. . . . "\uCD95\uD3D0\uC120"@ko . "Na geometria diferencial de curvas, a evoluta de uma curva \u00E9 o lugar geom\u00E9trico de todos suas (centros de curvatura)."@pt . "D\u00E9velopp\u00E9e"@fr . . . . . "1098605472"^^ . . . "L'evoluta di una curva piana \u00E8 un'altra curva piana che si ottiene come luogo geometrico dei centri di curvatura di (ovvero i centri dei cerchi osculatori, che meglio approssimano la curva nei punti). Per esempio, l'evoluta di un cerchio \u00E8 il suo centro stesso. In questo modo viene detta involuta o evolvente di ."@it . . . "En g\u00E9om\u00E9trie, la d\u00E9velopp\u00E9e d'une courbe plane est le lieu de ses centres de courbure. On peut aussi la d\u00E9crire comme l'enveloppe de la famille des droites normales \u00E0 la courbe."@fr . . "Ewoluta"@pl . "En la diferenciala geometrio, evoluto de kurbo estas la de \u0109iuj \u011Diaj (centroj de kurbeco). Ekvivalente, \u011Di estas la de perpendikularoj al la fonta kurbo. La originala kurbo estas de \u011Dia evoluto."@eo . "Die Evolute einer ebenen Kurve ist \n* die Bahn, auf der sich der Mittelpunkt des Kr\u00FCmmungskreises bewegt, wenn der zugeh\u00F6rige Punkt die gegebene Kurve durchl\u00E4uft. Oder auch: \n* die H\u00FCllkurve (Enveloppe) der Normalen der gegebenen Kurve. Evoluten stehen in engem Zusammenhang mit den Evolventen einer gegebenen Kurve, denn es gilt: Eine Kurve ist die Evolute jeder ihrer Evolventen."@de . "Geometrian, \"K\" kurba baten eboluta beste kurba bat da, \"K\" kurbaren osatzen duten leku geometrikoa dena. Beste hitzez, eboluta kurbarekiko normalen da. Jatorrizko kurbari bilkari esaten zaio."@eu . "In the differential geometry of curves, the evolute of a curve is the locus of all its centers of curvature. That is to say that when the center of curvature of each point on a curve is drawn, the resultant shape will be the evolute of that curve. The evolute of a circle is therefore a single point at its center. Equivalently, an evolute is the envelope of the normals to a curve. Evolutes are closely connected to involutes: A curve is the evolute of any of its involutes."@en . . "\u042D\u0432\u043E\u043B\u044E\u0442\u0430"@ru . . . "En , l'evoluta d'una corba \u00E9s el lloc geom\u00E8tric de tots els seus centres de curvatura. O el que \u00E9s equivalent, \u00E9s la de les normals a una corba. La corba original \u00E9s una involuta de la seva evoluta. (Compareu i )"@ca . "\u6F38\u5C48\u7DDA\u662F\u66F2\u7DDA\u5FAE\u5206\u5E7E\u4F55\u4E2D\u7684\u6982\u5FF5\uFF0C\u5B83\u662F\u66F2\u7DDA\u4E0A\u5713\u5FC3\u7684\u8ECC\u8DE1\u3002\u7B49\u50F9\u7684\u63CF\u8FF0\u662F\u4E00\u689D\u66F2\u7DDA\u7684\u6F38\u5C48\u7DDA\u5373\u662F\u5176\u6CD5\u7DDA\u7684\u5305\u7D61\u3002 \u6F38\u5C48\u7DDA\u8207\u6F38\u4F38\u7DDA\u662F\u4E00\u5C0D\u76F8\u5C0D\u7684\u6982\u5FF5\uFF0C\u82E5\u66F2\u7DDAA\u662F\u66F2\u7DDAB\u7684\u6F38\u5C48\u7DDA\uFF0C\u66F2\u7DDAB\u5373\u70BA\u66F2\u7DDAA\u7684\u6F38\u4F38\u7DDA\u3002\u6BCF\u689D\u66F2\u7DDA\u7684\u6F38\u5C48\u7DDA\u552F\u4E00\u78BA\u5B9A\uFF0C\u4F46\u537B\u53EF\u4EE5\u6709\u7121\u7AAE\u591A\u689D\u6F38\u4F38\u7DDA\u3002"@zh . "Eboluta"@eu . . "\uCD95\uD3D0\uC120(evolute, \u7E2E\u9589\u7DDA) \uB610\uB294 \uC5D0\uBCFC\uB958\uD2B8, \uC5D0\uBCFC\uB958\uD2B8\uACE1\uC120(-\u66F2\u7DDA)\uC740 \uC5B4\uB5A4 \uACE1\uC120\uC758 \uAC01 \uC810\uC5D0 \uB300\uD55C \uC758 \uADA4\uC801\uC774 \uC774\uB8E8\uB294 \uB610 \uD558\uB098\uC758 \uACE1\uC120\uC774\uB2E4. \uBAA8\uB4E0 \uC810\uC5D0 \uB300\uD55C \uACE1\uB960 \uC911\uC2EC\uC744 \uCC3E\uC744 \uC218 \uC788\uB2E4\uBA74 \uACE1\uC120\uC758 \uC885\uB958\uB294 \uAD00\uACC4\uC5C6\uC774 \uD55C \uACE1\uC120\uC5D0\uC11C \uB2E4\uB978 \uACE1\uC120\uC744 \uC720\uB3C4\uD574\uB0B4\uB294 \uAC83\uC774\uBBC0\uB85C \uACE1\uC120\uC758 \uC758 \uC77C\uC885\uC774\uB2E4. \uC815\uC758\uC0C1, \uBAA8\uB4E0 \uC810\uC740 \uADF8 \uC810\uC744 \uC911\uC2EC\uC73C\uB85C \uD558\uB294 \uC784\uC758\uC758 \uC6D0\uC758 \uCD95\uD3D0\uC120\uC774\uB2E4. \uC2E0\uAC1C\uC120\uACFC\uB294 \uC30D\uB300\uC801\uC778 \uAD00\uACC4\uC5D0 \uC788\uB2E4. \uC989, \uACE1\uC120 A\uAC00 B\uC758 \uC2E0\uAC1C\uC120\uC774\uB77C\uBA74, \uC815\uC758\uC0C1 \uACE1\uC120 B\uB294 A\uC758 \uCD95\uD3D0\uC120\uC774\uB2E4."@ko . . "Evoluta"@it . "Evolute"@de . . . . . "Geometrian, \"K\" kurba baten eboluta beste kurba bat da, \"K\" kurbaren osatzen duten leku geometrikoa dena. Beste hitzez, eboluta kurbarekiko normalen da. Jatorrizko kurbari bilkari esaten zaio."@eu . . "Evoluta"@es . . . . "Evolute"@en . . . . . . . . . "\u6570\u5B66\u3001\u7279\u306B\u306B\u304A\u3051\u308B\u7E2E\u9589\u7DDA\uFF08\u3057\u3085\u304F\u3078\u3044\u305B\u3093\u3001\u82F1: evolute\uFF09\u3068\u306F\u3001\u66F2\u7DDA\u306E\u5404\u70B9\u306B\u304A\u3051\u308B\u306E\u8ECC\u8DE1\u3068\u3057\u3066\u5F97\u3089\u308C\u308B\u5225\u306E\u66F2\u7DDA\u3092\u3044\u3046\u3002\u66F2\u7DDA\u306E\u6CD5\u7DDA\u306E\u5305\u7D61\u7DDA\u3092\u7E2E\u9589\u7DDA\u3068\u547C\u3076\u3068\u3044\u3063\u3066\u3082\u540C\u3058\u3053\u3068\u3067\u3042\u308B\u3002 \u66F2\u7DDA\u3001\u66F2\u9762\u3001\u3042\u308B\u3044\u306F\u3082\u3063\u3068\u4E00\u822C\u306B\uFF08Rn \u306E\uFF09\u90E8\u5206\u591A\u69D8\u4F53\u306E\u7E2E\u9589\u3068\u306F\u3001\u305D\u306E\u6CD5\u5199\u50CF\u306E\uFF08\u5305\u7D61\u7DDA\uFF09\u3092\u3044\u3046\u3002\u5177\u4F53\u7684\u306B\u3001M \u3092\u6ED1\u3089\u304B\u3067\u975E\u7279\u7570\u306A Rn \u306E\u90E8\u5206\u591A\u69D8\u4F53\u3068\u3057\u3001M \u306E\u5404\u70B9 p \u3068 p \u3092\u57FA\u70B9\u3068\u3057\u3066 M \u306B\u76F4\u4EA4\u3059\u308B\u5404\u30D9\u30AF\u30C8\u30EB v \u306B\u5BFE\u3057\u3066\u3001\u70B9 p + v \u3092\u5BFE\u5FDC\u3055\u305B\u308B\u3068\u3001\u3053\u308C\u306F\u6CD5\u5199\u50CF\u3068\u547C\u3070\u308C\u308B\u3092\u5B9A\u3081\u308B\u3002\u6CD5\u5199\u50CF\u306E\u7126\u7DDA\u306F M \u306E\u7E2E\u9589\u3067\u3042\u308B\u3002"@ja . . . . . "\u0645\u0646\u0634\u0626 \u0627\u0644\u0645\u0646\u062D\u0646\u0649 \u0623\u0648 \u0645\u0637\u0648\u0631 \u0627\u0644\u0645\u0646\u062D\u0646\u0649 (\u0628\u0627\u0644\u0625\u0646\u062C\u0644\u064A\u0632\u064A\u0629: evolute)\u200F \u0647\u0648 \u0627\u0644\u0645\u062D\u0644 \u0627\u0644\u0647\u0646\u062F\u0633\u064A \u0644\u0645\u0631\u0627\u0643\u0632 \u0627\u0646\u062D\u0646\u0627\u0621 \u0645\u0646\u062D\u0646\u0649 \u0622\u062E\u0631\u060C \u0648\u064A\u0639\u0631\u0641 \u0627\u0644\u0623\u062E\u064A\u0631 \u0623\u0648 \u0627\u0644\u0625\u0646\u0641\u0648\u0644\u064A\u0648\u062A involute\u060C \u0643\u0645\u0627 \u064A\u0639\u0631\u0641 \u0623\u064A\u0636\u064B\u0627 \u0645\u0646\u0634\u0626 \u0627\u0644\u0645\u0646\u062D\u0646\u0649 \u0628\u0623\u0646\u0647 \u0645\u0646 \u0627\u0644\u062E\u0637\u0648\u0637 \u0627\u0644\u0645\u0633\u062A\u0642\u064A\u0645\u0629 \u0627\u0644\u0645\u062A\u0639\u0627\u0645\u062F\u0629 \u0639\u0644\u0649 \u0645\u0646\u062D\u0646\u0649. \u0627\u0644\u0645\u0646\u062D\u0646\u0649 \u0627\u0644\u0623\u0635\u0644\u064A \u0647\u0648 \u0623\u062D\u062F \u0644\u0645\u0646\u0634\u0626 \u0645\u0646\u062D\u0646\u0627\u0647."@ar . "10085"^^ . . . . "\u0645\u0646\u0634\u0626 \u0627\u0644\u0645\u0646\u062D\u0646\u0649"@ar . "In de vlakke meetkunde noemt men de evolute van een gladde kromme, de meetkundige plaats (verzameling) van alle plaatselijke krommingsmiddelpunten van die kromme. Als een gladde kromme is met kromtestraal overal verschillend van 0 en oneindig, en is de evolute van , dan is een evolvente van . Omgekeerd geldt dat de evolute van een evolvente, weer de oorspronkelijke kromme is."@nl . "\uCD95\uD3D0\uC120(evolute, \u7E2E\u9589\u7DDA) \uB610\uB294 \uC5D0\uBCFC\uB958\uD2B8, \uC5D0\uBCFC\uB958\uD2B8\uACE1\uC120(-\u66F2\u7DDA)\uC740 \uC5B4\uB5A4 \uACE1\uC120\uC758 \uAC01 \uC810\uC5D0 \uB300\uD55C \uC758 \uADA4\uC801\uC774 \uC774\uB8E8\uB294 \uB610 \uD558\uB098\uC758 \uACE1\uC120\uC774\uB2E4. \uBAA8\uB4E0 \uC810\uC5D0 \uB300\uD55C \uACE1\uB960 \uC911\uC2EC\uC744 \uCC3E\uC744 \uC218 \uC788\uB2E4\uBA74 \uACE1\uC120\uC758 \uC885\uB958\uB294 \uAD00\uACC4\uC5C6\uC774 \uD55C \uACE1\uC120\uC5D0\uC11C \uB2E4\uB978 \uACE1\uC120\uC744 \uC720\uB3C4\uD574\uB0B4\uB294 \uAC83\uC774\uBBC0\uB85C \uACE1\uC120\uC758 \uC758 \uC77C\uC885\uC774\uB2E4. \uC815\uC758\uC0C1, \uBAA8\uB4E0 \uC810\uC740 \uADF8 \uC810\uC744 \uC911\uC2EC\uC73C\uB85C \uD558\uB294 \uC784\uC758\uC758 \uC6D0\uC758 \uCD95\uD3D0\uC120\uC774\uB2E4. \uC2E0\uAC1C\uC120\uACFC\uB294 \uC30D\uB300\uC801\uC778 \uAD00\uACC4\uC5D0 \uC788\uB2E4. \uC989, \uACE1\uC120 A\uAC00 B\uC758 \uC2E0\uAC1C\uC120\uC774\uB77C\uBA74, \uC815\uC758\uC0C1 \uACE1\uC120 B\uB294 A\uC758 \uCD95\uD3D0\uC120\uC774\uB2E4."@ko . "In the differential geometry of curves, the evolute of a curve is the locus of all its centers of curvature. That is to say that when the center of curvature of each point on a curve is drawn, the resultant shape will be the evolute of that curve. The evolute of a circle is therefore a single point at its center. Equivalently, an evolute is the envelope of the normals to a curve. The evolute of a curve, a surface, or more generally a submanifold, is the caustic of the normal map. Let M be a smooth, regular submanifold in Rn. For each point p in M and each vector v, based at p and normal to M, we associate the point p + v. This defines a Lagrangian map, called the normal map. The caustic of the normal map is the evolute of M. Evolutes are closely connected to involutes: A curve is the evolute of any of its involutes."@en . "In de vlakke meetkunde noemt men de evolute van een gladde kromme, de meetkundige plaats (verzameling) van alle plaatselijke krommingsmiddelpunten van die kromme. Als een gladde kromme is met kromtestraal overal verschillend van 0 en oneindig, en is de evolute van , dan is een evolvente van . Omgekeerd geldt dat de evolute van een evolvente, weer de oorspronkelijke kromme is."@nl . "Se llama evoluta de una curva \"C\" dada, al lugar geom\u00E9trico de los centros de curvatura de \"C\"."@es . "Sokolov"@en . . . . "\u0415\u0432\u043E\u043B\u044E\u0442\u0430"@uk . "Evolute"@nl . "L'evoluta di una curva piana \u00E8 un'altra curva piana che si ottiene come luogo geometrico dei centri di curvatura di (ovvero i centri dei cerchi osculatori, che meglio approssimano la curva nei punti). Per esempio, l'evoluta di un cerchio \u00E8 il suo centro stesso. In questo modo viene detta involuta o evolvente di ."@it . . . . "En g\u00E9om\u00E9trie, la d\u00E9velopp\u00E9e d'une courbe plane est le lieu de ses centres de courbure. On peut aussi la d\u00E9crire comme l'enveloppe de la famille des droites normales \u00E0 la courbe."@fr . . . . . . . . . "\u0645\u0646\u0634\u0626 \u0627\u0644\u0645\u0646\u062D\u0646\u0649 \u0623\u0648 \u0645\u0637\u0648\u0631 \u0627\u0644\u0645\u0646\u062D\u0646\u0649 (\u0628\u0627\u0644\u0625\u0646\u062C\u0644\u064A\u0632\u064A\u0629: evolute)\u200F \u0647\u0648 \u0627\u0644\u0645\u062D\u0644 \u0627\u0644\u0647\u0646\u062F\u0633\u064A \u0644\u0645\u0631\u0627\u0643\u0632 \u0627\u0646\u062D\u0646\u0627\u0621 \u0645\u0646\u062D\u0646\u0649 \u0622\u062E\u0631\u060C \u0648\u064A\u0639\u0631\u0641 \u0627\u0644\u0623\u062E\u064A\u0631 \u0623\u0648 \u0627\u0644\u0625\u0646\u0641\u0648\u0644\u064A\u0648\u062A involute\u060C \u0643\u0645\u0627 \u064A\u0639\u0631\u0641 \u0623\u064A\u0636\u064B\u0627 \u0645\u0646\u0634\u0626 \u0627\u0644\u0645\u0646\u062D\u0646\u0649 \u0628\u0623\u0646\u0647 \u0645\u0646 \u0627\u0644\u062E\u0637\u0648\u0637 \u0627\u0644\u0645\u0633\u062A\u0642\u064A\u0645\u0629 \u0627\u0644\u0645\u062A\u0639\u0627\u0645\u062F\u0629 \u0639\u0644\u0649 \u0645\u0646\u062D\u0646\u0649. \u0627\u0644\u0645\u0646\u062D\u0646\u0649 \u0627\u0644\u0623\u0635\u0644\u064A \u0647\u0648 \u0623\u062D\u062F \u0644\u0645\u0646\u0634\u0626 \u0645\u0646\u062D\u0646\u0627\u0647."@ar . "\u042D\u0432\u043E\u043B\u044E\u0301\u0442\u0430 \u043F\u043B\u043E\u0441\u043A\u043E\u0439 \u043A\u0440\u0438\u0432\u043E\u0439 \u2014 \u0433\u0435\u043E\u043C\u0435\u0442\u0440\u0438\u0447\u0435\u0441\u043A\u043E\u0435 \u043C\u0435\u0441\u0442\u043E \u0442\u043E\u0447\u0435\u043A, \u044F\u0432\u043B\u044F\u044E\u0449\u0438\u0445\u0441\u044F \u0446\u0435\u043D\u0442\u0440\u0430\u043C\u0438 \u043A\u0440\u0438\u0432\u0438\u0437\u043D\u044B \u043A\u0440\u0438\u0432\u043E\u0439. \u041F\u043E \u043E\u0442\u043D\u043E\u0448\u0435\u043D\u0438\u044E \u043A \u0441\u0432\u043E\u0435\u0439 \u044D\u0432\u043E\u043B\u044E\u0442\u0435 \u043B\u044E\u0431\u0430\u044F \u043A\u0440\u0438\u0432\u0430\u044F \u044F\u0432\u043B\u044F\u0435\u0442\u0441\u044F \u044D\u0432\u043E\u043B\u044C\u0432\u0435\u043D\u0442\u043E\u0439."@ru . . . "Evoluta"@ca . "D.D."@en . . . . . . . . "\u6F38\u5C48\u7DDA\u662F\u66F2\u7DDA\u5FAE\u5206\u5E7E\u4F55\u4E2D\u7684\u6982\u5FF5\uFF0C\u5B83\u662F\u66F2\u7DDA\u4E0A\u5713\u5FC3\u7684\u8ECC\u8DE1\u3002\u7B49\u50F9\u7684\u63CF\u8FF0\u662F\u4E00\u689D\u66F2\u7DDA\u7684\u6F38\u5C48\u7DDA\u5373\u662F\u5176\u6CD5\u7DDA\u7684\u5305\u7D61\u3002 \u6F38\u5C48\u7DDA\u8207\u6F38\u4F38\u7DDA\u662F\u4E00\u5C0D\u76F8\u5C0D\u7684\u6982\u5FF5\uFF0C\u82E5\u66F2\u7DDAA\u662F\u66F2\u7DDAB\u7684\u6F38\u5C48\u7DDA\uFF0C\u66F2\u7DDAB\u5373\u70BA\u66F2\u7DDAA\u7684\u6F38\u4F38\u7DDA\u3002\u6BCF\u689D\u66F2\u7DDA\u7684\u6F38\u5C48\u7DDA\u552F\u4E00\u78BA\u5B9A\uFF0C\u4F46\u537B\u53EF\u4EE5\u6709\u7121\u7AAE\u591A\u689D\u6F38\u4F38\u7DDA\u3002"@zh . "E/e036670"@en . "Die Evolute einer ebenen Kurve ist \n* die Bahn, auf der sich der Mittelpunkt des Kr\u00FCmmungskreises bewegt, wenn der zugeh\u00F6rige Punkt die gegebene Kurve durchl\u00E4uft. Oder auch: \n* die H\u00FCllkurve (Enveloppe) der Normalen der gegebenen Kurve. Evoluten stehen in engem Zusammenhang mit den Evolventen einer gegebenen Kurve, denn es gilt: Eine Kurve ist die Evolute jeder ihrer Evolventen."@de . "Se llama evoluta de una curva \"C\" dada, al lugar geom\u00E9trico de los centros de curvatura de \"C\"."@es . . . . "\u0415\u0432\u043E\u043B\u044E\u0442\u0430 (\u043B\u0430\u0442. evolutus \u2014 \u0440\u043E\u0437\u0433\u043E\u0440\u043D\u0443\u0442\u0438\u0439) \u2014 \u043C\u043D\u043E\u0436\u0438\u043D\u0430 \u0442\u043E\u0447\u043E\u043A \u0446\u0435\u043D\u0442\u0440\u0456\u0432 \u043A\u0440\u0438\u0432\u0438\u0437\u043D\u0438 \u043A\u0440\u0438\u0432\u043E\u0457. \u041F\u043E \u0432\u0456\u0434\u043D\u043E\u0448\u0435\u043D\u043D\u044E \u0434\u043E \u0441\u0432\u043E\u0454\u0457 \u0435\u0432\u043E\u043B\u044E\u0442\u0438 \u0431\u0443\u0434\u044C-\u044F\u043A\u0430 \u043A\u0440\u0438\u0432\u0430 \u0454 \u0435\u0432\u043E\u043B\u044C\u0432\u0435\u043D\u0442\u043E\u044E. \u0414\u043B\u044F \u043F\u043E\u0431\u0443\u0434\u043E\u0432\u0438 \u0435\u0432\u043E\u043B\u044E\u0442\u0438 \u043A\u0440\u0438\u0432\u043E\u0457, \u043A\u0440\u0438\u0432\u0430 \u0432 \u043E\u043A\u043E\u043B\u0456 \u043A\u043E\u0436\u043D\u043E\u0457 \u0442\u043E\u0447\u043A\u0438 \u0430\u043F\u0440\u043E\u043A\u0441\u0438\u043C\u0443\u0454\u0442\u044C\u0441\u044F \u0447\u0430\u0441\u0442\u0438\u043D\u043E\u044E \u043A\u043E\u043B\u0430, \u0434\u043E\u0442\u0438\u0447\u043D\u043E\u0433\u043E \u0434\u043E \u043A\u0440\u0438\u0432\u043E\u0457. \u0426\u0435\u043D\u0442\u0440\u0438 \u0442\u0430\u043A\u0438\u0445 \u043A\u0456\u043B \u0456 \u0443\u0442\u0432\u043E\u0440\u044E\u044E\u0442\u044C \u0435\u0432\u043E\u043B\u044E\u0442\u0443. \u0415\u0432\u043E\u043B\u044E\u0442\u0430 \u0454 \u043E\u0431\u0432\u0456\u0434\u043D\u043E\u044E \u0441\u0456\u043C\u0435\u0439\u0441\u0442\u0432\u0430 \u0457\u0457 \u043D\u043E\u0440\u043C\u0430\u043B\u0435\u0439. \u041F\u043E\u043D\u044F\u0442\u0442\u044F \u0435\u0432\u043E\u043B\u044E\u0442\u0438 \u0456 \u0442\u0435\u0440\u043C\u0456\u043D \u0432\u0432\u0435\u0434\u0435\u043D\u0456 \u0425. \u0413\u044E\u0439\u0433\u0435\u043D\u0441\u043E\u043C (1673)."@uk . "Na geometria diferencial de curvas, a evoluta de uma curva \u00E9 o lugar geom\u00E9trico de todos suas (centros de curvatura)."@pt . . "Ewoluta (\u0142ac. evolutus, rozwini\u0119ty) albo rozwini\u0119ta krzywej \u2013 krzywa utworzona ze \u015Brodk\u00F3w krzywizny krzywej . Ka\u017Cda krzywa jest ewolut\u0105 swojej ewolwenty. Je\u015Bli krzywa jest ewolut\u0105 danej krzywej to jej styczne s\u0105 normalnymi do krzywej Przyk\u0142ady \n* ewolut\u0105 traktrysy jest krzywa \u0142a\u0144cuchowa, \n* ewolut\u0105 cykloidy jest cykloida."@pl . . "\u042D\u0432\u043E\u043B\u044E\u0301\u0442\u0430 \u043F\u043B\u043E\u0441\u043A\u043E\u0439 \u043A\u0440\u0438\u0432\u043E\u0439 \u2014 \u0433\u0435\u043E\u043C\u0435\u0442\u0440\u0438\u0447\u0435\u0441\u043A\u043E\u0435 \u043C\u0435\u0441\u0442\u043E \u0442\u043E\u0447\u0435\u043A, \u044F\u0432\u043B\u044F\u044E\u0449\u0438\u0445\u0441\u044F \u0446\u0435\u043D\u0442\u0440\u0430\u043C\u0438 \u043A\u0440\u0438\u0432\u0438\u0437\u043D\u044B \u043A\u0440\u0438\u0432\u043E\u0439. \u041F\u043E \u043E\u0442\u043D\u043E\u0448\u0435\u043D\u0438\u044E \u043A \u0441\u0432\u043E\u0435\u0439 \u044D\u0432\u043E\u043B\u044E\u0442\u0435 \u043B\u044E\u0431\u0430\u044F \u043A\u0440\u0438\u0432\u0430\u044F \u044F\u0432\u043B\u044F\u0435\u0442\u0441\u044F \u044D\u0432\u043E\u043B\u044C\u0432\u0435\u043D\u0442\u043E\u0439."@ru . . "Evolute"@en . . . "Ewoluta (\u0142ac. evolutus, rozwini\u0119ty) albo rozwini\u0119ta krzywej \u2013 krzywa utworzona ze \u015Brodk\u00F3w krzywizny krzywej . Ka\u017Cda krzywa jest ewolut\u0105 swojej ewolwenty. Je\u015Bli krzywa jest ewolut\u0105 danej krzywej to jej styczne s\u0105 normalnymi do krzywej Przyk\u0142ady \n* ewolut\u0105 traktrysy jest krzywa \u0142a\u0144cuchowa, \n* ewolut\u0105 cykloidy jest cykloida."@pl . "\u6E10\u5C48\u7EBF"@zh . "En la diferenciala geometrio, evoluto de kurbo estas la de \u0109iuj \u011Diaj (centroj de kurbeco). Ekvivalente, \u011Di estas la de perpendikularoj al la fonta kurbo. La originala kurbo estas de \u011Dia evoluto."@eo . . . . . . . "\u7E2E\u9589\u7DDA"@ja . "Evolute"@en . . . . . "Evoluto"@eo . "\u6570\u5B66\u3001\u7279\u306B\u306B\u304A\u3051\u308B\u7E2E\u9589\u7DDA\uFF08\u3057\u3085\u304F\u3078\u3044\u305B\u3093\u3001\u82F1: evolute\uFF09\u3068\u306F\u3001\u66F2\u7DDA\u306E\u5404\u70B9\u306B\u304A\u3051\u308B\u306E\u8ECC\u8DE1\u3068\u3057\u3066\u5F97\u3089\u308C\u308B\u5225\u306E\u66F2\u7DDA\u3092\u3044\u3046\u3002\u66F2\u7DDA\u306E\u6CD5\u7DDA\u306E\u5305\u7D61\u7DDA\u3092\u7E2E\u9589\u7DDA\u3068\u547C\u3076\u3068\u3044\u3063\u3066\u3082\u540C\u3058\u3053\u3068\u3067\u3042\u308B\u3002 \u66F2\u7DDA\u3001\u66F2\u9762\u3001\u3042\u308B\u3044\u306F\u3082\u3063\u3068\u4E00\u822C\u306B\uFF08Rn \u306E\uFF09\u90E8\u5206\u591A\u69D8\u4F53\u306E\u7E2E\u9589\u3068\u306F\u3001\u305D\u306E\u6CD5\u5199\u50CF\u306E\uFF08\u5305\u7D61\u7DDA\uFF09\u3092\u3044\u3046\u3002\u5177\u4F53\u7684\u306B\u3001M \u3092\u6ED1\u3089\u304B\u3067\u975E\u7279\u7570\u306A Rn \u306E\u90E8\u5206\u591A\u69D8\u4F53\u3068\u3057\u3001M \u306E\u5404\u70B9 p \u3068 p \u3092\u57FA\u70B9\u3068\u3057\u3066 M \u306B\u76F4\u4EA4\u3059\u308B\u5404\u30D9\u30AF\u30C8\u30EB v \u306B\u5BFE\u3057\u3066\u3001\u70B9 p + v \u3092\u5BFE\u5FDC\u3055\u305B\u308B\u3068\u3001\u3053\u308C\u306F\u6CD5\u5199\u50CF\u3068\u547C\u3070\u308C\u308B\u3092\u5B9A\u3081\u308B\u3002\u6CD5\u5199\u50CF\u306E\u7126\u7DDA\u306F M \u306E\u7E2E\u9589\u3067\u3042\u308B\u3002"@ja . . . "En , l'evoluta d'una corba \u00E9s el lloc geom\u00E8tric de tots els seus centres de curvatura. O el que \u00E9s equivalent, \u00E9s la de les normals a una corba. La corba original \u00E9s una involuta de la seva evoluta. (Compareu i )"@ca . . . . "\u0415\u0432\u043E\u043B\u044E\u0442\u0430 (\u043B\u0430\u0442. evolutus \u2014 \u0440\u043E\u0437\u0433\u043E\u0440\u043D\u0443\u0442\u0438\u0439) \u2014 \u043C\u043D\u043E\u0436\u0438\u043D\u0430 \u0442\u043E\u0447\u043E\u043A \u0446\u0435\u043D\u0442\u0440\u0456\u0432 \u043A\u0440\u0438\u0432\u0438\u0437\u043D\u0438 \u043A\u0440\u0438\u0432\u043E\u0457. \u041F\u043E \u0432\u0456\u0434\u043D\u043E\u0448\u0435\u043D\u043D\u044E \u0434\u043E \u0441\u0432\u043E\u0454\u0457 \u0435\u0432\u043E\u043B\u044E\u0442\u0438 \u0431\u0443\u0434\u044C-\u044F\u043A\u0430 \u043A\u0440\u0438\u0432\u0430 \u0454 \u0435\u0432\u043E\u043B\u044C\u0432\u0435\u043D\u0442\u043E\u044E. \u0414\u043B\u044F \u043F\u043E\u0431\u0443\u0434\u043E\u0432\u0438 \u0435\u0432\u043E\u043B\u044E\u0442\u0438 \u043A\u0440\u0438\u0432\u043E\u0457, \u043A\u0440\u0438\u0432\u0430 \u0432 \u043E\u043A\u043E\u043B\u0456 \u043A\u043E\u0436\u043D\u043E\u0457 \u0442\u043E\u0447\u043A\u0438 \u0430\u043F\u0440\u043E\u043A\u0441\u0438\u043C\u0443\u0454\u0442\u044C\u0441\u044F \u0447\u0430\u0441\u0442\u0438\u043D\u043E\u044E \u043A\u043E\u043B\u0430, \u0434\u043E\u0442\u0438\u0447\u043D\u043E\u0433\u043E \u0434\u043E \u043A\u0440\u0438\u0432\u043E\u0457. \u0426\u0435\u043D\u0442\u0440\u0438 \u0442\u0430\u043A\u0438\u0445 \u043A\u0456\u043B \u0456 \u0443\u0442\u0432\u043E\u0440\u044E\u044E\u0442\u044C \u0435\u0432\u043E\u043B\u044E\u0442\u0443. \u0415\u0432\u043E\u043B\u044E\u0442\u0430 \u0454 \u043E\u0431\u0432\u0456\u0434\u043D\u043E\u044E \u0441\u0456\u043C\u0435\u0439\u0441\u0442\u0432\u0430 \u0457\u0457 \u043D\u043E\u0440\u043C\u0430\u043B\u0435\u0439. \u041F\u043E\u043D\u044F\u0442\u0442\u044F \u0435\u0432\u043E\u043B\u044E\u0442\u0438 \u0456 \u0442\u0435\u0440\u043C\u0456\u043D \u0432\u0432\u0435\u0434\u0435\u043D\u0456 \u0425. \u0413\u044E\u0439\u0433\u0435\u043D\u0441\u043E\u043C (1673)."@uk . . . "Evoluta"@pt . "842387"^^ . . . . . . . .