[{"@context":"http:\/\/schema.org\/","@type":"BlogPosting","@id":"https:\/\/wiki.edu.vn\/all2jp\/wiki11\/archives\/20725#BlogPosting","mainEntityOfPage":"https:\/\/wiki.edu.vn\/all2jp\/wiki11\/archives\/20725","headline":"nephroid – \u30a6\u30a3\u30ad\u30da\u30c7\u30a3\u30a2","name":"nephroid – \u30a6\u30a3\u30ad\u30da\u30c7\u30a3\u30a2","description":"before-content-x4 \u4e8c\u91cd\u534a\u5f84\u3067\u5186\u306e\u5186\u3092\u4e38\u304f\u3059\u308b\u3053\u3068\u306b\u3088\u308b\u814e\u81d3\u306e\u69cb\u7bc9 after-content-x4 \u534a\u5f842\/3\u306e\u5186\u306e\u5468\u308a\u306b\u5186\u3092\u56de\u8ee2\u3055\u305b\u308b\u3053\u3068\u306b\u3088\u308a\u3001\u540c\u3058\u814e\u6027\u306e\u69cb\u7bc9 \u4e00 nephroide \uff08aus altgriechisch\u1f41\u814e\u81d3 \u30db\u30fc\u30cd\u30d5\u30ed\u30b9 \u3001\u300c\u814e\u81d3\u300d\u3001\u305d\u306e\u5f62\u72b6\u306b\u5fdc\u3058\u3066\uff09\u306f\u4ee3\u6570\u66f2\u7dda\u3067\u3059\u3002 \u30cd\u30d5\u30ed\u30a4\u30c9\u306f\u3001\u534a\u5f84\u3067\u5186\u3092\u8ee2\u304c\u3059\u3053\u3068\u306b\u3088\u3063\u3066\u4f5c\u6210\u3055\u308c\u307e\u3059 a {displaystyle a} \u534a\u5f84\u306e\u3042\u308b\u5186\u306e\u5916\u5074 after-content-x4 2 a {displaystyle 2a}","datePublished":"2019-11-26","dateModified":"2019-11-26","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\/0\/02\/EpitrochoidOn2.gif\/250px-EpitrochoidOn2.gif","url":"https:\/\/upload.wikimedia.org\/wikipedia\/commons\/thumb\/0\/02\/EpitrochoidOn2.gif\/250px-EpitrochoidOn2.gif","height":"254","width":"250"},"url":"https:\/\/wiki.edu.vn\/all2jp\/wiki11\/archives\/20725","wordCount":16029,"articleBody":" (adsbygoogle = window.adsbygoogle || []).push({});before-content-x4\u4e8c\u91cd\u534a\u5f84\u3067\u5186\u306e\u5186\u3092\u4e38\u304f\u3059\u308b\u3053\u3068\u306b\u3088\u308b\u814e\u81d3\u306e\u69cb\u7bc9 (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4\u534a\u5f842\/3\u306e\u5186\u306e\u5468\u308a\u306b\u5186\u3092\u56de\u8ee2\u3055\u305b\u308b\u3053\u3068\u306b\u3088\u308a\u3001\u540c\u3058\u814e\u6027\u306e\u69cb\u7bc9 \u4e00 nephroide \uff08aus altgriechisch\u1f41\u814e\u81d3 \u30db\u30fc\u30cd\u30d5\u30ed\u30b9 \u3001\u300c\u814e\u81d3\u300d\u3001\u305d\u306e\u5f62\u72b6\u306b\u5fdc\u3058\u3066\uff09\u306f\u4ee3\u6570\u66f2\u7dda\u3067\u3059\u3002\u30cd\u30d5\u30ed\u30a4\u30c9\u306f\u3001\u534a\u5f84\u3067\u5186\u3092\u8ee2\u304c\u3059\u3053\u3068\u306b\u3088\u3063\u3066\u4f5c\u6210\u3055\u308c\u307e\u3059 a {displaystyle a} \u534a\u5f84\u306e\u3042\u308b\u5186\u306e\u5916\u5074 (adsbygoogle = window.adsbygoogle || []).push({});after-content-x42 a {displaystyle 2a} \u3002\u3053\u308c\u306f\u3001\u814e\u75c7\u304c\u4e0a\u817a\u4f53\u306e\u30af\u30e9\u30b9\u306b\u5c5e\u3057\u3066\u3044\u308b\u3053\u3068\u3092\u610f\u5473\u3057\u307e\u3059\u3002 \u306f a {displaystyle a} \u5c0f\u3055\u306a\uff08\u30ed\u30fc\u30ea\u30f3\u30b0\uff09\u5186\u306e\u534a\u5f84\u3068 \uff08 0 \u3001 0 \uff09\uff09 \u3001 2 a {displaystyle\uff080,0\uff09\u3001; 2a} \u5927\u304d\u306a\uff08\u56fa\u4f53\uff09\u5186\u306e\u4e2d\u5fc3\u3068\u534a\u5f84\u3001 (adsbygoogle = window.adsbygoogle || []).push({});after-content-x42 \u30d5\u30a1\u30a4 {displaystyle 2varphi} \uff08\u5c0f\u3055\u306a\u5186\u306e\uff09\u30ed\u30fc\u30e9\u30fc\u89d2\u5ea6\u3068\u30dd\u30a4\u30f3\u30c8 \uff08 2 a \u3001 0 \uff09\uff09 {displaystyle\uff082a\u30010\uff09} \u51fa\u767a\u70b9\uff08\u5199\u771f\u3092\u53c2\u7167\uff09\u3001\u305d\u308c\u304c\u3042\u306a\u305f\u304c\u5f97\u308b\u65b9\u6cd5\u3067\u3059 \u30d0\u30c4 \uff08 \u30d5\u30a1\u30a4 \uff09\uff09 = 3 a cos \u2061 \u30d5\u30a1\u30a4 – a cos \u2061 3 \u30d5\u30a1\u30a4 = 6 a cos \u2061 \u30d5\u30a1\u30a4 – 4 a cos 3\u2061 \u30d5\u30a1\u30a4 \u3001 {displaystyle x\uff08varphi\uff09= 3acos varphi -acos 3varphi = 6acos varphi -4acos ^{3} varphi\u3001} \u3068 \uff08 \u30d5\u30a1\u30a4 \uff09\uff09 = 3 a \u7f6a \u2061 \u30d5\u30a1\u30a4 – a \u7f6a \u2061 3 \u30d5\u30a1\u30a4 = 4 a \u7f6a 3\u2061 \u30d5\u30a1\u30a4 \u3001 0 \u2264 \u30d5\u30a1\u30a4 < 2 pi {displaystyle y\uff08varphi\uff09= 3asin varphi -asin 3varphi = 4asin ^{3} varphi\u3001qqad 0leq varphi {displaystyle varphi} \u306e\u4e57\u7b97\u3092\u901a\u3058\u3066\u3067\u3059 \u305d\u3046\u3067\u3059 \u79c1 \u30d5\u30a1\u30a4 {displaystyle e^{ivarphi}} \u5f15\u304d\u8d77\u3053\u3055\u308c\u305f\u3002 \u56de\u8ee2 \u30d5\u30a1\u30a4 3{displaystyle phi _ {3}} \u30dd\u30a4\u30f3\u30c8\u3078 3 a {displaystyle 3a} \u89d2\u5ea6\u306e\u5468\u308a 2 \u30d5\u30a1\u30a4 {displaystyle 2varphi} \u306f \u3068 \u21a6 3 a + \uff08 \u3068 – 3 a \uff09\uff09 \u305d\u3046\u3067\u3059 i2\u03c6{displaystyle zmapsto 3a+\uff08z-3a\uff09e^{i2varphi}}}}}} \u3002 \u56de\u8ee2 \u30d5\u30a1\u30a4 0{displaystyle phi _ {0}} \u30dd\u30a4\u30f3\u30c8\u3078 0 {displaystyle 0} \u89d2\u5ea6\u306e\u5468\u308a \u30d5\u30a1\u30a4 {displaystyle varphi} \u306f \u3068 \u21a6 \u3068 \u305d\u3046\u3067\u3059 i\u03c6{dispastaStyle mopsto z^{ivarphi}} \u3002 nephroid\u30dd\u30a4\u30f3\u30c8 p \uff08 \u30d5\u30a1\u30a4 \uff09\uff09 {displaystyle P\uff08varphi\uff09} \u30dd\u30a4\u30f3\u30c8\u3092\u56de\u8ee2\u3055\u305b\u308b\u3053\u3068\u306b\u3088\u3063\u3066\u4f5c\u6210\u3055\u308c\u307e\u3059 2 a {displaystyle 2a} \u3068 \u30d5\u30a1\u30a4 3 {displaystyle phi _ {3}} \u3068\u5f8c\u7d9a\u306e\u56de\u8ee2 \u30d5\u30a1\u30a4 0 {displaystyle phi _ {0}} \uff1a p \uff08 \u30d5\u30a1\u30a4 \uff09\uff09 = \u30d5\u30a1\u30a4 0\uff08 \u30d5\u30a1\u30a4 3\uff08 2 a \uff09\uff09 \uff09\uff09 = \u30d5\u30a1\u30a4 0\uff08 3 a – a \u305d\u3046\u3067\u3059 i2\u03c6\uff09\uff09 = \uff08 3 a – a \u305d\u3046\u3067\u3059 i2\u03c6\uff09\uff09 \u305d\u3046\u3067\u3059 i\u03c6= 3 a \u305d\u3046\u3067\u3059 i\u03c6 – a \u305d\u3046\u3067\u3059 i3\u03c6{displaystyle p\uff08varphi\uff09= phi _ {0}\uff08phi _ _ {3}\uff09= phi _ _ _ _ {0}\uff083a-i {{i2varphi}\uff09=\uff083a-i2varphi}\uff09e\u200b\u200b {{{{{} = 3a} -aa \u3002 \u3053\u308c\u306f\u3053\u308c\u306b\u8d77\u56e0\u3057\u307e\u3059 x(\u03c6)=3acos\u2061\u03c6\u2212acos\u20613\u03c6=6acos\u2061\u03c6\u22124acos3\u2061\u03c6\u00a0,y(\u03c6)=3asin\u2061\u03c6\u2212asin\u20613\u03c6=4asin3\u2061\u03c6.{displaystyle {begin {array} {cclcccc} x\uff08varphi\uff09\uff06=\uff063acos varphi -acos 3varphi\uff06\uff066acos varphi -4acos {3} varphi\u3001\uff063\uff08varphi\uff09\uff06\uff063 =\uff063 =\uff064asin ^{3} varphi\uff06\u3002 \uff08\u5f0f\u306f\u306a\u308a\u307e\u3057\u305f \u305d\u3046\u3067\u3059 \u79c1 \u30d5\u30a1\u30a4 = cos \u2061 \u30d5\u30a1\u30a4 + \u79c1 \u7f6a \u2061 \u30d5\u30a1\u30a4 \u3001 cos 2 \u2061 \u30d5\u30a1\u30a4 + \u7f6a 2 \u2061 \u30d5\u30a1\u30a4 = \u521d\u3081 \u3001 cos \u2061 3 \u30d5\u30a1\u30a4 = 4 cos 3 \u2061 \u30d5\u30a1\u30a4 – 3 cos \u2061 \u30d5\u30a1\u30a4 \u3001 \u7f6a \u2061 3 \u30d5\u30a1\u30a4 = 3 \u7f6a \u2061 \u30d5\u30a1\u30a4 – 4 \u7f6a 3 \u2061 \u30d5\u30a1\u30a4 {displaystyle e ^{ivarphi} = cos varphi +isin varphi\u3001cos ^{2} varphi +sin ^{2} varphi = 1\u3001cos 3varphi = 4cos hi -4sin ^{3} varphi} \u4f7f\u7528\u6e08\u307f\u3002\u30d5\u30a9\u30fc\u30df\u30e5\u30e9\u30b3\u30ec\u30af\u30b7\u30e7\u30f3\u306e\u4e09\u89d2\u6cd5\u3092\u53c2\u7167\u3057\u3066\u304f\u3060\u3055\u3044\u3002\uff09 \u6697\u9ed9\u306e\u8868\u73fe\u306e\u8a3c\u660e \u3068 \u30d0\u30c4 2 + \u3068 2 – 4 a 2 = \uff08 3 a cos \u2061 \u30d5\u30a1\u30a4 – a cos \u2061 3 \u30d5\u30a1\u30a4 \uff09\uff09 2 + \uff08 3 a \u7f6a \u2061 \u30d5\u30a1\u30a4 – a \u7f6a \u2061 3 \u30d5\u30a1\u30a4 \uff09\uff09 2 – 4 a 2 = \u22ef = 6 a 2 \uff08 \u521d\u3081 – cos \u2061 2 \u30d5\u30a1\u30a4 \uff09\uff09 = 12\u756a\u76ee a 2 \u7f6a 2 \u2061 \u30d5\u30a1\u30a4 {displaystyle x^{2}+y^{2} -4a^{2} =\uff083cos varphi -acos 3varphi\uff09^{2}+\uff083asin varsin\uff09arphi\uff09= 12a^{2} sin^{2} varphi}} varphi} \u964d\u4f0f\u3057\u305f \uff08 \u30d0\u30c4 2+ \u3068 2 – 4 a 2\uff09\uff09 3= \uff08 12\u756a\u76ee a 2\uff09\uff09 3\u7f6a 6\u2061 \u30d5\u30a1\u30a4 = 108 a 4\uff08 4 a \u7f6a 3\u2061 \u30d5\u30a1\u30a4 \uff09\uff09 2= 108 a 4\u3068 2 \u3002 {displaystyle\uff08x^{2}+y^{2} -4a^{2}\uff09^{3} =\uff0812a^{2}\uff09^{3} sin^{6} varphi = 108a^{4}\uff084asin^{3} varphi\uff09^{2} = 108a^ \u7570\u306a\u308b\u65b9\u5411 \u30d2\u30f3\u30c8\u304cy\u8ef8\u4e0a\u306b\u3042\u308b\u5834\u5408\uff1a \u30d1\u30e9\u30e1\u30fc\u30bf\u30fc\u30d7\u30ec\u30bc\u30f3\u30c6\u30fc\u30b7\u30e7\u30f3\uff1a \u30d0\u30c4 = 3 a cos \u2061 \u30d5\u30a1\u30a4 + a cos \u2061 3 \u30d5\u30a1\u30a4 \u3001 \u3068 = 3 a \u7f6a \u2061 \u30d5\u30a1\u30a4 + a \u7f6a \u2061 3 \u30d5\u30a1\u30a4 \uff09\uff09 \u3002 {displaystyle x = 3acos varphi +acos 3varphi\u3001quad y = 3asin varphi +asin 3varphi\uff09\u3002} \u65b9\u7a0b\u5f0f\uff1a \uff08 \u30d0\u30c4 2+ \u3068 2 – 4 a 2\uff09\uff09 3= 108 a 4\u30d0\u30c4 2\u3002 {displaystyle\uff08x^{2}+y^{2} -4a^{2}\uff09^{3} = 108a^{4} x^{2}\u3002} \u4e0a\u8a18\u306e\u30cd\u30d5\u30ed\u30a4\u30c9\u306e\u5834\u5408 \u8a3c\u62e0\u306f\u3001\u30d1\u30e9\u30e1\u30fc\u30bf\u30fc\u30d7\u30ec\u30bc\u30f3\u30c6\u30fc\u30b7\u30e7\u30f3\u3092\u4f7f\u7528\u3057\u307e\u3059 \u30d0\u30c4 \uff08 \u30d5\u30a1\u30a4 \uff09\uff09 = 6 a cos \u2061 \u30d5\u30a1\u30a4 – 4 a cos 3\u2061 \u30d5\u30a1\u30a4 \u3001 {displaystyle x\uff08varphi\uff09= 6acos varphi -4acos ^{3} varphi\u3001} \u3068 \uff08 \u30d5\u30a1\u30a4 \uff09\uff09 = 4 a \u7f6a 3\u2061 \u30d5\u30a1\u30a4 {displaystyle y\uff08varphi\uff09= 4asin ^{3} varphi} \u4e0a\u8a18\u306e\u814e\u81d3\u3068\u305d\u306e\u6d3e\u751f x\u02d9= – 6 a \u7f6a \u2061 \u30d5\u30a1\u30a4 \uff08 \u521d\u3081 – 2 cos 2\u2061 \u30d5\u30a1\u30a4 \uff09\uff09 \u3001 x\u00a8= – 6 a cos \u2061 \u30d5\u30a1\u30a4 \uff08 5 – 6 cos 2\u2061 \u30d5\u30a1\u30a4 \uff09\uff09 \u3001 {displaystyle {dot {x} = -6asin varphi\uff081-2cos ^{2} varphi\uff09\u3001quad {ddot {x} = -6acos varphi\uff085-6cos ^{2} varphi\uff09\u3001} y\u02d9= 12\u756a\u76ee a \u7f6a 2\u2061 \u30d5\u30a1\u30a4 cos \u2061 \u30d5\u30a1\u30a4 \u3001 y\u00a8= 12\u756a\u76ee a \u7f6a \u2061 \u30d5\u30a1\u30a4 \uff08 3 cos 2\u2061 \u30d5\u30a1\u30a4 – \u521d\u3081 \uff09\uff09 \u3002 {displasyStle {dot}} = 12asin ^{2} varphi cos varphi quad\u3001quad quad quad quad {dot {y}} = 12asin varphi\uff083cos ^{2} varphi -1\uff09\u3002}} \u9818\u57df\u306e\u9762\u7a4d\u3068\u66f2\u7dda\u9577\u306e\u5f0fz\u3092\u898b\u3064\u3051\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002 B.\u3053\u3061\u3089\u3002 [\u521d\u3081] \u66f2\u7dda\u9577\u306e\u8a3c\u660e \u30d1\u30e9\u30e1\u30fc\u30bf\u30fc\u5316\u3055\u308c\u305f\u66f2\u7dda\u306e\u9577\u3055\u306e\u5f0f\u3067\u7d50\u679c l = 2 \u222b 0\u03c0x\u02d92+y\u02d92d \u30d5\u30a1\u30a4 = \u22ef = 12\u756a\u76ee a \u222b 0\u03c0\u7f6a \u2061 \u30d5\u30a1\u30a4 d \u30d5\u30a1\u30a4 = 24 a {displaystyle l = 2int _ {0 ^^ {pi} {sqrt {{dot {x}}}^{2} hi = 24a} \u3002 \u5730\u57df\u306e\u8a3c\u660e\uff08\u30e9\u30a4\u30d7\u30cb\u30c3\u30c4\u30bb\u30af\u30bf\u30fc\u306e\u5f0f\uff09 a = 2 de 12| \u222b 0\u03c0[ \u30d0\u30c4 y\u02d9 – \u3068 x\u02d9] d \u30d5\u30a1\u30a4 | = \u22ef = 24 a 2\u222b 0\u03c0\u7f6a 2\u2061 \u30d5\u30a1\u30a4 d \u30d5\u30a1\u30a4 = 12\u756a\u76ee pi a 2{displaystyle a = 2cdot {tfrac {1} {2}} | int _ {0} ^^ {pi} [x {dot {y}} – y {dot {x}; dvarphi | = cdots = 24a {2} varphi; dvarphi \u3002 \u66f2\u7387\u534a\u5f84\u306e\u8a3c\u660e r = | (x\u02d92+y\u02d92)32x\u02d9y\u00a8\u2212y\u02d9x\u00a8| = \u22ef = | 3 a \u7f6a \u2061 \u30d5\u30a1\u30a4 | \u3002 {displaystle rhod = left | {frac {left\uff08{{dot}}^{2}+{dot {y}}^{2}}\u53f3\uff09^{frac {3} {2}}}}}}}}\u53f3| = cdots = | 3asin varphi |}}}} \u5186\u5f62\u306e\u5186\u306e\u5c01\u7b52\u3068\u3057\u3066\u306e\u814e\u81d3 \u9069\u7528\u3055\u308c\u307e\u3059\uff1a \u8a3c\u62e0 \u305d\u3046\u3067\u3059 k 0 {displaystyle k_ {0}} \u5186 \uff08 2 a cos \u2061 \u30d5\u30a1\u30a4 \u3001 2 a \u7f6a \u2061 \u30d5\u30a1\u30a4 \uff09\uff09 {displaystyle\uff082acos varphi\u30012asin varphi\uff09} \u4e2d\u5fc3\u306b \uff08 0 \u3001 0 \uff09\uff09 {displaystyle\uff080.0\uff09} \u305d\u3057\u3066\u534a\u5f84 2 a {displaystyle 2a} \u3002\u5fc5\u8981\u306a\u76f4\u5f84\u306fX\u8ef8\u306b\u3042\u308a\u307e\u3059\uff08\u5199\u771f\u3092\u53c2\u7167\uff09\u3002\u5186\u306f\u6b21\u306e\u3068\u304a\u308a\u3067\u3059\u3002 f \uff08 \u30d0\u30c4 \u3001 \u3068 \u3001 \u30d5\u30a1\u30a4 \uff09\uff09 = \uff08 \u30d0\u30c4 – 2 a cos \u2061 \u30d5\u30a1\u30a4 \uff09\uff09 2+ \uff08 \u3068 – 2 a \u7f6a \u2061 \u30d5\u30a1\u30a4 \uff09\uff09 2 – \uff08 2 a \u7f6a \u2061 \u30d5\u30a1\u30a4 \uff09\uff09 2= 0 \u3002 {displaystyle f\uff08x\u3001y\u3001varphi\uff09=\uff08x -2acos varphi\uff09^{2}+\uff08y-2asin varphi\uff09^{2} – \uff082asin varphi\uff09^{2} = 0.} \u5c01\u7b52\u306e\u72b6\u614b\u306f\u3067\u3059 f \u03c6\uff08 \u30d0\u30c4 \u3001 \u3068 \u3001 \u30d5\u30a1\u30a4 \uff09\uff09 = 2 a \uff08 \u30d0\u30c4 \u7f6a \u2061 \u30d5\u30a1\u30a4 – \u3068 cos \u2061 \u30d5\u30a1\u30a4 – 2 a cos \u2061 \u30d5\u30a1\u30a4 \u7f6a \u2061 \u30d5\u30a1\u30a4 \uff09\uff09 = 0 \u3002 {displaysyllyle f_ {varphi}\uff08x\u3001y\u3001varphi\uff09= 2a\uff08xsin varphi -ycos varphi-2acos varphi-2acos varphi-2acos varphi-2acos varphi-2acos varphi-2acos varphi nephroid\u30dd\u30a4\u30f3\u30c8\u304c\u671f\u5f85\u3055\u308c\u3066\u3044\u307e\u3059 p \uff08 \u30d5\u30a1\u30a4 \uff09\uff09 = \uff08 6 a cos \u2061 \u30d5\u30a1\u30a4 – 4 a cos 3 \u2061 \u30d5\u30a1\u30a4 \u3001 4 a \u7f6a 3 \u2061 \u30d5\u30a1\u30a4 \uff09\uff09 {displaystyle P\uff08varphi\uff09=\uff086acos varphi -4acos ^{3} varphi;\u3001; 4asin ^{3} varphi\uff09} 2\u3064\u306e\u65b9\u7a0b\u5f0f f \uff08 \u30d0\u30c4 \u3001 \u3068 \u3001 \u30d5\u30a1\u30a4 \uff09\uff09 = 0 \u3001 f \u30d5\u30a1\u30a4 \uff08 \u30d0\u30c4 \u3001 \u3068 \u3001 \u30d5\u30a1\u30a4 \uff09\uff09 = 0 {displaystyle f\uff08x\u3001y\u3001varphi\uff09= 0\u3001; f_ {varphi}\uff08x\u3001y\u3001varphi\uff09= 0} \u5145\u8db3\u3055\u308c\u3001\u3057\u305f\u304c\u3063\u3066\u5186\u306e\u5c01\u7b52\u306e\u30dd\u30a4\u30f3\u30c8\u3002 \u7fa4\u8846\u306e\u5c01\u7b52\u3068\u3057\u3066\u306e\u814e\u81d3\uff1a\u814e\u81d3\u306e\u63a5\u7dda\u306f\u5186\u306e\u8171\u3067\u3059\u3002\u8171\u306f\u3001\u5186\u5f62\u7d4c\u8def\u3067\u30dd\u30a4\u30f3\u30c8n\u3068\u30dd\u30a4\u30f3\u30c83n\u306e\u9593\u3092\u8d70\u884c\u3057\u307e\u3059\u3002\u3053\u308c\u306f\u30013\u306e\u500d\u6570\u306b\u5bfe\u5fdc\u3059\u308b\u3044\u304f\u3064\u304b\u306e\u30b9\u30c6\u30c3\u30d7\u306b\u5747\u7b49\u306b\u5206\u5272\u3055\u308c\u307e\u3059\u3002 \u76f4\u7dda\u306e\u7fa4\u8846\u306e\u5c01\u7b52\u3068\u3057\u3066\u306e\u30cd\u30d5\u30ed\u30a4\u30c9\uff1a\u814e\u81d3\u306e\u63a5\u7dda\u306f\u5186\u306e\u8171\u3067\u3059 \u7fa4\u8846\u306b\u5305\u307e\u308c\u305f\u30ab\u30fc\u30c7\u30a3\u30aa\u30a4\u30c9\u306e\u751f\u6210\u3068\u540c\u69d8\u306b\u3001\u6b21\u306e\u3053\u3068\u304c\u3053\u3053\u306b\u5f53\u3066\u306f\u307e\u308a\u307e\u3059\u3002 \u5186\u3092\u63cf\u304d\u3001\u305d\u308c\u3092\u5747\u7b49\u306b\u5171\u6709\u3057\u307e\u3057\u305f 3 n {displaystyle 3n} \u30dd\u30a4\u30f3\u30c8\uff08\u5199\u771f\u3092\u53c2\u7167\uff09\u3068\u7d99\u7d9a\u7684\u306b\u756a\u53f7\u3002 \u8171\u3092\u63cf\u304f\uff1a \uff08 \u521d\u3081 \u3001 3 \uff09\uff09 \u3001 \uff08 2 \u3001 6 \uff09\uff09 \u3001 \u3002 \u3002 \u3002 \u3002 \u3001 \uff08 n \u3001 3 n \uff09\uff09 \u3001 \u3002 \u3002 \u3002 \u3002 \u3001 \uff08 n \u3001 3 n \uff09\uff09 \u3001 \uff08 n + \u521d\u3081 \u3001 3 \uff09\uff09 \u3001 \uff08 n + 2 \u3001 6 \uff09\uff09 \u3001 \u3002 \u3002 \u3002 \u3002 \u3001 {displaystyle\uff081,3\uff09\u3001\uff082,6\uff09\u3001….\u3001\uff08n\u30013n\uff09\u3001….\u3001\uff08n\u30013n\uff09\u3001\uff08n+1,3\uff09\u3001\uff08n+2,6\uff09\u3001….\u3001} \u3002 \uff08\u3053\u306e\u3088\u3046\u306b\u8868\u73fe\u3067\u304d\u307e\u3059\u3002\u8171\u306e2\u756a\u76ee\u306e\u30dd\u30a4\u30f3\u30c8\u306f\u3001\u4e09\u91cd\u901f\u5ea6\u3067\u52d5\u304d\u307e\u3059\u3002\uff09 \u5c01\u7b52 \u3053\u306e\u30eb\u30fc\u30c8\u306f\u814e\u81d3\u3067\u3059\u3002 \u8a3c\u62e0 \u306e\u4e09\u89d2\u5f0f\u306e\u5f0f cos \u2061 a + cos \u2061 b \u3001 \u7f6a \u2061 a + \u7f6a \u2061 b \u3001 cos \u2061 \uff08 a + b \uff09\uff09 \u3001 cos \u2061 2 a {displaystyle cos alpha +cos beta\u3001sin alpha +sin beta\u3001cos\uff08alpha +beta\uff09\u3001cos 2alpha} \u4f7f\u7528\u6e08\u307f\u3002\u8acb\u6c42\u66f8\u3092\u7c21\u5358\u306b\u4fdd\u3064\u305f\u3081\u306b\u3001Y\u8ef8\u306e\u30d2\u30f3\u30c8\u3092\u6301\u3064\u814e\u81d3\u306e\u8a3c\u660e\u304c\u5c0e\u304b\u308c\u307e\u3059\u3002 \u63a5\u7dda\u306e\u65b9\u7a0b\u5f0f \u30d1\u30e9\u30e1\u30fc\u30bf\u30fc\u30d7\u30ec\u30bc\u30f3\u30c6\u30fc\u30b7\u30e7\u30f3\u3092\u4f7f\u7528\u3057\u3066\u814e\u81d3\u3078 \u30d0\u30c4 = 3 cos \u2061 \u30d5\u30a1\u30a4 + cos \u2061 3 \u30d5\u30a1\u30a4 \u3001 \u3068 = 3 \u7f6a \u2061 \u30d5\u30a1\u30a4 + \u7f6a \u2061 3 \u30d5\u30a1\u30a4 {displaystyle x = 3cos varphi +cos 3varphi\u3001y = 3sin varphi +sin 3varphi} \uff1a \u30d1\u30e9\u30e1\u30fc\u30bf\u30fc\u8868\u73fe\u304b\u3089\u6700\u521d\u306b\u901a\u5e38\u306e\u30d9\u30af\u30c8\u30eb\u3092\u8a08\u7b97\u3057\u307e\u3059 n\u2192= \uff08 y\u02d9\u3001 – x\u02d9\uff09\uff09 t {displaystyle {vec {n}} =\uff08{dot {y}}\u3001 – {dot {x}}\uff09^{t}} \u3002 \u63a5\u7dda\u306e\u65b9\u7a0b\u5f0f y\u02d9\uff08 \u30d5\u30a1\u30a4 \uff09\uff09 de \uff08 \u30d0\u30c4 – \u30d0\u30c4 \uff08 \u30d5\u30a1\u30a4 \uff09\uff09 \uff09\uff09 – x\u02d9\uff08 \u30d5\u30a1\u30a4 \uff09\uff09 de \uff08 \u3068 – \u3068 \uff08 \u30d5\u30a1\u30a4 \uff09\uff09 \uff09\uff09 = 0 {displaystyle {dot {dot {y}\uff08varphi\uff09cdot\uff08x-x\uff08varphi\uff09\uff09 – {dot {x}}\uff08varphi\uff09cdot\uff08y-y\uff08varphi\uff09\uff09= 0} \u305d\u306e\u5f8c\uff1a \uff08 cos \u2061 2 \u30d5\u30a1\u30a4 de \u30d0\u30c4 + \u7f6a \u2061 2 \u30d5\u30a1\u30a4 de \u3068 \uff09\uff09 cos \u2061 \u30d5\u30a1\u30a4 = 4 cos 2\u2061 \u30d5\u30a1\u30a4 \u3002 {displaystyle\uff08cos 2varphi cdot x + sin 2varphi cdot y\uff09cos varphi = 4cos ^{2} varphi\u3002} \u305f\u3081\u306b \u30d5\u30a1\u30a4 = \u03c02\u3001 3\u03c02{displaystyle varphi = {tfrac {pi} {2}}\u3001{tfrac {3pi} {2}}} \u30cd\u30d5\u30ed\u30a4\u30c9\u306b\u306f\u305d\u306e\u5148\u7aef\u304c\u3042\u308a\u3001\u305d\u3053\u3067\u306f\u63a5\u7dda\u304c\u3042\u308a\u307e\u305b\u3093\u3002\u305f\u3081\u306b \u30d5\u30a1\u30a4 \u2260 \u03c02\u3001 3\u03c02{displaystyle varphi neq {tfrac {pi} {2}}\u3001{tfrac {3pi} {2}}} \u901a\u308a\u629c\u3051\u3066\u3082\u3089\u3048\u307e\u3059\u304b cos \u2061 \u30d5\u30a1\u30a4 {displaystyle cos varphi} \u5206\u5272\u3057\u3066\u6700\u7d42\u7684\u306b\u53d7\u4fe1\u3057\u307e\u3059 cos \u2061 2 \u30d5\u30a1\u30a4 de \u30d0\u30c4 + \u7f6a \u2061 2 \u30d5\u30a1\u30a4 de \u3068 = 4 cos \u2061 \u30d5\u30a1\u30a4 \u3002 {displaystyle cos 2varphi cdot x+sin 2varphi cdot y = 4cos varphi\u3002} \u30bb\u30ab\u30f3\u30c8\u306e\u65b9\u7a0b\u5f0f \u4e2d\u5fc3\u306e\u3042\u308b\u5186\u306b \uff08 0 \u3001 0 \uff09\uff09 {displaystyle\uff080.0\uff09} \u305d\u3057\u3066\u534a\u5f84 4 {displaystyle 4} \uff1a2\u3064\u306e\u30dd\u30a4\u30f3\u30c8\u304b\u30892\u756a\u76ee\u306e\u65b9\u7a0b\u5f0f\u306e\u5834\u5408 \uff08 4 cos \u2061 th \u3001 4 \u7f6a \u2061 th \uff09\uff09 \u3001 \uff08 4 cos \u2061 3th \u3001 4 \u7f6a \u2061 3th \uff09\uff09 \uff09\uff09 {displaystyle\uff084cos theta\u30014sin theta\uff09\u3001\uff084cos {color {red} 3} theta\u30014sin {color {red} 3} theta\uff09\uff09} \u964d\u4f0f\uff1a \uff08 cos \u2061 2 th de \u30d0\u30c4 + \u7f6a \u2061 2 th de \u3068 \uff09\uff09 \u7f6a \u2061 th = 4 cos \u2061 th \u7f6a \u2061 th \u3002 {displaystyle\uff08cos 2theta cdot x+sin 2theta cdot y\uff09sin theta = 4cos theta sin theta\u3002} \u305f\u3081\u306b th = 0 \u3001 pi {displaystyletheta = 0\u3001pi} \u30bb\u30ab\u30f3\u30c8\u304c\u30dd\u30a4\u30f3\u30c8\u306e1\u3064\u3067\u3042\u308b\u5834\u5408\u3002\u305f\u3081\u306b th \u2260 0 pi {displaystyle theta neq 0pi} \u901a\u308a\u629c\u3051\u3066\u3082\u3089\u3048\u307e\u3059\u304b \u7f6a \u2061 th {displaystyle sin theta} \u5206\u5272\u3068sekant\u306e\u65b9\u7a0b\u5f0f\u306e\u7d50\u679c\uff1a cos \u2061 2 th de \u30d0\u30c4 + \u7f6a \u2061 2 th de \u3068 = 4 cos \u2061 th \u3002 {displaystyle cos 2theta cdot x+2theta cdot y = 4cos theta\u3002}} 2\u3064\u306e\u89d2\u5ea6 \u30d5\u30a1\u30a4 \u3001 th {displaystyle varphi\u3001theta} \u610f\u5473\u304c\u7570\u306a\u308a\u307e\u3059\uff08 \u30d5\u30a1\u30a4 {displaystyle varphi} \u30ed\u30fc\u30e9\u30fc\u89d2\u306e\u534a\u5206\u3001 th {displaystyletheta} \u30bb\u30ab\u30f3\u30bf\u30fc\u304c\u8a08\u7b97\u3055\u308c\u308b\u5186\u306e\u30d1\u30e9\u30e1\u30fc\u30bf\u30fc\u3067\u3059\uff09 \u30d5\u30a1\u30a4 = th {displaystyle varphi = theta} \u3057\u304b\u3057\u3001\u540c\u3058\u7d50\u679c\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u4e0a\u8a18\u306e\u5404\u79d2\u306f\u814e\u81d3\u306e\u63a5\u7dda\u3067\u3042\u308a\u3001 \u814e\u81d3\u306f\u5730\u533a\u8171\u306e\u5305\u307f\u8fbc\u307f\u3067\u3059\u3002 \u5186\u306e\u82db\u6027\u3068\u3057\u3066\u306e\u814e\u81d3\uff1a\u539f\u7406 \u534a\u5186\u306e\u82db\u6027\u3068\u3057\u3066\u306e\u814e\u81d3 \u4ee5\u524d\u306e\u8003\u616e\u4e8b\u9805\u306f\u3001\u814e\u81d3\u304c\u534a\u5186\u306eca\u7523\u696d\u3068\u3057\u3066\u767a\u751f\u3059\u308b\u3053\u3068\u306e\u8a3c\u62e0\u3082\u63d0\u4f9b\u3057\u307e\u3059\u3002 \u30ec\u30d9\u30eb\u306e\u56f3\u306b\u5f93\u3063\u3066\u5e73\u884c\u5149\u7dda\u304c\u53cd\u5c04\u7684\u306a\u534a\u5186\u306b\u843d\u3061\u305f\u5834\u5408\u3001\u53cd\u5c04\u5149\u7dda\u306f\u814e\u81d3\u306e\u63a5\u7dda\u3067\u3059\u3002 \uff08\u30bb\u30af\u30b7\u30e7\u30f3\u3092\u53c2\u7167\uff1a\u65e5\u5e38\u751f\u6d3b\u306b\u304a\u3051\u308b\u30cd\u30d5\u30ed\u30a4\u30c9\uff09 \u8a3c\u62e0 \u5186\uff08\u524d\u306e\u30bb\u30af\u30b7\u30e7\u30f3\u306e\u3088\u3046\u306b\uff09\u306e\u4e2d\u5fc3\u3068\u305d\u306e\u534a\u5f84\u306f\u30bc\u30ed\u30dd\u30a4\u30f3\u30c8\u304c\u3042\u308a\u307e\u3057\u305f 4 {displaystyle 4} \u3002\u305d\u306e\u5f8c\u3001\u5186\u306b\u306f\u30d1\u30e9\u30e1\u30fc\u30bf\u30fc\u30d7\u30ec\u30bc\u30f3\u30c6\u30fc\u30b7\u30e7\u30f3\u304c\u3042\u308a\u307e\u3059 k \uff08 \u30d5\u30a1\u30a4 \uff09\uff09 = 4 \uff08 cos \u2061 \u30d5\u30a1\u30a4 \u3001 \u7f6a \u2061 \u30d5\u30a1\u30a4 \uff09\uff09 \u3002 {displaystyle K\uff08varphi\uff09= 4\uff08cos varphi\u3001sin varphi\uff09\u3002} \u5186\u5f62\u30dd\u30a4\u30f3\u30c8\u306e\u63a5\u7dda k = k \uff08 \u30d5\u30a1\u30a4 \uff09\uff09 {displaystyle k = k\uff08varphi\uff09} \u901a\u5e38\u306e\u30d9\u30af\u30c8\u30eb\u304c\u3042\u308a\u307e\u3059 n\u2192t = \uff08 cos \u2061 \u30d5\u30a1\u30a4 \u3001 \u7f6a \u2061 \u30d5\u30a1\u30a4 \uff09\uff09 t {displaystyle {vec {n}} _ {t} =\uff08cos varphi\u3001sin varphi\uff09^{t}} \u3002\u53cd\u5c04\u30d3\u30fc\u30e0\u306f\uff08\u56f3\u306b\u5f93\u3063\u3066\uff09\u901a\u5e38\u306e\u30d9\u30af\u30c8\u30eb\u3067\u306a\u3051\u308c\u3070\u306a\u308a\u307e\u305b\u3093 n\u2192r = \uff08 cos \u2061 2 \u30d5\u30a1\u30a4 \u3001 \u7f6a \u2061 2 \u30d5\u30a1\u30a4 \uff09\uff09 t {displaystyle {vec {n}} _ {r} =\uff08cos {coler {red} 2} varphi\u3001sin {color {red} 2} varphi\uff09^{t}}} \u4e38\u3044\u30dd\u30a4\u30f3\u30c8\u3092\u4ecb\u3057\u3066 k \uff1a 4 \uff08 cos \u2061 \u30d5\u30a1\u30a4 \u3001 \u7f6a \u2061 \u30d5\u30a1\u30a4 \uff09\uff09 {displaystyle K\uff1a4\uff08cos varphi\u3001sin varphi\uff09} \u884c\u304f\u3002\u53cd\u5c04\u30d3\u30fc\u30e0\u306f\u65b9\u7a0b\u5f0f\u3068\u3068\u3082\u306b\u76f4\u7dda\u306b\u3042\u308a\u307e\u3059 cos \u2061 2\u30d5\u30a1\u30a4 de \u30d0\u30c4 + \u7f6a \u2061 2\u30d5\u30a1\u30a4 de \u3068 = 4 cos \u2061 \u30d5\u30a1\u30a4 \u3001 {displaystyle cos {color {red} 2} varphi cdot x + sin {color {red} 2} varphi cdot y = 4cos varphi\u3001} \u3053\u308c\u306f\u3001\u30dd\u30a4\u30f3\u30c8\u306e\u524d\u306e\u30bb\u30af\u30b7\u30e7\u30f3\u306e\u814e\u81d3\u306e\u63a5\u7dda\u3067\u3059 p \uff1a \uff08 3 cos \u2061 \u30d5\u30a1\u30a4 + cos \u2061 3 \u30d5\u30a1\u30a4 \u3001 3 \u7f6a \u2061 \u30d5\u30a1\u30a4 + \u7f6a \u2061 3 \u30d5\u30a1\u30a4 \uff09\uff09 {displaystyle P\uff1a\uff083COS varphi +cos 3varphi\u30013sin varphi +sin 3varphi\uff09} IS\uff08\u4e0a\u8a18\u53c2\u7167\uff09\u3002 nephroid\uff08\u8d64\uff09\u3068\u305d\u306e\u9032\u5316\uff08\u7dd1\uff09\u3001 \u30de\u30bc\u30f3\u30bf\uff1a\u30dd\u30a4\u30f3\u30c8P\u3001\u305d\u306e\u66f2\u7387\u4e2d\u5fc3M\u3001\u304a\u3088\u3073\u95a2\u9023\u3059\u308b\u66f2\u7387\u5186 \u5e73\u3089\u306a\u66f2\u7dda\u306e\u9032\u5316\u306f\u3001\u3053\u306e\u66f2\u7dda\u306e\u3059\u3079\u3066\u306e\u66f2\u7387\u70b9\u306e\u5e7e\u4f55\u5b66\u7684\u306a\u5834\u6240\u3067\u3059\u3002\u30d1\u30e9\u30e1\u30fc\u30bf\u30fc\u5316\u3055\u308c\u305f\u66f2\u7dda\u306e\u5834\u5408 x\u2192\uff08 s \uff09\uff09 = c\u2192\uff08 s \uff09\uff09 {displayStyle {thing {x}}\uff08s\uff09= {thing {c}}\uff08s\uff09} \u66f2\u7387\u534a\u5f84\u304c\u3042\u308a\u307e\u3059 r \uff08 s \uff09\uff09 {displaystyle rho\uff08s\uff09} Evolute\u306b\u306f\u30d1\u30e9\u30e1\u30fc\u30bf\u30fc\u30d7\u30ec\u30bc\u30f3\u30c6\u30fc\u30b7\u30e7\u30f3\u304c\u3042\u308a\u307e\u3059 X\u2192\uff08 s \uff09\uff09 = c\u2192\uff08 s \uff09\uff09 + r \uff08 s \uff09\uff09 n\u2192\uff08 s \uff09\uff09 \u3002 {displayStyle {thing {x}}\uff08s\uff09= {thing {c}}\uff08s\uff09+rho\uff08s\uff09{thing {n}}\u3002} \u3057\u305f\u304c\u3063\u3066 n\u2192\uff08 s \uff09\uff09 {displaystyle {vec {n}}\uff08s\uff09} \u9069\u5207\u306a\u30e6\u30cb\u30c3\u30c8\u306f\u6b63\u5e38\u3067\u3059\u3002 \uff08\uff08\uff09 n\u2192\uff08 s \uff09\uff09 {displaystyle {vec {n}}\uff08s\uff09} \u66f2\u7387\u306e\u200b\u200b\u5e73\u5747\u3092\u6307\u3057\u307e\u3059\u3002\uff09 \u4ee5\u4e0b\u306f\u3001\u5199\u771f\u306e\u814e\u81d3\u306b\u9069\u7528\u3055\u308c\u307e\u3059\u3002 \u9032\u5316\u3057\u307e\u3057\u305f \u30cd\u30d5\u30ed\u30a4\u30c9\u306f\u518d\u3073\u814e\u81d3\u3067\u3001\u534a\u5206\u306e\u5927\u304d\u3055\u3067\u3059\u3002 \u8a3c\u62e0 \u5199\u771f\u306e\u814e\u81d3\uff08\u30d2\u30f3\u30c8\u306fy\u8ef8\u4e0a\u306b\u3042\u308a\u307e\u3059\uff01\uff09\u306b\u306f\u30d1\u30e9\u30e1\u30fc\u30bf\u30fc\u8868\u73fe\u304c\u3042\u308a\u307e\u3059 \u30d0\u30c4 = 3 cos \u2061 \u30d5\u30a1\u30a4 + cos \u2061 3 \u30d5\u30a1\u30a4 \u3001 \u3068 = 3 \u7f6a \u2061 \u30d5\u30a1\u30a4 + \u7f6a \u2061 3 \u30d5\u30a1\u30a4 \u3001 {displaystyle x = 3cos varphi +cos 3varphi\u3001quad y = 3sin varphi +sin 3varphi\u3001} \u30e6\u30cb\u30c3\u30c8\u306f\u6b63\u5e38\u3067\u3059 n\u2192\uff08 \u30d5\u30a1\u30a4 \uff09\uff09 = \uff08 – cos \u2061 2 \u30d5\u30a1\u30a4 \u3001 – \u7f6a \u2061 2 \u30d5\u30a1\u30a4 \uff09\uff09 T{displaystyle {vec {n}}\uff08varphi\uff09=\uff08-cos 2varphi\u3001-sin 2varphi\uff09^{t}} \uff08\u4e0a\u8a18\u3092\u53c2\u7167\uff09 \u66f2\u7387\u306e\u200b\u200b\u534a\u5f84\u304c\u3042\u308a\u307e\u3059\uff08\u4e0a\u8a18\u53c2\u7167\uff09 r \uff08 \u30d5\u30a1\u30a4 \uff09\uff09 = 3 cos \u2061 \u30d5\u30a1\u30a4 {displaystyle rho\uff08varphi\uff09= 3cos varphi} \u3002 \u3057\u305f\u304c\u3063\u3066\u3001Evolute\u306b\u306f\u30d1\u30e9\u30e1\u30fc\u30bf\u30fc\u30d7\u30ec\u30bc\u30f3\u30c6\u30fc\u30b7\u30e7\u30f3\u304c\u3042\u308a\u307e\u3059 \u30d0\u30c4 = 3 cos \u2061 \u30d5\u30a1\u30a4 + cos \u2061 3 \u30d5\u30a1\u30a4 – 3 cos \u2061 \u30d5\u30a1\u30a4 de cos \u2061 2 \u30d5\u30a1\u30a4 = \u22ef = 3 cos \u2061 \u30d5\u30a1\u30a4 – 2 cos 3\u2061 \u30d5\u30a1\u30a4 \u3001 {displaystyle x = 3cos varphi +cos 3varphi -3cos varphi cdot cos 2varphi = cdots = 3cos varphi -2cos \u3068 = 3 \u7f6a \u2061 \u30d5\u30a1\u30a4 + \u7f6a \u2061 3 \u30d5\u30a1\u30a4 – 3 cos \u2061 \u30d5\u30a1\u30a4 de \u7f6a \u2061 2 \u30d5\u30a1\u30a4 = \u22ef = 2 \u7f6a 3\u2061 \u30d5\u30a1\u30a4 \u3001 {displaystyle y = 3sin varphi +sin 3varphi -3cos varphi cdot sin 2varphi = cdots = 2sin ^ ^ {3} varphi\u3001} \u3053\u308c\u3089\u306e\u65b9\u7a0b\u5f0f\u306f\u3001\u534a\u5206\u306e\u5927\u304d\u3055\u306790\u5ea6\u306b\u5909\u308f\u3063\u305f\u814e\u81d3\u3092\u8868\u3057\u3066\u3044\u307e\u3059\uff08\u5199\u771f\u3068\u30bb\u30af\u30b7\u30e7\u30f3\u3092\u53c2\u7167\u3057\u3066\u304f\u3060\u3055\u3044 \u814e\u81d3\u306e\u65b9\u7a0b\u5f0f \uff09\u3002 \u9752\u3044\u5186\u306e\u30cb\u30d5\u30ed\u30a4\u30c9\uff08\u8d64\uff09\u306e\u53cd\u8ee2\uff08\u7dd1\uff09 \u53cd\u5c04 \u30d0\u30c4 \u21a6 4a2xx2+y2\u3001 \u3068 \u21a6 4a2yx2+y2{displaystyle xmapsto {frac {4a^{2} x} {x^{2}+y^{2}}}\u3001quad ymapsto {frac {2} y} {x^{2}+y^{2}}}}}}}} \u4e2d\u5fc3\u306e\u3042\u308b\u5186\u3067 \uff08 0 \u3001 0 \uff09\uff09 {displaystyle\uff080.0\uff09} \u305d\u3057\u3066\u534a\u5f84 2 a {displaystyle 2a} \u65b9\u7a0b\u5f0f\u3067\u30cd\u30d5\u30ed\u30a4\u30c9\u3092\u5f62\u6210\u3057\u307e\u3059 \uff08 \u30d0\u30c4 2+ \u3068 2 – 4 a 2\uff09\uff09 3= 108 a 4\u3068 2{displaystyle\uff08x^{2}+y^{2} -4a^{2}\uff09^{3} = 108a^{4} y^{2}} \u65b9\u7a0b\u5f0f\u306e\u3042\u308b\u66f2\u7dda6\u5ea6 \uff08 4 a 2 – \uff08 \u30d0\u30c4 2+ \u3068 2\uff09\uff09 \uff09\uff09 3= 27 a 2\uff08 \u30d0\u30c4 2+ \u3068 2\uff09\uff09 \u3068 2{displaystyle\uff084a^{2} – \uff08x^{2}+y^{2}\uff09\uff09^{3} = 27a^{2}\uff08x^{2}+y^{2}\uff09y^{2}} from\uff08\u5199\u771f\u3092\u53c2\u7167\uff09\u3002 \u5149\u304c\u51f9\u72b6\u306e\u5186\u5f62\u53cd\u5c04\u8868\u9762\u306e\u5074\u9762\u306b\u3042\u308b\u7121\u9650\u306b\u9060\u3044\u5149\u6e90\u306e\u5074\u9762\u306b\u5149\u304c\u5f53\u3066\u3089\u308c\u305f\u5834\u5408\u3001\u5149\u7dda\u306e\u5305\u307f\u304c\u814e\u81d3\u306e\u4e00\u90e8\u3092\u5f62\u6210\u3057\u307e\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u300c\u30b3\u30fc\u30d2\u30fc\u30ab\u30c3\u30d7Caustic\u300d\uff08Kaustik = Fuel Line\uff09\u3068\u3082\u547c\u3070\u308c\u308b\u3053\u3068\u3082\u3042\u308a\u307e\u3059\u3002\u307e\u305f\u3001\u81ea\u8ee2\u8eca\u306e\u88f8\u306e\u7e01\u304c\u5e8a\u306e\u5149\u3092\u53cd\u6620\u3057\u3066\u3044\u308b\u3068\u304d\u306b\u8def\u4e0a\u3067\u305d\u308c\u3089\u3092\u898b\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u65e5\u5149\u304c\u81ea\u8ee2\u8eca\u306e\u30ea\u30e0\u306e\u30b7\u30ea\u30f3\u30c0\u30fc\u30b3\u30fc\u30c8\u306b\u4e26\u884c\u3057\u3066\u30d2\u30c3\u30c8\u3059\u308b\u305f\u3081\u3001\u30d2\u30e5\u30fc\u30ba\u306f\u534a\u5206\u30cd\u30d5\u30ed\u30a4\u30c9\u306e\u5f62\u72b6\u3092\u6301\u3064\u30d7\u30ed\u30d5\u30a1\u30a4\u30eb\u3092\u63cf\u3044\u3066\u304a\u308a\u3001\u30ec\u30d9\u30eb\u306e\u5730\u4e0b\u5f62\u72b6\u306e\u30cd\u30d5\u30ed\u30a4\u30c9\u306e\u4e00\u90e8\u3092\u30ab\u30c3\u30c8\u3059\u308b\u3088\u3046\u306b\u3057\u307e\u3059\u3002 \u2191 Kurt Meyberg\u3001Peter Vachenauer\uff1a \u3088\u308a\u9ad8\u3044\u6570\u5b661\u3002 Springs-Publising\u30011995\u3001ISBN 3-540-59188-5\u3001S\u30021948\u3001.. 194\u30012008\u3002 D.\u30a2\u30fc\u30ac\u30f3\u30d6\u30e9\u30a4\u30c8\uff1a \u30b9\u30d7\u30ec\u30c3\u30c9\u30b7\u30fc\u30c8\u66f2\u7dda\u3068\u5e7e\u4f55\u5b66\u7684\u69cb\u9020\u306e\u5b9f\u7528\u7684\u306a\u30cf\u30f3\u30c9\u30d6\u30c3\u30af\u3002 CRC Press\u30011993\u3001ISBN 0-8493-8938-0\u3001S\u300254\u3002 F. Borceux\uff1a \u30b8\u30aa\u30e1\u30c8\u30ea\u3078\u306e\u5fae\u5206\u30a2\u30d7\u30ed\u30fc\u30c1\uff1a\u5e7e\u4f55\u5b66\u7684\u4e09\u90e8\u4f5cIII\u3002 Springer\u30012014\u3001ISBN 978-3-319-01735-8\u3001S\u3002148\u3002 E. H.\u30ed\u30c3\u30af\u30a6\u30c3\u30c9\uff1a \u66f2\u7dda\u306e\u672c\u3002 \u30b1\u30f3\u30d6\u30ea\u30c3\u30b8\u5927\u5b66\u51fa\u7248\u5c40\u30011978\u5e74\u3001ISBN 0-521-05585-7\u3001S\u30027\u3002 (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\/20725#breadcrumbitem","name":"nephroid – \u30a6\u30a3\u30ad\u30da\u30c7\u30a3\u30a2"}}]}]