[{"@context":"http:\/\/schema.org\/","@type":"BlogPosting","@id":"https:\/\/wiki.edu.vn\/all2jp\/wiki10\/archives\/15062#BlogPosting","mainEntityOfPage":"https:\/\/wiki.edu.vn\/all2jp\/wiki10\/archives\/15062","headline":"Zykloide von Something-\u30a6\u30a3\u30ad\u30da\u30c7\u30a3\u30a2","name":"Zykloide von Something-\u30a6\u30a3\u30ad\u30da\u30c7\u30a3\u30a2","description":"before-content-x4 zykloide von\u4f55\u304b \u307e\u305f Trisektrix von Ceva Tommaso Ceva\uff081648\u20131736\uff09\u306b\u5f93\u3063\u3066\u540d\u524d\u304c\u4ed8\u3051\u3089\u308c\u305f\u30ec\u30a4\u30e4\u30fc\u3067\u30013\u3064\u306e\u9664\u7b97\u306e\u4e09\u89d2\u5f62\u3092\u5206\u5272\u3059\u308b\u305f\u3081\u306b\u4f7f\u7528\u3067\u304d\u307e\u3059\uff08\u3057\u305f\u304c\u3063\u3066Trisectrix\uff09\u3002 Ceva\u81ea\u4f53\u306f\u3001\u66f2\u7dda\u3092\u6b21\u306e\u3088\u3046\u306b\u8aac\u660e\u3057\u307e\u3057\u305f \u30b5\u30a4\u30af\u30ed\u30a4\u30c9\u7570\u5e38 \u3002 CEVA\u30b5\u30a4\u30af\u30ed\u30a4\u30c9\u306e\u69cb\u9020\u306e\u30a2\u30cb\u30e1\u30fc\u30b7\u30e7\u30f3 CEVA\u306e\u30b5\u30a4\u30af\u30ed\u30a4\u30c9\u306e\u89d2\u5ea6\u7279\u6027\uff1a after-content-x4 \u03c6=\u2220P1OP2=\u2220P1P2O{displaystyle varphi = angle p_","datePublished":"2021-08-28","dateModified":"2021-08-28","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\/0\/06\/Cycloid_of_ceva.svg\/390px-Cycloid_of_ceva.svg.png","url":"https:\/\/upload.wikimedia.org\/wikipedia\/commons\/thumb\/0\/06\/Cycloid_of_ceva.svg\/390px-Cycloid_of_ceva.svg.png","height":"178","width":"390"},"url":"https:\/\/wiki.edu.vn\/all2jp\/wiki10\/archives\/15062","wordCount":5669,"articleBody":"     (adsbygoogle = window.adsbygoogle || []).push({});before-content-x4  zykloide von\u4f55\u304b \u307e\u305f Trisektrix von Ceva Tommaso Ceva\uff081648\u20131736\uff09\u306b\u5f93\u3063\u3066\u540d\u524d\u304c\u4ed8\u3051\u3089\u308c\u305f\u30ec\u30a4\u30e4\u30fc\u3067\u30013\u3064\u306e\u9664\u7b97\u306e\u4e09\u89d2\u5f62\u3092\u5206\u5272\u3059\u308b\u305f\u3081\u306b\u4f7f\u7528\u3067\u304d\u307e\u3059\uff08\u3057\u305f\u304c\u3063\u3066Trisectrix\uff09\u3002 Ceva\u81ea\u4f53\u306f\u3001\u66f2\u7dda\u3092\u6b21\u306e\u3088\u3046\u306b\u8aac\u660e\u3057\u307e\u3057\u305f \u30b5\u30a4\u30af\u30ed\u30a4\u30c9\u7570\u5e38 \u3002  CEVA\u30b5\u30a4\u30af\u30ed\u30a4\u30c9\u306e\u69cb\u9020\u306e\u30a2\u30cb\u30e1\u30fc\u30b7\u30e7\u30f3  CEVA\u306e\u30b5\u30a4\u30af\u30ed\u30a4\u30c9\u306e\u89d2\u5ea6\u7279\u6027\uff1a        (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4\u03c6=\u2220P1OP2=\u2220P1P2O{displaystyle varphi = angle p_ {1} op_ {2} = angle p_ {1} p_ {2} o}        (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4\uff08\u57fa\u672c\u89d2\u5ea6\u30bb\u30c3\u30c8\uff09 2\u03c6=\u2220P3P1P2=\u2220P3P1P2{displaystyle 2varphi = angle p_ {3} p_ {1} p_ {2} = angle p_ {3} p_ {1} p_ {2}}} \uff08\u5916\u90e8\u89d2\u5ea6\u30bb\u30c3\u30c8\u3001\u30d9\u30fc\u30b9\u89d2\u5ea6\u30bb\u30c3\u30c8\uff09 3\u03c6=180\u2218\u2212(180\u2218\u22124\u03c6)\u2212\u03c6{displaystyle 3varphi = 180^{circ}  &#8211; \uff08180 ^^ {circ} -4varphi\uff09-varphi} \uff08\u30b5\u30a4\u30c9\u30a2\u30f3\u30b0\u30eb\u3001\u89d2\u5ea6\u306e\u89d2\u5ea6\uff09 \u30dd\u30a4\u30f3\u30c8\u306e\u305f\u3081\u306b p 1{displaystyle p_ {1}} \u63a5\u7d9a\u30b9\u30c8\u30ec\u30fc\u30c8\u306f\u3001\u30e6\u30cb\u30c3\u30c8\u56de\u8def\u306b\u69cb\u7bc9\u3055\u308c\u307e\u3059        (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4o p 1{displaystyle on_ {1}} \u8d77\u6e90\u306b o {displaystyle o} \u3002\u6b21\u306b\u3001\u305d\u308c\u3092\u6c7a\u5b9a\u3057\u307e\u3059 o {displaystyle o} \u5225\u306e\u30dd\u30a4\u30f3\u30c8 p 2{displaystyle p_ {2}} \u306e1\u3064 p 1{displaystyle p_ {1}} \u8ddd\u96e21\u304c\u3042\u308a\u307e\u3059\u3002\u6700\u5f8c\u306b\u3001\u305d\u308c\u3092\u6c7a\u5b9a\u3057\u307e\u3059 p 1{displaystyle p_ {1}} \u5225\u306e\u30dd\u30a4\u30f3\u30c8 p 3{displaystyle p_ {3}} \u30b9\u30c8\u30ec\u30fc\u30c8\u3067 o p 1{displaystyle on_ {1}} \u306e1\u3064 p 2{displaystyle p_ {2}} \u8ddd\u96e21\u304c\u3042\u308a\u307e\u3059\u3002 CEVA\u30b5\u30a4\u30af\u30ed\u30a4\u30c9\u306f\u73fe\u5728\u3001\u5c40\u6240\u66f2\u7dda\u3067\u3059 p 3{displaystyle p_ {3}} \u3042\u306a\u305f\u304c\u3042\u306a\u305f\u304c\u5f97\u308b\u3068\u304d p 1{displaystyle p_ {1}} \u305d\u3057\u3066\u305d\u308c\u3082\u305d\u308c\u3067 o p 1{displaystyle on_ {1}} \u8d77\u6e90\u306b o {displaystyle o} \u56de\u8ee2\u3002 \u4f4d\u7f6e\u66f2\u7dda\u306f\u3001\u30aa\u30ea\u30b8\u30ca\u30eb\u306e4\u3064\u306e\u8ef8\u5bfe\u79f0\u30eb\u30fc\u30d7\u3067\u69cb\u6210\u3055\u308c\u3001X\u8ef8\u4e0a\u306b2\u3064\u306e\u30eb\u30fc\u30d7\u304cY\u8ef8\u4e0a\u306e2\u3064\u3088\u308a\u3082\u306f\u308b\u304b\u306b\u5927\u304d\u3044\u8ef8\u4e0a\u306b\u3042\u308a\u307e\u3059\u3002\u30b9\u30c8\u30ec\u30fc\u30c8\u306e\u4ee3\u308f\u308a\u306b\u4f7f\u7528\u3057\u307e\u3059 o p 1{displaystyle on_ {1}} \u305f\u3060\u306e\u30d3\u30fc\u30e0 o p 1{displaystyle on_ {1}} \u3001\u3057\u305f\u304c\u3063\u3066\u3001y\u8ef8\u3067\u306f2\u3064\u306e\u5c0f\u3055\u306a\u30eb\u30fc\u30d7\u304c\u7701\u7565\u3055\u308c\u3066\u3044\u307e\u3059\u3002 \u69cb\u9020\u306b\u3088\u308a\u3001\u89d2\u5ea6\u306f\u30b9\u30c8\u30ec\u30fc\u30c8\u306e\u9593\u306b\u3042\u308a\u307e\u3059 o p 1{displaystyle on_ {1}} X\u8ef8\u306f\u3001\u30eb\u30fc\u30c8\u9593\u306e\u89d2\u5ea6\u306e\u6b63\u78ba\u306a3\u5206\u306e3 p 2p 3{displaystyle p_ {2} p_ {3}} \u307e\u305f\u3001X\u8ef8\uff08\u56f3\u9762\u3092\u53c2\u7167\uff09\u306f\u3001\u3053\u306e\u30d7\u30ed\u30d1\u30c6\u30a3\u306b\u3088\u308a\u3001Tris Electrix\u3068\u3057\u3066\u4f7f\u7528\u3067\u304d\u307e\u3059\u3002 \u30dd\u30a4\u30f3\u30c8\u306e\u5efa\u8a2d\u30d7\u30ed\u30bb\u30b9\u3092\u8a2d\u5b9a\u3057\u305f\u5834\u5408 p 1{displaystyle p_ {1}} \u3001 p 2{displaystyle p_ {2}} \u3068 p 3{displaystyle p_ {3}} \u3055\u3089\u306a\u308b\u30dd\u30a4\u30f3\u30c8\u306e\u305f\u3081\u306b p k{displaystyle p_ {k}} \u3060\u304b\u3089\u3042\u306a\u305f\u306f\u5947\u5999\u306b\u306a\u308a\u307e\u3059 k {displaystyle k} \u306e\u5c40\u6240\u66f2\u7dda\u3068\u3057\u3066 p k{displaystyle p_ {k}} \u6b7b\u3093\u3060sektrizen von\u4f55\u304b\u3002 \u5e7e\u4f55\u5b66\u7684\u5b9a\u7fa9\u304b\u3089\u3001\u30b3\u30b5\u30a4\u30f3\u30bb\u30c3\u30c8\u306e\u52a9\u3051\u3092\u501f\u308a\u3066\u3001\u6b21\u306e\u65b9\u7a0b\u5f0f\u3092\u6975\u5ea7\u6a19\u3067\u5c0e\u304d\u51fa\u3059\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002 r = \u521d\u3081 + 2 cos \u2061 \uff08 2 \u30d5\u30a1\u30a4 \uff09\uff09 {displaystyle r = 1+2cos\uff082varphi\uff09} \u3002 \u30d1\u30e9\u30e1\u30fc\u30bf\u30fc\u66f2\u7dda\u3068\u3057\u3066 c \uff1a [ 0 \u3001 2 pi ] \u2192 R2{displaystyle\u30ac\u30f3\u30de\uff1a[0,2pi] rightarrow mathbb {r} ^{2}} \u30c7\u30ab\u30eb\u30c8\u5ea7\u6a19\u3067\u306f\u3001\u6b21\u306e\u30d7\u30ec\u30bc\u30f3\u30c6\u30fc\u30b7\u30e7\u30f3\u3092\u53d6\u5f97\u3057\u307e\u3059\u3002 c \uff08 t \uff09\uff09 = (x(t)y(t))= (2cos\u2061(t)+cos\u2061(3t)sin\u2061(3t)){displaystyle gamma\uff08t\uff09= {begin {pmatrix} x\uff08t\uff09\\ y\uff08t\uff09end {pmatrix}} = {begin {pmatrix} 2cos\uff08t\uff09+cos\uff083t\uff09\\ sin\uff083t\uff09end {pmatrix}}}}} \u3002 \u3055\u3089\u306b\u3001\u6b21\u306e\u65b9\u7a0b\u5f0f\u306e\u7d50\u679c\u3001\u30c7\u30ab\u30eb\u30c8\u5ea7\u6a19\u304c\u5f97\u3089\u308c\u307e\u3059\u3002\u3064\u307e\u308a\u3001CEVA\u30b5\u30a4\u30af\u30ed\u30a4\u30c9\u306f6\u5ea6\u306e\u4ee3\u6570\u66f2\u7dda\u3067\u3042\u308b\u3053\u3068\u3092\u610f\u5473\u3057\u307e\u3059\u3002 \uff08 x2+ y2)3= \uff08 3 x2 &#8211;  y2)2{displaystyle\uff08x^{2}+y^{2}\uff09^{3} =\uff083x^{2} -y^{2}\uff09^{2}}} \u3002  \u89d2\u5ea6\u30c8\u30ec\u30a4\u30b7\u30e7\u30f3\u306f\u3001CEVA\u306e\u30b5\u30a4\u30af\u30ed\u30a4\u30c9\u3068\u89d2\u5ea6\u3092\u6307\u3057\u305f  CEVA\u304b\u3089\u306e\u30b5\u30a4\u30af\u30ed\u30a4\u30c9\u3068\u306e\u89d2\u5ea6\u30c8\u30ec\u30a4\u30b7\u30e7\u30f3\u920d\u3044\u89d2\u5ea6 CEVA\u30b5\u30a4\u30af\u30ed\u30a4\u30c9\u306e\u4e0a\u8a18\u306e\u89d2\u5ea6\u7279\u6027\u306f\u3001\u89d2\u5ea6\u306e3\u3064\u306e\u90e8\u54c1\u5206\u5272\u306b\u6b21\u306e\u69cb\u9020\u3092\u63d0\u4f9b\u3057\u307e\u3059\u3002\u7279\u5b9a\u306e\u89d2\u5ea6\u3067 \uf097 c b a {displaystyle angle cba} \u6700\u521d\u306b\u592a\u3082\u3082\u3092\u4f38\u3070\u3057\u307e\u3059 a b {displaystyle ab} \u62e1\u5f35\u4e0a\u306b\u30b5\u30a4\u30af\u30ed\u30a4\u30c9\u3092\u63cf\u304d\u307e\u3059 a b {displaystyle ab} X\u8ef8\u3068\u3057\u3066\u3002\u305d\u306e\u5f8c\u3001\u4ed6\u306e\u592a\u3082\u3082\u306b\u7740\u307e\u3059 b c {displaystyle bc} \u8ddd\u96e2 b d {displaystyle bd} \u9577\u30551\u3067\u3001\u5e73\u884c\u3092\u63cf\u753b\u3057\u307e\u3059 a b {displaystyle ab} \u30dd\u30a4\u30f3\u30c8\u3092\u901a\u3057\u3066 d {displaystyle d} \u3002\u3053\u308c\u306b\u3088\u308a\u3001\u305d\u306e\u70b9\u3067\u30b5\u30a4\u30af\u30ed\u30a4\u30c9\u304c\u524a\u6e1b\u3055\u308c\u307e\u3059 p 3{displaystyle p_ {3}} \u3002\u3053\u308c\u3067\u3001\u30dd\u30a4\u30f3\u30c8\u3092\u63a5\u7d9a\u3057\u307e\u3059 p 3{displaystyle p_ {3}} \u30b5\u30a4\u30af\u30ed\u30a4\u30c9\u306e\u4e2d\u5fc3 o {displaystyle o} \uff08\u5ea7\u6a19\u7cfb\u306e\u8d77\u6e90\uff09\u3001\u30eb\u30fc\u30c8\u304c\u5f62\u6210\u3055\u308c\u307e\u3059 o p 3{displaystyle on_ {3}} \u306e\u62e1\u5f35\u4ed8\u304d a b {displaystyle ab} \u89d2\u5ea6\u3001\u51fa\u529b\u89d2\u306e\u89d2\u5ea6\u5c3a\u5ea6\u306e\u6b63\u78ba\u306a3\u5206\u306e1\u306e\u89d2\u5ea6\u5bf8\u6cd5 \uf097 c b a {displaystyle angle cba} \u306b\u76f8\u5f53\u3057\u307e\u3059\u3002\u30b9\u30d4\u30c3\u30c4\u30a1\u30fc\u307e\u305f\u306f\u920d\u3044\u89d2\u5ea6\u306e\u5834\u5408\u306e\u5e73\u884c\u306f\u3001\u5e38\u306b2\u3064\u306e\u30dd\u30a4\u30f3\u30c8\u3067\u30b5\u30a4\u30af\u30ed\u30a4\u30c9\u3092\u30ab\u30c3\u30c8\u3057\u3001\u3057\u305f\u304c\u3063\u3066\u6700\u521d\u306b2\u3064\u306e\u30dd\u30a4\u30f3\u30c8\u3092\u6c7a\u5b9a\u3059\u308b\u3053\u3068\u306b\u6ce8\u610f\u3057\u3066\u304f\u3060\u3055\u3044\u3002 p 3{displaystyle p_ {3}} \u5229\u7528\u53ef\u80fd\u306b\u306a\u308a\u307e\u3059\u3002\u305d\u308c\u306f\u5c16\u3063\u305f\u89d2\u5ea6\u3067\u3059\uff08 \uf097 c b a < 90 \u2218{displaystyle angle cba "},{"@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\/15062#breadcrumbitem","name":"Zykloide von Something-\u30a6\u30a3\u30ad\u30da\u30c7\u30a3\u30a2"}}]}]