In mathematics, the Hadwiger–Finsler inequality is a result on the geometry of triangles in the Euclidean plane, named after the mathematicians Hugo Hadwiger and Paul Finsler. It states that if a triangle in the plane has side lengths a, b and c and area A, then <math>a^{2} + b^{2} + c^{2} \geq (a - b)^{2} + (b - c)^{2} + (c - a)^{2} + 4 \sqrt{3} A \quad \mbox{(HF)}.

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  • In mathematics, the Hadwiger–Finsler inequality is a result on the geometry of triangles in the Euclidean plane, named after the mathematicians Hugo Hadwiger and Paul Finsler. It states that if a triangle in the plane has side lengths a, b and c and area A, then <math>a^{2} + b^{2} + c^{2} \geq (a - b)^{2} + (b - c)^{2} + (c - a)^{2} + 4 \sqrt{3} A \quad \mbox{(HF)}. </math> Weitzenböck's inequality is a straightforward corollary of the Hadwiger–Finsler inequality: if a triangle in the plane has side lengths a, b and c and area A, then <math>a^{2} + b^{2} + c^{2} \geq 4 \sqrt{3} A \quad \mbox{(W)}. </math> Weitzenböck's inequality can also be proved using Heron's formula, by which route it can be seen that equality holds in (W) if and only if the triangle is an equilateral triangle, i.e. a = b = c. The Hadwiger–Finsler inequality is a special case of Pedoe's inequality.
  • Geometriassa Hadwigerin–Finslerin on epäyhtälö kolmion sivun pituuksien ja pinta-alan välillä. Sen mukaan jos annetun kolmion sivun pituudet ovat a, b ja c ja pinta-ala A, on voimassa <math>2ab+2bc+2ac-(a^2+b^2+c^2)\geq 4\sqrt{3}A. </math> Yhtälö on nimetty matemaatikkojen Hugo Hadwigerin ja Paul Finslerin mukaan.
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  • Hadwiger-Finsler inequality
  • Weizenbock's inequality
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  • HadwigerFinslerInequality
  • WeizenbocksInequality
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  • In mathematics, the Hadwiger–Finsler inequality is a result on the geometry of triangles in the Euclidean plane, named after the mathematicians Hugo Hadwiger and Paul Finsler. It states that if a triangle in the plane has side lengths a, b and c and area A, then <math>a^{2} + b^{2} + c^{2} \geq (a - b)^{2} + (b - c)^{2} + (c - a)^{2} + 4 \sqrt{3} A \quad \mbox{(HF)}.
  • Geometriassa Hadwigerin–Finslerin on epäyhtälö kolmion sivun pituuksien ja pinta-alan välillä. Sen mukaan jos annetun kolmion sivun pituudet ovat a, b ja c ja pinta-ala A, on voimassa <math>2ab+2bc+2ac-(a^2+b^2+c^2)\geq 4\sqrt{3}A. </math> Yhtälö on nimetty matemaatikkojen Hugo Hadwigerin ja Paul Finslerin mukaan.
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  • Hadwiger–Finsler inequality
  • Hadwigerin–Finslerin epäyhtälö
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