629e\u3057\u305f\u901a\u5e38\u306e\u30d9\u30af\u30c8\u30eb\u304c\u53bb\u308b\u3082\u306e\u3067\u3059\u3002 [3] M\u00f6biusband\u306a\u3069\u3001\u6307\u5411\u3055\u308c\u3066\u3044\u306a\u3044\u9818\u57df\u304c\u3042\u308a\u307e\u3059\u3002 \u4e00\u5b9a\u306e\u30e6\u30cb\u30c3\u30c8\u6a19\u6e96\u30d5\u30a3\u30fc\u30eb\u30c9\u3092\u5099\u3048\u305f\u901a\u5e38\u306e\u30a8\u30ea\u30a2 \u901a\u5e38\u306e\u30a8\u30ea\u30a2\uff08\u307e\u305f\u306f\u30a8\u30c3\u30b8\u306e\u3042\u308b\u901a\u5e38\u306e\u30a8\u30ea\u30a2\uff09 s \u2282 r 3 {displaystyle ssubset mathbb","datePublished":"2023-06-23","dateModified":"2023-06-23","author":{"@type":"Person","@id":"https:\/\/wiki.edu.vn\/all2jp\/wiki10\/archives\/author\/lordneo#Person","name":"lordneo","url":"https:\/\/wiki.edu.vn\/all2jp\/wiki10\/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\/a\/a5\/Normal_vectors2.svg\/220px-Normal_vectors2.svg.png","url":"https:\/\/upload.wikimedia.org\/wikipedia\/commons\/thumb\/a\/a5\/Normal_vectors2.svg\/220px-Normal_vectors2.svg.png","height":"281","width":"220"},"url":"https:\/\/wiki.edu.vn\/all2jp\/wiki10\/archives\/10988","wordCount":4856,"articleBody":" \u4e00 \u5411\u304d\u306e\u3042\u308b\u30a8\u30ea\u30a2 \u521d\u7b49\u9818\u57df\u306e\u6570\u5b66\u7684\u30b5\u30d6\u30a8\u30ea\u30a2\u306e\u57fa\u672c\u5dee\u306e\u5e7e\u4f55\u5b66\u306e\u5225\u306e\u9818\u57df\u3067\u3059 \u30aa\u30ea\u30a8\u30f3\u30c6\u30eb\u30a8\u30ea\u30a2 \u3001\u305d\u306e\u53cc\u65b9\u306e\u3069\u308c\u304c\u5916\u5074\u307e\u305f\u306f\u5185\u5074\u306b\u3042\u308b\u304b\u3092\u6c7a\u5b9a\u3057\u307e\u3057\u305f\u3002 [\u521d\u3081] \u9762\u7a4d\u306e\u5411\u304d\u306f\u30012\u3064\u306e\u53ef\u80fd\u306a\u30b7\u30e3\u30de\u30eb\u578b\u30d9\u30af\u30c8\u30eb\u306e1\u3064\u3092\u9078\u629e\u3057\u3066\u6c7a\u5b9a\u3055\u308c\u307e\u3059\u3002 [2] \u8868\u9762\u306e\u5916\u5074\u306f\u3001\u9078\u629e\u3057\u305f\u901a\u5e38\u306e\u30d9\u30af\u30c8\u30eb\u304c\u53bb\u308b\u3082\u306e\u3067\u3059\u3002 [3] M\u00f6biusband\u306a\u3069\u3001\u6307\u5411\u3055\u308c\u3066\u3044\u306a\u3044\u9818\u57df\u304c\u3042\u308a\u307e\u3059\u3002  \u4e00\u5b9a\u306e\u30e6\u30cb\u30c3\u30c8\u6a19\u6e96\u30d5\u30a3\u30fc\u30eb\u30c9\u3092\u5099\u3048\u305f\u901a\u5e38\u306e\u30a8\u30ea\u30a2 \u901a\u5e38\u306e\u30a8\u30ea\u30a2\uff08\u307e\u305f\u306f\u30a8\u30c3\u30b8\u306e\u3042\u308b\u901a\u5e38\u306e\u30a8\u30ea\u30a2\uff09 s \u2282 r 3 {displaystyle ssubset mathbb {r} ^{3}} \u5b9a\u5e38\u30e6\u30cb\u30c3\u30c8\u306e\u6b63\u5e38\u30d9\u30af\u30c8\u30eb\u30d5\u30a3\u30fc\u30eb\u30c9\u304c\u3042\u308b\u5834\u5408\u3001\u65b9\u5411\u3092\u610f\u5473\u3057\u307e\u3059 s {displaystyleS} \u4e0e\u3048\u307e\u3059\u3002 [4] \u3053\u306e\u3088\u3046\u306a\u5b89\u5b9a\u3057\u305f\u5358\u4f4d\u6b63\u5e38\u30d9\u30af\u30c8\u30eb\u30d5\u30a3\u30fc\u30eb\u30c9 n\u2192{displaystyle {vec {n}}} \u306e\u4e0a s {displaystyleS} \u306e\u65b9\u5411\u3092\u7f6e\u304d\u307e\u3059 s {displaystyleS} \u3057\u3063\u304b\u308a\u3068\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u65b9\u5411\u306e\u8868\u9762\u306f\u3001\u5b9a\u5e38\u5358\u4f4d\u6b63\u5e38\u30d9\u30af\u30c8\u30eb\u30d5\u30a3\u30fc\u30eb\u30c9\u304c\u3042\u308b\u65b9\u5411\u306e\u3042\u308b\u9818\u57df\u3067\u3059 n\u2192{displaystyle {vec {n}}} \u9078\u629e\u3055\u308c\u307e\u3057\u305f\u3002\u6b63\u5f0f\u306b\u306f\u3001\u5411\u304d\u306e\u3042\u308b\u30a8\u30ea\u30a2\u306f\u30ab\u30c3\u30d7\u30eb\u3067\u3059 \uff08 s \u3001 n\u2192\uff09\uff09 {displaystyle\uff08s\u3001{vec {n}}\uff09} \u30aa\u30ea\u30a8\u30f3\u30c6\u30eb\u30a8\u30ea\u30a2\u304b\u3089 s {displaystyleS} \u5b89\u5b9a\u3057\u305f\u30e6\u30cb\u30c3\u30c8\u6b63\u5e38\u30d9\u30af\u30c8\u30eb\u30d5\u30a3\u30fc\u30eb\u30c9 n\u2192{displaystyle {vec {n}}} \u306e\u4e0a s {displaystyleS} \u3002 \u5b9a\u6570\u30e6\u30cb\u30c3\u30c8\u306e\u901a\u5e38\u306e\u30d9\u30af\u30c8\u30eb\u30d5\u30a3\u30fc\u30eb\u30c9\u3092\u4ecb\u3057\u3066\u3044\u307e\u3059 n\u2192\u521d\u3081 {displaystyle {vec {n}} _ {1}} \u30a8\u30ea\u30a2\u306e\u30aa\u30ea\u30a8\u30f3\u30c6\u30fc\u30b7\u30e7\u30f3 s {displaystyleS} \u4e0e\u3048\u3089\u308c\u305f\u3001\u305d\u3046\u3067\u3042\u308b n\u21922 =  –  n\u2192\u521d\u3081 {displayStyle {thing {n}} _ {2} =  –  {thing {n}} _ {1}} \u3055\u3089\u306a\u308b\u65b9\u5411\u3092\u6301\u3064\u5b9a\u5e38\u30e6\u30cb\u30c3\u30c8\u6b63\u5e38\u30d9\u30af\u30c8\u30eb\u30d5\u30a3\u30fc\u30eb\u30c9 s {displaystyleS} \u5b9a\u7fa9\u3055\u308c\u3066\u3044\u307e\u3059\u3002\u30aa\u30ea\u30a8\u30f3\u30c6\u30eb\u306a\u30a8\u30ea\u30a2\u3067\u3059 s {displaystyleS} \u63a5\u7d9a\u3001\u307e\u3055\u306b\u3053\u308c\u3089\u306e2\u3064\u306e\u65b9\u5411\u304c\u3042\u308a\u307e\u3059\u3002\u9818\u57df\u304c\u3044\u304f\u3064\u304b\u306e\u30b3\u30f3\u30c6\u30ad\u30b9\u30c8\u30b3\u30f3\u30dd\u30fc\u30cd\u30f3\u30c8\u3067\u69cb\u6210\u3055\u308c\u3066\u3044\u308b\u5834\u5408\u3001\u5404\u30b3\u30f3\u30c6\u30ad\u30b9\u30c8\u30b3\u30f3\u30dd\u30fc\u30cd\u30f3\u30c8\u306e\u4ed6\u306e\u30b3\u30f3\u30dd\u30fc\u30cd\u30f3\u30c8\u306b\u95a2\u4fc2\u306a\u304f\u65b9\u5411\u3092\u9078\u629e\u3067\u304d\u307e\u3059\u3002 \u30a8\u30ea\u30a2\u3067\u65b9\u5411\u304c\u9078\u629e\u3055\u308c\u3066\u3044\u308b\u5834\u5408\u3001\u3053\u308c\u306f \u30dd\u30b8\u30c6\u30a3\u30d6 \u53cd\u5bfe\u306e\u65b9\u5411\u3092\u6307\u3057\u307e\u3059 \u30cd\u30ac\u30c6\u30a3\u30d6 \u3002 \u9589\u3058\u305f\u8868\u9762 [ \u7de8\u96c6 | \u30bd\u30fc\u30b9\u30c6\u30ad\u30b9\u30c8\u3092\u7de8\u96c6\u3057\u307e\u3059 ] \u7403\u4f53\uff08\u7403\u9762\u8868\u9762\uff09\u3084\u30c8\u30fc\u30e9\u30b9\u306a\u3069\u306e\u4e00\u8cab\u3057\u305f\u9589\u3058\u305f\u8868\u9762\u306f\u3001\u90e8\u5c4b\u30922\u3064\u306e\u30b3\u30d2\u30fc\u30ec\u30f3\u30c8\u306a\u90e8\u5206\u3001\u5185\u90e8\u3068\u5916\u5074\u306b\u3082\u305f\u3089\u3057\u307e\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u8868\u9762\u306e\u5185\u5074\u3068\u5916\u5074\u306b\u3064\u3044\u3066\u8a71\u3057\u307e\u3059\u3002\u5916\u5074\u306e\u9078\u629e\u306f\u3001\u5916\u5074\u306e\u53c2\u7167\u3001\u5185\u5074\u306e\u5185\u5074\u306e\u7d71\u4e00\u6cd5\u7dda\u30d9\u30af\u30c8\u30eb\u30d5\u30a3\u30fc\u30eb\u30c9\u306e\u9078\u629e\u306b\u5bfe\u5fdc\u3057\u307e\u3059\u3002\u7279\u306b\u8a00\u308f\u306a\u3044\u9650\u308a\u3001\u5916\u5411\u304d\u306e\u30e6\u30cb\u30c3\u30c8\u306e\u901a\u5e38\u306e\u30d9\u30af\u30c8\u30eb\u30d5\u30a3\u30fc\u30eb\u30c9\u3092\u4ecb\u3057\u3066\u65b9\u5411\u3092\u9078\u629e\u3057\u307e\u3059\u3002 [5] \u3053\u308c\u306f\u3001\u30ac\u30a6\u30b9\u7a4d\u5206\u30bb\u30c3\u30c8\u306e\u4f7f\u7528\u306b\u5fc5\u8981\u3067\u3059\u3002 \u30a8\u30c3\u30b8\u306e\u3042\u308b\u8868\u9762 [ \u7de8\u96c6 | \u30bd\u30fc\u30b9\u30c6\u30ad\u30b9\u30c8\u3092\u7de8\u96c6\u3057\u307e\u3059 ]  \u30a8\u30c3\u30b8\u3068\u3001\u95a2\u9023\u3059\u308b\u9650\u754c\u66f2\u7dda\u306e\u30b9\u30eb\u30fc\u30d7\u30c3\u30c8\u306e\u30b9\u30c6\u30a3\u30f3\u30c8\u3092\u5099\u3048\u305f\u65b9\u5411\u306e\u8868\u9762\u3002 \u30a8\u30c3\u30b8\u306e\u3042\u308b\u8868\u9762\u306e\u5834\u5408\u3001\u5468\u8fba\u66f2\u7dda\u306e\u65b9\u5411\uff08\u611f\u899a\u5168\u4f53\uff09\u306f\u3001\u8868\u9762\u306e\u5411\u304d\u306b\u3088\u3063\u3066\u6c7a\u307e\u308a\u307e\u3059\u3002 \u8868\u793a\uff1a\u9818\u57df\u306e\u9078\u629e\u3055\u308c\u305f\u5074\u3092\u300c\u4e0a\u300d\u3068\u898b\u306a\u3057\u3001\u7aef\u306b\u6cbf\u3063\u3066\u9818\u57df\u306e\u4e0a\u90e8\u306b\u6cbf\u3063\u3066\u884c\u304f\u89b3\u6e2c\u8005\u3092\u60f3\u50cf\u3059\u308b\u3068\u3001\u305d\u306e\u9818\u57df\u304c\u305d\u306e\u5de6\u5074\u306b\u3042\u308b\u3088\u3046\u306b\u3001\u89b3\u5bdf\u8005\u306f\u6b63\u306e\u65b9\u5411\u306b\u66f2\u7dda\u3092\u901a\u904e\u3057\u307e\u3059\u3002\u9762\u7a4d\u306e\u5f62\u72b6\u3092\u4f34\u3046\u5468\u8fba\u66f2\u7dda\u306e\u5faa\u74b0\u306f1\u3064\u3067\u3042\u308b\u3068\u8a00\u308f\u308c\u3066\u3044\u307e\u3059 \u5408\u6cd5\u7684\u306a\u30cd\u30b8 \u307e\u305f \u5408\u6cd5\u7684\u306a\u30cd\u30b8 [6] \u5e73\u884c\u306a\u5f62\u306e\u5408\u6cd5\u7684\u306a\u30cd\u30b8\u304c\u8868\u9762\u306e\u65b9\u5411\u306e\u8868\u9762\u306e\u65b9\u5411\u306b\u524d\u65b9\u306b\u79fb\u52d5\u3059\u308b\u305f\u3081\u3001\u5f62\u5f0f\u3002\u8868\u9762\u304c\u5358\u4e00\u306e\u30a8\u30c3\u30b8\u66f2\u7dda\u306b\u3088\u3063\u3066\u5236\u9650\u3055\u308c\u3066\u3044\u308b\u5834\u5408\u3001\u8fba\u7e01\u66f2\u7dda\u306e\u60aa\u611f\u306f\u9818\u57df\u306e\u5411\u304d\u3092\u6c7a\u5b9a\u3057\u307e\u3059\u3002 [7] \u30b9\u30c8\u30fc\u30af\u30b9\u306e\u53e4\u5178\u7684\u306a\u7a4d\u5206\u30bb\u30c3\u30c8\u3067\u306f\u3001\u8868\u9762\u306e\u65b9\u5411\u3068\u5468\u8fba\u66f2\u7dda\u306e\u5168\u4f53\u7684\u306a\u611f\u899a\u304c\u8a00\u53ca\u3055\u308c\u305f\u7a2e\u306b\u95a2\u9023\u3057\u3066\u3044\u308b\u3068\u60f3\u5b9a\u3055\u308c\u3066\u3044\u307e\u3059\u3002 \u65b9\u5411\u30ec\u30d9\u30eb [ \u7de8\u96c6 | \u30bd\u30fc\u30b9\u30c6\u30ad\u30b9\u30c8\u3092\u7de8\u96c6\u3057\u307e\u3059 ] 3\u6b21\u5143\u7a7a\u9593\u306e\u30ec\u30d9\u30eb r 3 {displaystyle mathbb {r} ^{3}} \u305d\u308c\u3092\u6b63\u3068\u8ca0\u306e\u534a\u30b9\u30da\u30fc\u30b9\u306b\u767b\u9332\u3057\u307e\u3059\u3002\u3053\u308c\u306b\u3088\u308a\u3001\u30ec\u30d9\u30eb\u306e\u65b9\u5411\uff08\u5143\u306e\u30ec\u30d9\u30eb\u306e\u672a\u5b9a\u7fa9\u306e\u7279\u6b8a\u306a\u30b1\u30fc\u30b9\u3092\u9664\u304f\uff09\u306f\u3001\u5ea7\u6a19\u8d77\u70b9\u304c\u30cd\u30ac\u30c6\u30a3\u30d6\u30cf\u30fc\u30d5\u30b9\u30da\u30fc\u30b9\u306b\u3042\u308b\u3082\u306e\u3001\u6b63\u306e\u534a\u5206\u306e\u7a7a\u9593\u306e\u65b9\u5411\u306b\u30ec\u30d9\u30eb\u306e\u6b63\u5e38\u30d9\u30af\u30c8\u30eb\u306b\u3042\u308b\u3082\u306e\u3092\u9078\u629e\u3057\u307e\u3059\u3002 \u65b9\u5411\u30ec\u30d9\u30eb Z\u3092\u518d\u751f\u3057\u307e\u3059\u3002 B.\u30d9\u30af\u30c8\u30eb\u30ec\u30d9\u30eb\u65b9\u7a0b\u5f0f\u306e\u901a\u5e38\u306e\u5f62\u5f0f\u306e\u52a9\u3051\u3092\u501f\u308a\u3066\u3001\u8ddd\u96e2\u8a08\u7b97\u306e\u5834\u5408\u306e\u5f79\u5272\u3002 3\u6b21\u5143\u7a7a\u9593\u3067\u30ec\u30d9\u30eb\u306e\u30a2\u30a4\u30c7\u30a2\u3092\u4e00\u822c\u5316\u3059\u308b r 3 {displaystyle mathbb {r} ^{3}} n\u6b21\u5143\u7a7a\u9593\u306e\u30cf\u30a4\u30d1\u30fc\u30d9\u30f3\u306e\u305d\u308c\u306b r n {displaystyle mathbb {r} ^{n}} \u3001\u3088\u308a\u9ad8\u3044\u6b21\u5143\u307e\u305f\u306f\u4f4e\u6b21\u5143\u306e\u914d\u5411\u30cf\u30a4\u30d1\u30fc\u30ec\u30d9\u30eb\u306b\u985e\u4f3c\u3057\u3066\u3044\u307e\u3059\u3002 2\u6b21\u5143\u7a7a\u9593\u3067 r 2 {displaystyle mathbb {r} ^{2}} \u305f\u3068\u3048\u3070\u3001\u3053\u308c\u306f1\u3064\u3067\u3059 \u65b9\u5411\u306e\u30b9\u30c8\u30ec\u30fc\u30c8 \u90e8\u5c4b r 2 {displaystyle mathbb {r} ^{2}} 2\u3064\u306e\u30cf\u30fc\u30d5\u30ec\u30d9\u30eb\u306b\u5206\u5272\u3057\u307e\u3059\u3002\u3053\u308c\u306b\u3088\u308a\u3001\u3053\u306e\u5834\u5408\u3001\u3053\u306e\u5834\u5408\u306f\u6b63\u306e\u534a\u30b9\u30da\u30fc\u30b9\u306e\u901a\u5e38\u306e\u30d9\u30af\u30c8\u30eb\uff08\u3053\u3053\u3067\u306f\u6b63\u306e\u534a\u5206\uff09 \u30ec\u30d9\u30eb \uff09\u306f\u3001\u5ea7\u6a19\u30dc\u30fc\u30ab\u30eb\u30b8\u30e3\u30f3\u30d7\u304b\u3089\uff08\u539f\u70b9\u306e\u672a\u5b9a\u7fa9\u306e\u7279\u5225\u306a\u30b1\u30fc\u30b9\u3068\u306f\u5225\u306b\uff09\u3092\u793a\u3057\u307e\u3059\u3002\u4e00\u65b9\u3001\u9ad8\u6b21\u5143\u306e\u30cf\u30a4\u30d1\u30fc\u30ec\u30d9\u30eb\u3067\u306f\u3001z\u3092\u898b\u3064\u3051\u307e\u3059\u3002 B.\u7279\u5b9a\u306e\u30d3\u30b8\u30cd\u30b9\u6570\u5b66\u7684\u8cea\u554f\u3092\u89e3\u6c7a\u3059\u308b\u3068\u304d\u306e\u30a2\u30d7\u30ea\u30b1\u30fc\u30b7\u30e7\u30f3\u3002 \u30a8\u30ea\u30a2\u306e\u65b9\u5411\u306e\u4e00\u81f4\u306f\u3001\u30d9\u30af\u30c8\u30eb\u8868\u9762\u7a4d\u5206\u3092\u8a08\u7b97\u3059\u308b\u5834\u5408\u306b\u7279\u306b\u91cd\u8981\u3067\u3059\u3002 B.\u30ac\u30a6\u30b9\u7a4d\u5206\u30bb\u30c3\u30c8\u3092\u4f7f\u7528\u3059\u308b\u5834\u5408\u306e\u9759\u96fb\u75c7\u306e\u5834\u5408\u3002\u65b9\u5411\u306f\u7d50\u679c\u306e\u5146\u5019\u3092\u6c7a\u5b9a\u3057\u307e\u3059\u3002z\u304c\u5fc5\u8981\u306a\u5834\u5408\u3002 B.\u8ca8\u7269 Q \u7279\u5b9a\u306e\u30dc\u30ea\u30e5\u30fc\u30e0\u5185\u3067\u8a08\u7b97\u3059\u308b\u3068\u3001\u305d\u308c\u306f\u96fb\u754c\u306e\u307f\u3067\u3059 E\u2192\uff08 x\u2192\uff09\uff09 {displayStyle {thing {e}}\uff08{thing {x}}\uff09} \u30dc\u30ea\u30e5\u30fc\u30e0\u306e\u8868\u9762\u3067\u77e5\u3089\u308c\u3066\u3044\u308b\u305f\u3081\u3001\u3053\u306e\u6587\u3092\u4f7f\u7528\u3057\u3066\u56f2\u307e\u308c\u305f\u8ca0\u8377\u3092\u793a\u3059\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002 Q = \u222b Vd \u306e \u03f1 \uff08 x\u2192\uff09\uff09 = e 0\u222b Vd \u306e d \u79c1 \u306e E\u2192\uff08 x\u2192\uff09\uff09 {displaystyle q = int _ {v} mathrm {d} vvarro \u3002 \u3053\u3053\u306f \u306e \u672a\u77e5\u306e\u8ca8\u7269\u304c\u542b\u307e\u308c\u3066\u3044\u308b\u91cf\u3001\u305d\u3057\u3066 \u03f1 {displaystyle varrho} \u672a\u77e5\u306e\u8ca0\u8377\u5bc6\u5ea6\u3002\u6700\u521d\u306e\u30de\u30c3\u30af\u30b9\u30a6\u30a7\u30eb\u65b9\u7a0b\u5f0f\u306e\u52a9\u3051\u3092\u501f\u308a\u3066\u3001\u3042\u306a\u305f\u306f\u53f3\u5074\u306e\u5f0f\u306b\u5230\u9054\u3057\u3001 e 0 {displaystyle varepsilon _ {0}} \u8a98\u96fb\u7387\u3068 div \u767a\u6563\u3002\u30ac\u30a6\u30b9\u7a4d\u5206\u30bb\u30c3\u30c8\u306e\u52a9\u3051\u3092\u501f\u308a\u3066\u3001\u30dc\u30ea\u30e5\u30fc\u30e0\u7a4d\u5206\u3092\u8868\u9762\u7a4d\u5206\u306b\u7b56\u5b9a\u3067\u304d\u308b\u3088\u3046\u306b\u306a\u308a\u307e\u3057\u305f\u3002 Q = e 0\u222b \u2202Vd A\u2192de E\u2192\uff08 x\u2192\uff09\uff09 {displaystyle q = varepsilon _ {0} int _ {partial v} mathrm {d} {thing {a}} cdot {thing {e}}\uff08{thing {x}}\uff09}}} \u3002 d A\u2192{displaystyle mathrm {d} {vec {a}}} \u8868\u9762\u306e\u7121\u9650\u30d9\u30fc\u30b9\u306e\u8868\u9762\u8981\u7d20\u3067\u3059 \u2202 \u306e {displaystyle partial v} \u30dc\u30ea\u30e5\u30fc\u30e0\u306e\u3002\u30b9\u30ab\u30e9\u30fc\u88fd\u54c1\u306e\u30b5\u30a4\u30f3 d A\u2192de E\u2192{displaystyle mathrm {d} {vec {a}} cdot {vec {e}}}}} \u306e\u65b9\u5411\u306b\u4f9d\u5b58\u3057\u307e\u3059 d A\u2192{displaystyle mathrm {d} {vec {a}}} \u3042\u3061\u3089\u3078\u3002\u306f d A\u2192{displaystyle mathrm {d} {vec {a}}} \u3068\u4e26\u884c\u3057\u3066 E\u2192{displaystyle {vec {e}}} \u3001\u305d\u308c\u304c\u30b9\u30ab\u30e9\u30fc\u88fd\u54c1\u3067\u3059 d a \u3068 {displaystyle mathrm {d} a\u3001e} \u3001\u4e00\u65b9\u3067\u3001\u4e21\u65b9\u3068\u3082\u30d9\u30af\u30c8\u30eb\u30a2\u30f3\u30c1\u30d1\u30e9\u30ec\u30eb\u3067\u3059\u3002\u30b9\u30ab\u30e9\u30fc\u7a4d\u306f  –  d a \u3068 {displaystyle -mathrm {d} a\u3001e} \u3002\u3057\u305f\u304c\u3063\u3066\u3001\u8868\u9762\u7a4d\u5206\u306e\u7b26\u53f7\u306f\u3001\u8868\u9762\u306e\u9078\u629e\u3055\u308c\u305f\u65b9\u5411\u306b\u4f9d\u5b58\u3057\u307e\u3059\u3002\u6163\u7fd2\u3068\u3057\u3066\u30011\u3064\u306e\u9078\u629e \u30dd\u30b8\u30c6\u30a3\u30d6\u306a\u65b9\u5411 \u540c\u610f\u3057\u307e\u3057\u305f\u3002\u3064\u307e\u308a\u3001\u9818\u57df\u306e\u65b9\u5411\u3068\u3057\u3066\u30e6\u30cb\u30c3\u30c8\u306e\u901a\u5e38\u306e\u30d9\u30af\u30c8\u30eb\u30d5\u30a3\u30fc\u30eb\u30c9\uff08\u4e0a\u8a18\u3092\u53c2\u7167\uff09\u3092\u9078\u629e\u3057\u307e\u3059\u3002 \u2191  Ilia N. Bronstein\u3001K\u3002A\u3002Semendjaj\u307e\u305f\u306f\uff1a \u6570\u5b66\u306e\u30da\u30fc\u30d1\u30fc\u30d0\u30c3\u30af \u3002 Harri Deutsch Verlag\u30012008\u3001ISBN 978-3-8171-2007-9\u3001 S.  538 \uff08 \u30aa\u30f3\u30e9\u30a4\u30f3 [2012\u5e748\u670824\u65e5\u306b\u30a2\u30af\u30bb\u30b9]\uff09\u3002   \u2191  \u30ed\u30eb\u30d5\u30fb\u30b7\u30e5\u30ed\u30e0\u30ba\uff1a \u7269\u7406\u5b66\u3092\u7406\u89e3\u3059\u308b\uff1a\u7269\u7406\u5b66\u306e\u8003\u3048\u65b9\u306e\u7d39\u4ecb\u3002\u5747\u8cea\u306a\u30b7\u30b9\u30c6\u30e0 \u3002 Oldenbourg Verlag\u30012008\u3001ISBN 978-3-486-58582-7\u3001 S.  107 \uff08 \u30aa\u30f3\u30e9\u30a4\u30f3 [2012\u5e748\u670824\u65e5\u306b\u30a2\u30af\u30bb\u30b9]\uff09\u3002   \u2191  ThoralfR\u00e4sch\uff1a \u30c0\u30df\u30fc\u306e\u7269\u7406\u5b66\u306e\u6570\u5b66 \u3002 John Wiley\uff06Sons\u30012011\u3001ISBN 978-3-527-70576-4\u3001 S.  398 \uff08 \u30aa\u30f3\u30e9\u30a4\u30f3 [2012\u5e748\u670824\u65e5\u306b\u30a2\u30af\u30bb\u30b9]\uff09\u3002   \u2191  \u30af\u30ea\u30b9\u30c1\u30e3\u30f3\u306f\u30ad\u30e3\u30ea\u30fc\uff1a \u57fa\u672c\u7684\u306a\u9451\u5225\u578b\u3002 de Gruyter\u3001\u30d9\u30eb\u30ea\u30f3u\u3002 a\u3002 2001\u3001ISBN 3-11-015519-2\u3001S\u3002117\u2013118\u3002  \u2191  \u30b8\u30a7\u30fc\u30e0\u30ba\u30fb\u30b9\u30c1\u30e5\u30ef\u30fc\u30c8\uff1a \u591a\u5909\u6570\u8a08\u7b97 \u3002 Cengage Learning\u30012011\u3001ISBN 978-0-538-49787-9\u3001 S.  1140 \uff08 \u30aa\u30f3\u30e9\u30a4\u30f3 [2012\u5e748\u670824\u65e5\u306b\u30a2\u30af\u30bb\u30b9]\uff09\u3002   \u2191  Kurt Meyberg\u3001Peter Vachenauer\uff1a \u3088\u308a\u9ad8\u3044\u6570\u5b661\uff1a\u5dee\u5206\u304a\u3088\u3073\u7a4d\u5206\u8a08\u7b97\u3002\u30d9\u30af\u30c8\u30eb\u304a\u3088\u3073\u5165\u5b66\u8acb\u6c42\u66f8 \u3002 Springer\u3001Berlin\u3001Heidelberg 2001\u3001ISBN 978-3-642-56654-7\u3001 S.  482 \uff08 books.google.de [2014\u5e741\u67084\u65e5\u306b\u30a2\u30af\u30bb\u30b9]\uff09\u3002   \u2191  \u30b0\u30ec\u30b4\u30fc\u30ebM.\u30d5\u30a3\u30af\u30c6\u30f3\u30db\u30eb\u30c4\uff1a \u5fae\u5206\u304a\u3088\u3073\u7a4d\u5206\u8a08\u7b97 \u3002 Harri Deutsch Verlag\u30011992\u3001ISBN 978-3-8171-1280-7\u3001 S.  219 \uff08 \u30aa\u30f3\u30e9\u30a4\u30f3 [2012\u5e748\u670824\u65e5\u306b\u30a2\u30af\u30bb\u30b9]\uff09\u3002   "},{"@context":"http:\/\/schema.org\/","@type":"BreadcrumbList","itemListElement":[{"@type":"ListItem","position":1,"item":{"@id":"https:\/\/wiki.edu.vn\/all2jp\/wiki10\/#breadcrumbitem","name":"Enzyklop\u00e4die"}},{"@type":"ListItem","position":2,"item":{"@id":"https:\/\/wiki.edu.vn\/all2jp\/wiki10\/archives\/10988#breadcrumbitem","name":"\u30aa\u30ea\u30a8\u30f3\u30c6\u30c3\u30c9\u30a8\u30ea\u30a2 – \u30a6\u30a3\u30ad\u30da\u30c7\u30a3\u30a2"}}]}]