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  2. List of triangle inequalities - Wikipedia

    en.wikipedia.org/wiki/List_of_triangle_inequalities

    The parameters most commonly appearing in triangle inequalities are: the side lengths a, b, and c;; the semiperimeter s = (a + b + c) / 2 (half the perimeter p);; the angle measures A, B, and C of the angles of the vertices opposite the respective sides a, b, and c (with the vertices denoted with the same symbols as their angle measures);

  3. Triangle inequality - Wikipedia

    en.wikipedia.org/wiki/Triangle_inequality

    In Euclidean geometry, for right triangles the triangle inequality is a consequence of the Pythagorean theorem, and for general triangles, a consequence of the law of cosines, although it may be proved without these theorems.

  4. Euler's theorem in geometry - Wikipedia

    en.wikipedia.org/wiki/Euler's_theorem_in_geometry

    Euler's inequality, in the form stating that, for all triangles inscribed in a given circle, the maximum of the radius of the inscribed circle is reached for the equilateral triangle and only for it, is valid in absolute geometry. [7]

  5. List of inequalities - Wikipedia

    en.wikipedia.org/wiki/List_of_inequalities

    Erdős–Mordell inequality; Euler's theorem in geometry; Gromov's inequality for complex projective space; Gromov's systolic inequality for essential manifolds; Hadamard's inequality; Hadwiger–Finsler inequality; Hinge theorem; Hitchin–Thorpe inequality; Isoperimetric inequality; Jordan's inequality; Jung's theorem; Loewner's torus ...

  6. Weitzenböck's inequality - Wikipedia

    en.wikipedia.org/wiki/Weitzenböck's_inequality

    Rewriting the inequality above allows for a more concrete geometric interpretation, which in turn provides an immediate proof. [1]+ +. Now the summands on the left side are the areas of equilateral triangles erected over the sides of the original triangle and hence the inequation states that the sum of areas of the equilateral triangles is always greater than or equal to threefold the area of ...

  7. Category:Triangle inequalities - Wikipedia

    en.wikipedia.org/wiki/Category:Triangle_inequalities

    Pages in category "Triangle inequalities" The following 8 pages are in this category, out of 8 total. ... Erdős–Mordell inequality; Euler's theorem in geometry; H.

  8. Category:Theorems about triangles - Wikipedia

    en.wikipedia.org/wiki/Category:Theorems_about...

    Triangle inequalities (8 P) Pages in category "Theorems about triangles" ... Maxwell's theorem (geometry) Menelaus's theorem;

  9. Erdős–Mordell inequality - Wikipedia

    en.wikipedia.org/wiki/Erdős–Mordell_inequality

    Erdős–Mordell inequality. Let be an arbitrary point P inside a given triangle , and let , , and be the perpendiculars from to the sides of the triangles. (If the triangle is obtuse, one of these perpendiculars may cross through a different side of the triangle and end on the line supporting one of the sides.)

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