. "In mathematical study of the differential geometry of curves, the total curvature of an immersed plane curve is the integral of curvature along a curve taken with respect to arc length: The total curvature of a closed curve is always an integer multiple of 2\u03C0, called the index of the curve, or turning number \u2013 it is the winding number of the unit tangent vector about the origin, or equivalently the degree of the map to the unit circle assigning to each point of the curve, the unit velocity vector at that point. This map is similar to the Gauss map for surfaces."@en . . . "4600"^^ . . . . "\u0412\u0430\u0440\u0456\u0430\u0446\u0456\u044F \u043F\u043E\u0432\u043E\u0440\u043E\u0442\u0443 \u043A\u0440\u0438\u0432\u043E\u0457"@uk . "\u5728\u6570\u5B66\u4E2D\u7684\u66F2\u7EBF\u5FAE\u5206\u51E0\u4F55\u7684\u7814\u7A76\u4E2D\uFF0C\u4E00\u4E2A\u6D78\u5165\u5728\u5E73\u9762\u4E0A\u7684\u66F2\u7EBF\u7684\u603B\u66F2\u7387\u662F\u66F2\u7387\u7684\u66F2\u7EBF\u79EF\u5206\uFF1A \u95ED\u66F2\u7EBF\u7684\u603B\u66F2\u7387\u662F 2\u03C0 \u7684\u6574\u6570\u500D\uFF0C\u8BE5\u6574\u6570\u79F0\u4E3A\u66F2\u7EBF\u7684\u6307\u6570\u6216\u8F6C\u6570\u3002\u5176\u4E2D\u8F6C\u6570\u662F\u5355\u4F4D\u5207\u5411\u91CF\u5173\u4E8E\u8D77\u70B9\u7684\u7ED5\u6570\uFF0C\u6216\u8005\u7B49\u4EF7\u7684\u9AD8\u65AF\u6620\u5C04\u7684\u6B21\u6570\u3002\u5C40\u90E8\u4E0D\u53D8\u91CF\u66F2\u7387\u548C\u6574\u4F53\u62D3\u6251\u4E0D\u53D8\u91CF\u6307\u6570\u7684\u5173\u7CFB\u662F\u9AD8\u7EF4\u9ECE\u66FC\u51E0\u4F55\u7684\u4EE3\u8868\u6027\u7ED3\u679C\uFF0C\u5982\u9AD8\u65AF\uFF0D\u535A\u5167\u5B9A\u7406\u3002"@zh . . . "\u0412\u0430\u0440\u0456\u0430\u0446\u0456\u044F \u043F\u043E\u0432\u043E\u0440\u043E\u0442\u0443 \u043A\u0440\u0438\u0432\u043E\u0457 \u2014 \u0456\u043D\u0442\u0435\u0433\u0440\u0430\u043B \u043A\u0440\u0438\u0432\u0438\u043D\u0438 \u043A\u0440\u0438\u0432\u043E\u0457 \u0437\u0430 \u0457\u0457 \u0434\u043E\u0432\u0436\u0438\u043D\u043E\u044E."@uk . . "Total curvature"@en . . . . . . . . . "1117702739"^^ . . . . . . . . . "Totalkr\u00FCmmung"@de . . . . . . . . . . . . . "19172363"^^ . . . . "In der Kurventheorie, einem Teilgebiet der Mathematik, wird die Totalkr\u00FCmmung einer Kurve definiert als das Integral ihrer Kr\u00FCmmung , also als ."@de . "\u0412\u0430\u0440\u0456\u0430\u0446\u0456\u044F \u043F\u043E\u0432\u043E\u0440\u043E\u0442\u0443 \u043A\u0440\u0438\u0432\u043E\u0457 \u2014 \u0456\u043D\u0442\u0435\u0433\u0440\u0430\u043B \u043A\u0440\u0438\u0432\u0438\u043D\u0438 \u043A\u0440\u0438\u0432\u043E\u0457 \u0437\u0430 \u0457\u0457 \u0434\u043E\u0432\u0436\u0438\u043D\u043E\u044E."@uk . . . . . . . "In mathematical study of the differential geometry of curves, the total curvature of an immersed plane curve is the integral of curvature along a curve taken with respect to arc length: The total curvature of a closed curve is always an integer multiple of 2\u03C0, called the index of the curve, or turning number \u2013 it is the winding number of the unit tangent vector about the origin, or equivalently the degree of the map to the unit circle assigning to each point of the curve, the unit velocity vector at that point. This map is similar to the Gauss map for surfaces."@en . . . "\u603B\u66F2\u7387"@zh . . . . . . "In der Kurventheorie, einem Teilgebiet der Mathematik, wird die Totalkr\u00FCmmung einer Kurve definiert als das Integral ihrer Kr\u00FCmmung , also als ."@de . . . . . "\u5728\u6570\u5B66\u4E2D\u7684\u66F2\u7EBF\u5FAE\u5206\u51E0\u4F55\u7684\u7814\u7A76\u4E2D\uFF0C\u4E00\u4E2A\u6D78\u5165\u5728\u5E73\u9762\u4E0A\u7684\u66F2\u7EBF\u7684\u603B\u66F2\u7387\u662F\u66F2\u7387\u7684\u66F2\u7EBF\u79EF\u5206\uFF1A \u95ED\u66F2\u7EBF\u7684\u603B\u66F2\u7387\u662F 2\u03C0 \u7684\u6574\u6570\u500D\uFF0C\u8BE5\u6574\u6570\u79F0\u4E3A\u66F2\u7EBF\u7684\u6307\u6570\u6216\u8F6C\u6570\u3002\u5176\u4E2D\u8F6C\u6570\u662F\u5355\u4F4D\u5207\u5411\u91CF\u5173\u4E8E\u8D77\u70B9\u7684\u7ED5\u6570\uFF0C\u6216\u8005\u7B49\u4EF7\u7684\u9AD8\u65AF\u6620\u5C04\u7684\u6B21\u6570\u3002\u5C40\u90E8\u4E0D\u53D8\u91CF\u66F2\u7387\u548C\u6574\u4F53\u62D3\u6251\u4E0D\u53D8\u91CF\u6307\u6570\u7684\u5173\u7CFB\u662F\u9AD8\u7EF4\u9ECE\u66FC\u51E0\u4F55\u7684\u4EE3\u8868\u6027\u7ED3\u679C\uFF0C\u5982\u9AD8\u65AF\uFF0D\u535A\u5167\u5B9A\u7406\u3002"@zh .