"WeizenbocksInequality"@en . . . "Proof of Hadwiger-Finsler inequality"@en . "Desigualdade de Hadwiger\u2013Finsler"@pt . "In mathematics, the Hadwiger\u2013Finsler inequality is a result on the geometry of triangles in the Euclidean plane. It states that if a triangle in the plane has side lengths a, b and c and area T, then"@en . . "Paul"@en . "\uD558\uD2B8\uBE44\uAC70-\uD540\uC2AC\uB7EC \uBD80\uB4F1\uC2DD"@ko . "Die Ungleichung von Hadwiger-Finsler (nach Hugo Hadwiger und Paul Finsler) ist eine elementargeometrische Aussage \u00FCber Dreiecke. Sie besagt, dass f\u00FCr jedes Dreieck mit Seiten a, b und c und Fl\u00E4che F die folgende Ungleichung gilt: Die Ungleichung von Weitzenb\u00F6ck ergibt sich hieraus sofort als Korollar."@de . . . . . . . "\u0641\u064A \u0627\u0644\u0631\u064A\u0627\u0636\u064A\u0627\u062A\u060C \u0645\u062A\u0628\u0627\u064A\u0646\u0629 \u0647\u0627\u062F\u0641\u0627\u064A\u063A\u0631-\u0641\u0646\u0633\u0644\u0631 (\u0628\u0627\u0644\u0625\u0646\u062C\u0644\u064A\u0632\u064A\u0629: Hadwiger\u2013Finsler inequality)\u200F \u0647\u064A \u0646\u062A\u064A\u062C\u0629 \u0641\u064A \u0647\u0646\u062F\u0633\u0629 \u0627\u0644\u0645\u062B\u0644\u062B\u0627\u062A \u0641\u064A \u0627\u0644\u0645\u0633\u062A\u0648\u0649 \u0627\u0644\u0625\u0642\u0644\u064A\u062F\u064A\u060C \u062A\u0646\u0635 \u0639\u0644\u0649 \u0623\u0646\u0647 \u0641\u064A \u0645\u062B\u0644\u062B \u0641\u064A \u0627\u0644\u0645\u0633\u062A\u0648\u0649\u060C \u0623\u0637\u0648\u0627\u0644 \u0623\u0636\u0644\u0627\u0639\u0647 b \u0648 a \u0648 c \u0648 \u0645\u0633\u0627\u062D\u062A\u0647 A\u060C \u062A\u062A\u062D\u0642\u0642 \u0627\u0644\u0645\u062A\u0631\u0627\u062C\u062D\u0629 \u0627\u0644\u062A\u0627\u0644\u064A\u0629: \u0645\u062A\u0628\u0627\u064A\u0646\u0629 \u0641\u0627\u064A\u062A\u0632\u064A\u0646\u0628\u0648\u062E \u0647\u064A \u0646\u062A\u064A\u062C\u0629 \u0628\u0633\u064A\u0637\u0629 \u0644\u0645\u062A\u0628\u0627\u064A\u0646\u0629 \u0647\u0627\u062F\u0641\u0627\u064A\u063A\u0631-\u0641\u0646\u0633\u0644\u0631: \u0625\u0630\u0627 \u0643\u0627\u0646\u062A b, a \u0648 c \u0623\u0637\u0648\u0627\u0644 \u0623\u0636\u0644\u0627\u0639 \u0645\u062B\u0644\u062B \u0641\u064A \u0627\u0644\u0645\u0633\u062A\u0648\u0649 \u0648 A \u0645\u0633\u0627\u062D\u062A\u0647\u060C \u0641\u0625\u0646: \u0633\u0645\u064A\u062A \u0645\u062A\u0628\u0627\u064A\u0646\u0629 \u0647\u0627\u062F\u0641\u0627\u064A\u063A\u0631-\u0641\u0646\u0633\u0644\u0631 \u0647\u0643\u0630\u0627 \u0646\u0633\u0628\u0629 \u0625\u0644\u0649 (1937)."@ar . . . . . "\u82AC\u65AF\u62C9\u4E0D\u7B49\u5F0F"@zh . . "Em Matem\u00E1tica, a desigualdade de Hadwiger\u2013Finsler \u00E9 um resultado em geometria de tri\u00E2ngulos (ou trigonometria) no plano euclidiano, assim chamado em homenagem aos matem\u00E1ticos Hugo Hadwiger e Paul Finsler. Afirma-se que se um tri\u00E2ngulo no plano tem seus lados com comprimentos a, b and c e \u00E1rea T, ent\u00E3o A desigualdade de Weitzenb\u00F6ck \u00E9 um corol\u00E1rio simples da desigualdade de Hadwiger\u2013Finsler: se um tri\u00E2ngulo no plano tem lados de comprimento a, b e c e \u00E1rea T, ent\u00E3o A desigualdade de Hadwiger\u2013Finsler \u00E9 um caso especial da desigualdade de Pedoe."@pt . "1937"^^ . . . . . "Finsler"@en . "Hadwiger\u2013Finsler inequality"@en . "Hadwiger"@en . "\u82AC\u65AF\u62C9\u4E0D\u7B49\u5F0F\uFF08Finsler's Inequality\uFF09\u662F\u4E00\u6761\u53CD\u6620\u4E86\u4E09\u89D2\u5F62\u4E09\u8FB9\u4E0E\u5176\u9762\u79EF\u4E4B\u95F4\u7684\u5173\u7CFB\u7684\u51E0\u4F55\u4E0D\u7B49\u5F0F\u3002 \u8BBE\u25B3ABC\u7684\u4E09\u8FB9\u957F\u5206\u522B\u4E3A, , \uFF0C\u9762\u79EF\u4E3A\uFF0C\u5219 \uFF08\u5F53\u4E14\u4EC5\u5F53\u65F6\uFF0C\u7B49\u53F7\u6210\u7ACB\uFF09\u2026\u2026\uFF081\uFF09 \u8BC1\u660E\u4E00\uFF1A\u5982\u56FE\uFF0C\u56E0\u4EFB\u610F\u25B3ABC\u7684\u4E09\u6761\u9AD8\u81F3\u5C11\u6709\u4E00\u6761\u5728\u25B3ABC\u5185\uFF0C\u4E0D\u59A8\u8BBEBC\u8FB9\u4E0A\u7684\u9AD8AD\u5728\u25B3ABC\u5185\uFF0C\u8BBE\uFF0C\uFF0C\uFF0C\u5219\u6709 \uFF0C\uFF0C\uFF0C\uFF0C\u2235 \u2026\u2026\uFF082\uFF09 \u7B49\u53F7\u5F53\u4E14\u4EC5\u5F53\uFF0C\u4E14\u65F6\uFF0C\u5373\u25B3ABC\u4E3A\u6B63\u4E09\u89D2\u5F62\u65F6\u6210\u7ACB\u3002\u5C55\u5F00\uFF082\uFF09\u5F0F\u5E76\u6574\u7406\u53EF\u5F97 \uFF0C\u2234 \u3002\uFF08\u5F53\u65F6\uFF0C\u7B49\u53F7\u6210\u7ACB\uFF09 \u6CE8\uFF1A\u8BC1\u660E\u7684\u5173\u952E\u662F\u5DE7\u5999\u5728\u6784\u9020\u4E0D\u7B49\u5F0F\uFF082\uFF09\uFF0C\u4E3A\u6B64\u5FC5\u987B\u9996\u5148\u731C\u60F3\u5230\u5F53\u65F6\uFF0C\u6B63\u4E09\u89D2\u5F62\u7684\u9762\u79EF\u6700\u5927\uFF0C\u6B64\u65F6\u6709\uFF0C\uFF0C\u5229\u7528\u8FD9\u4E24\u4E2A\u516C\u5F0F\u5C31\u53EF\u9020\u51FA\u4E0D\u7B49\u5F0F\uFF082\uFF09\u3002 \u8BC1\u660E\u4E8C\uFF1A\u7531\u4F59\u5F26\u5B9A\u7406\u53CA\u4E09\u89D2\u5F62\u9762\u79EF\u516C\u5F0F\uFF0C \u5F53\u4E14\u4EC5\u5F53\uFF0C\u2220C=60\u00B0\uFF0C\u5373\u65F6\uFF0C\u7B49\u53F7\u6210\u7ACB\u3002"@zh . . "\u0641\u064A \u0627\u0644\u0631\u064A\u0627\u0636\u064A\u0627\u062A\u060C \u0645\u062A\u0628\u0627\u064A\u0646\u0629 \u0647\u0627\u062F\u0641\u0627\u064A\u063A\u0631-\u0641\u0646\u0633\u0644\u0631 (\u0628\u0627\u0644\u0625\u0646\u062C\u0644\u064A\u0632\u064A\u0629: Hadwiger\u2013Finsler inequality)\u200F \u0647\u064A \u0646\u062A\u064A\u062C\u0629 \u0641\u064A \u0647\u0646\u062F\u0633\u0629 \u0627\u0644\u0645\u062B\u0644\u062B\u0627\u062A \u0641\u064A \u0627\u0644\u0645\u0633\u062A\u0648\u0649 \u0627\u0644\u0625\u0642\u0644\u064A\u062F\u064A\u060C \u062A\u0646\u0635 \u0639\u0644\u0649 \u0623\u0646\u0647 \u0641\u064A \u0645\u062B\u0644\u062B \u0641\u064A \u0627\u0644\u0645\u0633\u062A\u0648\u0649\u060C \u0623\u0637\u0648\u0627\u0644 \u0623\u0636\u0644\u0627\u0639\u0647 b \u0648 a \u0648 c \u0648 \u0645\u0633\u0627\u062D\u062A\u0647 A\u060C \u062A\u062A\u062D\u0642\u0642 \u0627\u0644\u0645\u062A\u0631\u0627\u062C\u062D\u0629 \u0627\u0644\u062A\u0627\u0644\u064A\u0629: \u0645\u062A\u0628\u0627\u064A\u0646\u0629 \u0641\u0627\u064A\u062A\u0632\u064A\u0646\u0628\u0648\u062E \u0647\u064A \u0646\u062A\u064A\u062C\u0629 \u0628\u0633\u064A\u0637\u0629 \u0644\u0645\u062A\u0628\u0627\u064A\u0646\u0629 \u0647\u0627\u062F\u0641\u0627\u064A\u063A\u0631-\u0641\u0646\u0633\u0644\u0631: \u0625\u0630\u0627 \u0643\u0627\u0646\u062A b, a \u0648 c \u0623\u0637\u0648\u0627\u0644 \u0623\u0636\u0644\u0627\u0639 \u0645\u062B\u0644\u062B \u0641\u064A \u0627\u0644\u0645\u0633\u062A\u0648\u0649 \u0648 A \u0645\u0633\u0627\u062D\u062A\u0647\u060C \u0641\u0625\u0646: \u0633\u0645\u064A\u062A \u0645\u062A\u0628\u0627\u064A\u0646\u0629 \u0647\u0627\u062F\u0641\u0627\u064A\u063A\u0631-\u0641\u0646\u0633\u0644\u0631 \u0647\u0643\u0630\u0627 \u0646\u0633\u0628\u0629 \u0625\u0644\u0649 (1937)."@ar . "Hugo"@en . . . "3025"^^ . . "In mathematics, the Hadwiger\u2013Finsler inequality is a result on the geometry of triangles in the Euclidean plane. It states that if a triangle in the plane has side lengths a, b and c and area T, then"@en . . "\uD558\uD2B8\uBE44\uAC70-\uD540\uC2AC\uB7EC \uBD80\uB4F1\uC2DD(Hadwiger-Finsler inequality, -\u4E0D\u7B49\u5F0F)\uC740 \uC720\uD074\uB9AC\uB4DC \uAE30\uD558\uD559 \uBC0F \uC0BC\uAC01\uBC95\uC758 \uBD80\uB4F1\uC2DD\uC73C\uB85C, \uC2A4\uC704\uC2A4 \uC218\uD559\uC790 (Hugo Hadwiger)\uC640 \uC5ED\uC2DC \uC2A4\uC704\uC2A4 \uC218\uD559\uC790\uC778 (Paul Finsler)\uC758 \uC774\uB984\uC774 \uBD99\uC5B4 \uC788\uB2E4. \uC784\uC758 \uC0BC\uAC01\uD615\uC758 \uC138 \uBCC0\uC758 \uAE38\uC774\uB97C \uAC01\uAC01 a, b, c, \uADF8 \uB113\uC774\uB97C S\uB77C \uD560 \uB54C \uB2E4\uC74C\uACFC \uAC19\uC774 \uD45C\uD604\uB41C\uB2E4. \n* \uBD80\uB4F1\uC2DD\uC758 \uB4F1\uD638\uAC00 \uC131\uB9BD\uD560 \uD544\uC694\uCDA9\uBD84\uC870\uAC74\uC740 \uC774 \uC0BC\uAC01\uD615\uC774 \uC815\uC0BC\uAC01\uD615\uC778 \uAC83\uC774\uB2E4. \uC774 \uBD80\uB4F1\uC2DD\uC740 \uBCF4\uB2E4 \uC77C\uBC18\uC801\uC778 \uBD80\uB4F1\uC2DD\uC778 \uD398\uB3C4\uC758 \uBD80\uB4F1\uC2DD\uC758 \uD2B9\uC218\uD55C \uD615\uD0DC\uB85C \uBCFC \uC218 \uC788\uB2E4. \uB610, \uC774 \uBD80\uB4F1\uC2DD\uC5D0\uC11C \uACE7\uBC14\uB85C \uB2E4\uC74C\uACFC \uAC19\uC740 \uBD80\uB4F1\uC2DD\uC744 \uB530\uB984\uC815\uB9AC\uB85C \uC5BB\uC744 \uC218 \uC788\uB2E4. \n* \uC774\uB294 \uBC14\uB85C \uBC14\uC774\uCCB8\uBD48\uD06C \uBD80\uB4F1\uC2DD\uC774 \uB41C\uB2E4."@ko . . . "Hugo Hadwiger"@en . . . . . "Ungleichung von Hadwiger-Finsler"@de . "Em Matem\u00E1tica, a desigualdade de Hadwiger\u2013Finsler \u00E9 um resultado em geometria de tri\u00E2ngulos (ou trigonometria) no plano euclidiano, assim chamado em homenagem aos matem\u00E1ticos Hugo Hadwiger e Paul Finsler. Afirma-se que se um tri\u00E2ngulo no plano tem seus lados com comprimentos a, b and c e \u00E1rea T, ent\u00E3o A desigualdade de Weitzenb\u00F6ck \u00E9 um corol\u00E1rio simples da desigualdade de Hadwiger\u2013Finsler: se um tri\u00E2ngulo no plano tem lados de comprimento a, b e c e \u00E1rea T, ent\u00E3o A desigualdade de Weitzenb\u00F6ck pode tamb\u00E9m ser provada usando a f\u00F3rmula de Heron, pelo que o caminho que pode ser visto na igualdade det\u00E9m em (W) se e somente se o tri\u00E2ngulo \u00E9 um tri\u00E2ngulo equil\u00E1tero, ou seja, a = b = c. A desigualdade de Hadwiger\u2013Finsler \u00E9 um caso especial da desigualdade de Pedoe."@pt . "\uD558\uD2B8\uBE44\uAC70-\uD540\uC2AC\uB7EC \uBD80\uB4F1\uC2DD(Hadwiger-Finsler inequality, -\u4E0D\u7B49\u5F0F)\uC740 \uC720\uD074\uB9AC\uB4DC \uAE30\uD558\uD559 \uBC0F \uC0BC\uAC01\uBC95\uC758 \uBD80\uB4F1\uC2DD\uC73C\uB85C, \uC2A4\uC704\uC2A4 \uC218\uD559\uC790 (Hugo Hadwiger)\uC640 \uC5ED\uC2DC \uC2A4\uC704\uC2A4 \uC218\uD559\uC790\uC778 (Paul Finsler)\uC758 \uC774\uB984\uC774 \uBD99\uC5B4 \uC788\uB2E4. \uC784\uC758 \uC0BC\uAC01\uD615\uC758 \uC138 \uBCC0\uC758 \uAE38\uC774\uB97C \uAC01\uAC01 a, b, c, \uADF8 \uB113\uC774\uB97C S\uB77C \uD560 \uB54C \uB2E4\uC74C\uACFC \uAC19\uC774 \uD45C\uD604\uB41C\uB2E4. \n* \uBD80\uB4F1\uC2DD\uC758 \uB4F1\uD638\uAC00 \uC131\uB9BD\uD560 \uD544\uC694\uCDA9\uBD84\uC870\uAC74\uC740 \uC774 \uC0BC\uAC01\uD615\uC774 \uC815\uC0BC\uAC01\uD615\uC778 \uAC83\uC774\uB2E4. \uC774 \uBD80\uB4F1\uC2DD\uC740 \uBCF4\uB2E4 \uC77C\uBC18\uC801\uC778 \uBD80\uB4F1\uC2DD\uC778 \uD398\uB3C4\uC758 \uBD80\uB4F1\uC2DD\uC758 \uD2B9\uC218\uD55C \uD615\uD0DC\uB85C \uBCFC \uC218 \uC788\uB2E4. \uB610, \uC774 \uBD80\uB4F1\uC2DD\uC5D0\uC11C \uACE7\uBC14\uB85C \uB2E4\uC74C\uACFC \uAC19\uC740 \uBD80\uB4F1\uC2DD\uC744 \uB530\uB984\uC815\uB9AC\uB85C \uC5BB\uC744 \uC218 \uC788\uB2E4. \n* \uC774\uB294 \uBC14\uB85C \uBC14\uC774\uCCB8\uBD48\uD06C \uBD80\uB4F1\uC2DD\uC774 \uB41C\uB2E4."@ko . . . . "\u82AC\u65AF\u62C9\u4E0D\u7B49\u5F0F\uFF08Finsler's Inequality\uFF09\u662F\u4E00\u6761\u53CD\u6620\u4E86\u4E09\u89D2\u5F62\u4E09\u8FB9\u4E0E\u5176\u9762\u79EF\u4E4B\u95F4\u7684\u5173\u7CFB\u7684\u51E0\u4F55\u4E0D\u7B49\u5F0F\u3002 \u8BBE\u25B3ABC\u7684\u4E09\u8FB9\u957F\u5206\u522B\u4E3A, , \uFF0C\u9762\u79EF\u4E3A\uFF0C\u5219 \uFF08\u5F53\u4E14\u4EC5\u5F53\u65F6\uFF0C\u7B49\u53F7\u6210\u7ACB\uFF09\u2026\u2026\uFF081\uFF09 \u8BC1\u660E\u4E00\uFF1A\u5982\u56FE\uFF0C\u56E0\u4EFB\u610F\u25B3ABC\u7684\u4E09\u6761\u9AD8\u81F3\u5C11\u6709\u4E00\u6761\u5728\u25B3ABC\u5185\uFF0C\u4E0D\u59A8\u8BBEBC\u8FB9\u4E0A\u7684\u9AD8AD\u5728\u25B3ABC\u5185\uFF0C\u8BBE\uFF0C\uFF0C\uFF0C\u5219\u6709 \uFF0C\uFF0C\uFF0C\uFF0C\u2235 \u2026\u2026\uFF082\uFF09 \u7B49\u53F7\u5F53\u4E14\u4EC5\u5F53\uFF0C\u4E14\u65F6\uFF0C\u5373\u25B3ABC\u4E3A\u6B63\u4E09\u89D2\u5F62\u65F6\u6210\u7ACB\u3002\u5C55\u5F00\uFF082\uFF09\u5F0F\u5E76\u6574\u7406\u53EF\u5F97 \uFF0C\u2234 \u3002\uFF08\u5F53\u65F6\uFF0C\u7B49\u53F7\u6210\u7ACB\uFF09 \u6CE8\uFF1A\u8BC1\u660E\u7684\u5173\u952E\u662F\u5DE7\u5999\u5728\u6784\u9020\u4E0D\u7B49\u5F0F\uFF082\uFF09\uFF0C\u4E3A\u6B64\u5FC5\u987B\u9996\u5148\u731C\u60F3\u5230\u5F53\u65F6\uFF0C\u6B63\u4E09\u89D2\u5F62\u7684\u9762\u79EF\u6700\u5927\uFF0C\u6B64\u65F6\u6709\uFF0C\uFF0C\u5229\u7528\u8FD9\u4E24\u4E2A\u516C\u5F0F\u5C31\u53EF\u9020\u51FA\u4E0D\u7B49\u5F0F\uFF082\uFF09\u3002 \u8BC1\u660E\u4E8C\uFF1A\u7531\u4F59\u5F26\u5B9A\u7406\u53CA\u4E09\u89D2\u5F62\u9762\u79EF\u516C\u5F0F\uFF0C \u5F53\u4E14\u4EC5\u5F53\uFF0C\u2220C=60\u00B0\uFF0C\u5373\u65F6\uFF0C\u7B49\u53F7\u6210\u7ACB\u3002"@zh . "Weizenbock's inequality"@en . . . . . "Die Ungleichung von Hadwiger-Finsler (nach Hugo Hadwiger und Paul Finsler) ist eine elementargeometrische Aussage \u00FCber Dreiecke. Sie besagt, dass f\u00FCr jedes Dreieck mit Seiten a, b und c und Fl\u00E4che F die folgende Ungleichung gilt: Die Ungleichung von Weitzenb\u00F6ck ergibt sich hieraus sofort als Korollar."@de . . "proofofhadwigerfinslerinequality"@en . "12802352"^^ . . "1017618105"^^ . "Paul Finsler"@en . . . . . "\u0645\u062A\u0628\u0627\u064A\u0646\u0629 \u0647\u0627\u062F\u0641\u0627\u064A\u063A\u0631-\u0641\u0646\u0633\u0644\u0631"@ar .